5984:"Causal" is clearly a distracting substitute for "linear, time invariant" to non-engineers. Signal flow graph analysis assumes that the time domain response and spectral domain response of the system transfer function are freely convertible. That requires the Laplace transform of the system transfer function to be valid, and therefore requires that the system's transfer function is linear (i.e. independent of amplitude) and time invariant (i.e. the same at all times). An analysis of a time varying, non-linear, or unstable system may not be valid, and usually isn't in proportion to the extent that it exhibits those traits. For example, a BJT amplifier with a particular feedback network may behave as indicated by signal flow graph analysis for small signals but at some sufficiently large signal level increased Miller effect delay may increase its phase delay enough to cause the amplifier's feedback to become reinforcing and it becomes a bistable, a square wave oscillator. When operating as a bistable it no longer exhibits any small signal gain and its output is no longer related to the input. Signal flow graph analysis won't be able to model the behavior of such a system, even though it's causal in the usual sense. PolychromePlatypus 00:33, 9 April 2019 (UTC)
705:
or to the application of flame decals) Conversely altering the forward ground velocity of the vehicle by any available means has a direct and proportional effect on the position of the speedometer's indicator needle. (note that because a modern instrument cluster doesn't have a speedometer the system also has to be powered to permit the microprocessor controlled stepper motor with gear reduction to simulates a speedometer) ... also there is no requirement that a signal flow graph be expressed in a canonical form. A signal flow graph can often be reduced Isee Mason, 1953) and sometimes its pleasant not to cover the page with boxes and arrows, but the validity of the analysis doesn't depend on reducing it.PolychromePlatypus 20:06, 9 April 2019 (UTC)
5467:
Karnopp mean by "Some perfectly reasonable physical models simply will not compute because of causal problems." Probably what I haven't clearly expressed is that I'm asking what the section means and expressing what the section seems to mean to me which is this: there are implementation problems that arise when attempting to use SFG's to represent systems with many acausal relationships. Given the age of many of these sources and the advance of computers and computer science, the criticisms may be insignificant. We have SPICE for analysis of circuits and all their acausal relationships. Is it meaningful to criticize a SFG because it is not very convenient for solving circuits? This is what the section seems to be saying to me.
3577:
equations are used to define the variable written on the left-hand side.â This quote is, of course, out of context. Its meaning is unclear without access to the contextual document. It is incumbent on the person contributing a quote to explain its meaning. Robichaud seems to be saying that if there is a SFG in which node A has an arrow to node B and A is to the left of B then a SFG in which node A has an arrow to node B and A is to the right of B is a different SFG. Or is he saying that a system of simultaneous equations in one order is different from the same equations written in a different order? Either way, if that is what he is saying, itâs specious. He must have meant something else, but what is it?
3918:
395:
4973:
5712:"An alternate approach to find the relationships among the system variables of a complicated network or system is the signal flow graph approach by SJ Mason. A signal-flow graph is a diagram which represents a set of simultaneous linear algebraic equations. It consists of a network in which nodes are connected by directed branches. Each node represents a system variable, and each branch connected between two nodes acts as a signal multiplier. A signal flow graph contains, essentially, the same information as a block-diagram representation...(p. 757)
4210:. We need the same thing here that we need on the statement about the mapping of SFG equations in standard form to SFG topology. We need a reliable source that says unambiguously that all SFG's can be solved by elementary transformations and unambiguously what those transformations are. I doubt that such a reference exists because Mason and Robichaud say you cannot reduce the index with elementary operations (Mason calls them explicit transformations). Robichau expressly distinguishes between elementary transformations and elimination of a loop.
5497:
best one. Your view might be that some approaches based on personal intuitions about causality will lead one to the most useful forms quickly. That, of course, depends upon the efficacy of those particular intuitions. Undoubtedly, some engineers will grasp key relationships intuitively, and get to a valuable SFG in a hurry, whether that intuition involves causal understandings or something else. Is it worthwhile to suggest "causality" has some role in arriving at a useful SFG? Not unless there are some pointers that generally are accepted.
1595:
my assessment of sources that digraphs include both SFG and flow graphs, but also other types of graphs. Specifically, digraphs include graphs that are not necessarily connected to matrices or linear equations (although that possibility might exist), while the SFG and the flow graph are both required to be so-connected. As for the connection between flow graphs and the SFG, there is some confusion in the literature. The predominant usage is that SFG ⥠Mason graph, while there is one set of authors that take flow graph âĄ
5388:
current forced through a resister causes a voltage across that resister. A voltage held across a resister causes a current through the resister. More commonly, in a circuit, neither causes the other, but they are related by ohms law. Whatever causes the voltage and current causes them in such a way that ohms law is not violated. In this case, ohm's law is an acausal relationship in which the neither voltage nor current strictly causes the other. SFG's can represent acausal relationships in both senses.
74:
53:
3243:
equations to treat more general coonections between nodes. That way the reader who is starting out can get their feet under them with the linear case, and for those few that wish the more general approach, well, they can be guided to build upon the linear case. I am afraid that beginning with the general case will prove too abstract for the novice and they will find such a beginning abstruse, an issue already raised even before this added abstraction.
150:
1671:
84:
1133:"A signal flow graph is a network of nodes (or points) interconnected by directed branches, representing a set of linear algebraic equations. The nodes in a flow graph are used to represent the variables, or parameters, and the connecting branches represent the coefficients relating these variables to one another. The flow graph is associated with a number of simple rules which enable every possible solution to be obtained."
4771:
4763:
5068:
constructed by Kouâs rules do not guarantee causal relationships. SFGs force non-causal relationships into quasi-causal forms that are complicated. The only reason to force these non-causal relationships into SFG form is because the system is made up of mostly causal relationships. The telescope servo illustrates this point. It is made up of mostly causal relationships, except the relationship between V
5972:
exception, not the rule. As a practicing art with significant commercial value only a small fraction of Ph.D. E.E.'s are willing to engage in the incessant intramural warfare of the academy for 1/3 pay or less. Consequently, the combination of the two should probably be listed an endangered species to protect them from being harassed for minor transgressions. PolychromePlatypus 00:33, 9 April 2019 (UTC)
1464:
always be drawn in the top row and the current nodes in the bottom row of the graph. In order to facilitate the interconnection of these graphs, it will be convenient to show explicitly the source and sink nodes. The source nodes will be drawn as black half-circles and the sink nodes as white half-circles. These flow graphs are in the form of quadri-poles and are therefore called quadripole flow graphs.
4866:. I suggest we remove the whole philosophy discussion, and replace it by the simple statement that sfgs do not contain causal information, but can under some circumstances be drawn in a way such that the way they are drawn does convey it. This is then not a mathematical property of the graph, but a meta-property of the way to draw the equations system. I think it is sufficient to cite Mason56 on this.
5158:? It is hardly surprising that the acausal nature of an SFG results in a noncausal formulation of system behavior. However, as a counterpoint, Newton's laws are causal and govern many systems. Their causality does not preclude a formulation in terms of ordinary algebraic equations where causality doesn't show up. In fact, numerical algorithms for solving most problems end up in matrix form.
4169:, but correspond to different SFGs, isn't it obvious that these SFGs are related, and moreover, that a transformation process exists that will map one SFG into the other? in fact, isn't the algebraic translation mapping one set of equations into an equivalent set one procedure used to justify valid transformations of SFGs, and the source of many of these allowed graph transformations?
5602:
22:
5511:.) However (and irrelevant here, I surmise), this idea has limited value today in view of the known formulations based upon minimizing functions of system variables and avoiding the concepts of past, present, and future and what exactly is an 'event'. (Each theory identifies its own set of 'events' it wants to deal with, and doesn't try to include everything.)
5508:
5092:. The SFG is made up of mostly unidirectional components such as amplifiers and sensors, but it has a little bit of circuitry involving the motor winding, its resistance and the current sense resistance. The reason to represent the circuitry as a SFG is because the SFG is so darn useful representing the rest of the system.
1996:, saying "In accounting for branch directions it is necessary to take an entirely different line of approach from that adopted in electrical network topology." However, he doesn't explicitly state the reason why directionality is significant, and one has to deduce that it is by looking at how he uses the signal flow graph.
959:
5727:"A signal-flow graph is a diagram consisting of nodes that are connected by directed branches and is a graphical representation of a set of linear relations...The flow graph is simply a pictorial method of writing a system of algebraic equations so as to indicate the interdependence of the variables." (9th edition, p. 67)
5254:
produced at the terminals of the resistor is a function of the source's current signal. Thus, there is no SFG model that can accommodate both usages of the same resistor (connected to a current source or connected to a voltage source). On the other hand, other modeling notations can capture an acausal equation such as
2126:
358:. This would be the case where the ports were driven by ideal voltage sources which are considered the inputs and the currents sourced by those ideal voltage sources are the outpurts. Usually, a two port is part of a circuit and not a stand alone circuit. I think I could provide a better example. Maybe his weekend.
1141:, it lies in a connection to a set of linear algebraic equations. Because of this generality, although the adjective 'signal' has crept into this definition, it is best omitted to allow that "flow graph" has a more general definition than the term "signal flow graph". That choice agrees with the common use of the term
1205:
4043:
5781:
1608:
1219:
1016:
4225:
this division. In any event quarreling over whether a transformation is elementary or not seems pointless. The real issue is how SFGs can aid in understanding the equations and presumably the simpler the SFG the clearer this understanding will be, so we want to arrive systematically at the simple forms.
5810:
of physical laws can therefore not be predetermined, but depends upon the particular use of that law. We cannot conclude whether it is the current flowing through a resistor that causes a voltage drop, or whether it is the difference in potentials at the two ends of the resistor that cause current to
5697:
The connection of Mason to cause and effect is open to discussion, but this entire paper is about the connections of flow graphs to equations, so the physical "cause and effect" connection seems to me to be more or less intended as an example of a construction process that leads to certain equations,
4428:
This section presents the view that SFGs are somehow tied to an interpretation using causality. These views are erroneous, at least for the SFG that is simply an expression of a system of algebraic equations. If the content of this subsection is to be retained it should be placed as a controversial
3242:
A revised approach is possible, of course. However, already a pretty good presentation is made for the linear case and it connects easily to the linear equations without much explanation. In a separate section on nonlinear applications the commonality can be identified and the differences from linear
2946:
the space devoted to nonlinear versions should be small, with the focus on the linear case. Because the nonlinear case has so little presence in the literature, I'd say it is not worthwhile to try to form the article for the general case, and just leave the general case to its own subsection. I don't
2759:
Constant: WP does not aim at explaining what WP editors find obvious, but rather what sources have to say. So we need sourced commentary, not editors' views. If you wish to engage in what is likely to be long technical discussion over whether every SFG leading to an equivalent set of equations shares
1991:
This note probably is clear to Pierre, but as non-expert in this area, I find it confusing rather than helpful. It seems to say that the goal of solving a set of equations is aided by the use of signal-flow graphs, but that they introduce causality unnecessarily. That seems to suggest that a a simple
866:
Pierre: Some clarification is needed. The first line of the article seems to say that signal-flow graphs are the same thing as Mason graphs, and the quote from Mason's paper in the history section appears to suggest that Mason thought the graphs he was proposing are what he called signal-flow graphs.
599:
The reason that a 2 port's admittance parameters are an unrevealing example is because it should have been transformed to the equivalent scattering parameters. See Mason's 1953 paper, fig 35 page 1196. IIRC a lossless transmission line can't be represented using an admittance matrix, although there's
584:
This seems to be a lot of algebra signifying nothing. At best it shows that you can change the weights on some of the branches and still have the same overall gain. The relationship of the SFG to anything is not defined. Even if you can represent asymptotic gain by a SFG, there is no useful reason
6101:
I think most people would write the content in their sandbox and then transfer it here. You have your own sandbox which you access by clicking the "Sandbox" link in the upper right corner of the page. Once you have it like you want it, you could invite us to view your sandbox; but in this case I'm
5496:
forms, there is no special form. The article's "standard form" is just a construct that shows an SFG always is possible (but clumsy), and all authors agree a "useful" SFG is one that displays only key relationships. It is obvious that one may have to struggle with many possible diagrams to find the
5448:
I'm not suggesting that any such set of equations is outside the reach of a SFG. I'm suggesting that the SFG for many sets of equations is complicated beyond the point of being useful. Your own example of converting three equations in three unknowns is an example. It is not completely useless in the
5212:
can refer to two distinct concepts: (1) physical causality inherent in the system being modeled by equations. For example, if you connect a resistor across a voltage source, the current flowing in the resistor is caused by the physical voltage across the resistor. (2) implementation causality in
4224:
The remark that "you can't make up a transformation rule just because it can be proved mathematically" makes no sense to me. If a rule is " proved" it isn't "made up". The division of transformations into "elementary" and "other" transformations has not been explained here nor what is the purpose of
2484:
1594:
Constant: Speaking for my take on the literature, SFG â flow graph and also SFG â digraph, as you say. However, contrary to your understanding, also flow graph â digraph. SFG â digraph, flow graph â digraph. According to some, SFG â flow graph. My understanding of Pierre is that he also agrees with
1343:
The proposal is to add this subsection. It's purpose is to point out that the most common usage of 'signal flow graph' is as a synonym for 'Mason graph', but that there are other kinds of flow graph that are used, some very similar to Mason graphs. More generally, digraphs are defined independent of
727:
The issue was settled to everyone's satisfaction long ago. The article talk page is not a forum for discussing the topic. It is a forum for discussing improvements in the article. If you think there is something to improve in the article, its best to just start a new topic rather than responding to
5514:
4. At the moment, the section on causality is primarily an attempt to correct misinformation about SFGs that they are somehow less useful because they don't express causality according to the "bond graph" people, or SFGs are limited because they are restricted to constructions based upon causality,
4944:
It is simpler than that. Mason and others construct SFGs using intuition about the systems they are interested in. So a node 'broadcasts' its output along emanating branches, and these signals are received by other nodes (cause a reaction there). The emanating node causes an effect at the receiving
4657:
Brews, I have no objection to a clear statement; I just don't think it needs a section. Pierre, I don't see anything that could be criticized. I think bringing in bond graphs is extraneous to this article, but a single sentence would be sufficient to say something like "The SFG may represent both
3844:
This section continues to suggest that general signal-flow graphs can be solved by repeated application of the simplification rules. This is not true. If it were true then there would be no need for Masonâs gain formula. Mason makes it clear that the only graphs that can be solved in this manner
3673:
I understand that a system of equations can be manipulated into a different system that is equivalent in the sense that that it has the same solution. After putting these equations into standard SFG form, they would have different SFGs. If that is it what the quote means, it needs to be explained
2000:
I will add some notes on the meaning of causality. Some research needed, but I think it is related to finding a proper sequence of assignments or analog computation when the SFG is simulated (the order of computation is defined by the SFG causality). Papers on
Modelica and Bond graph address this
1908:
is a network of directed branches which connect at nodes. Branch jk originates at node j and terminates upon node k, the direction from j to k being indicated by an arrowhead on the branch. Each branch jk has associated with it a quantity called the branch gain gik and each node j has an associated
1509:
Constant: From
Robichaud's presentation, quadripole flow graphs are the application of SFG's to networks comprised of two-ports, an application of the SFG. As such (and assuming that Robichaud means a Mason flow graph by his use of the term SFG, and not some other digraph, which I haven't checked),
911:
Mason introduced several types of flow graphs in his papers. Most important is the notion of a linear flow graph. He often uses the term Flow Graph (unqualified). It seems that "Mason Flow Graph" is a misnomer, and the qualifier "Mason" should be reserved for his method for solving the gain of a
704:
A signal flow graph should model the actual physical process. Note that removing the bezel from a speedometer to directly manipulate the indicator needle has no discernible effect on the forward velocity of the vehicle. (Feel free to insert an analagous humorous reference to a fuel or oil treatment
652:
If I have the equation V = kθ there are two possible graphs: an arrow pointing from θ to V with a weight of k, or an arrow pointing from V to θ with a weight of 1/k. If I have other knowledge such as V is the velocity of my car and θ is the deflection of the speedometer, then I know that the arrow
6050:
The re-write I suggest is to massively abbreviate "Systematic reduction to sources and sinks" by giving one reference to reduction rules and obe example, rewrite "Basic components" to the much shorter description originally used by Mason, and changing "Solving linear equations" to a correspondence
5971:
I think this discussion is hopelessly entangled by Kou's choice of words. Its best to consider this particular choice of idioms to be an unfortunate but risible error. (details below separately rather than as a reply) If you sample a few IEEE journals you'll find that E.E.'s who write well are the
5858:
defined ... â. I think he is using cause and effect as a way of describing the construction process. I also agree that none of the uses is connected to physical causality. I think that yes, computational causality is equivalent in every case. And I conclude that there is no controversy and the
5518:
5. You say this section is incomplete, in part from a failure to discuss "causality". I don't regard that as an issue - see point 3. However, you also have mentioned elsewhere it doesn't discuss utility of the SFG or how useful SFGs can be found efficiently instead of dealing with clumsy ones like
5475:
I don't disagree with what is written there. I am concerned with what is missing. A clear statement as to which meaning of causality is being used is an example. What is there is so incomplete and out of context that it could be summarized in a couple of sentences. I made responses to some of your
5253:
The causality in this discussion is simply a reference to the Input-Output representation inherent in an SFG or a block diagram: an input signal is processed by a block or a branch and produces an output signal. In the resistor example, if the resistor is connected to a current source, the voltage
4268:
That is an improvment but the sentence before it, "The rules presented below are applied over and over until the signal flow graph directly connects the sink nodes representing the dependent variables to the source nodes representing the independent variables. By using elementary equivalences, any
1402:
Yes, the piece states that 'Mason flow graph' and 'signal flow graph' are synonyms for most authors. One purpose of the piece is to point out that 'flow graph' is more general than 'signal flow graph', intending to avoid an easy confusion in the reader's mind. The piece is not intended to insert a
5541:
By SFG form I mean the form as defined by Kou. I agree that one meaning of the word causality is that future events can be predicted using only present and past events. Actually, I would say it means that future events do not affect the present. However, that is not the meaning that it is being
5171:
So there are a couple of points here that you raise concerning the utility and the applicability of SFGs that might be valid, although you haven't clearly expressed or sourced them. Have I got them straight? On the other hand, even with granting these points and their value (only an assumption at
3988:
I had a look. I can verify that all your intermediate results had the same gain. But, you clearly reduced the index of the flow graph which your own reference says cannot be done. One or more of your steps must be more than an elementary transformation. I don't know which one. Perhaps if you
3756:
Constant: Thank you for the clarification. The phrase "according to the order..." is indeed ambiguous in that simply permuting the equations makes no difference to the SFG. However, altering the terms in an equation by substituting say an equivalent for one variable into one of the equations will
3215:
The argument for an introductory section on basic concepts is to start with terminology that is not specific to either linear or non-linear flow graphs. The title should perhaps be rephrased as "general concepts" or "common concepts". All concerns related to topology of the signal flow is really
2993:
Let's keep in mind that this article's title is SFG, not linear SFG. I could support a split to a separate article "Linear SFG" if useful, but the SFG article should be kept broad in scope. I suggest waiting until this article has more materials in it (full example, formal methods, simulation).
2562:
Folks, these comments, whatever their merit, do not bear on the issue of topology and one-to-one mapping between SFG topology and the topology of a set of equations. For that matter, does any source suggest that 'topology' is a property of an equation set? Does any source say all of the many SFGs
1463:
It is to be noted that the left-hand nodes correspond to the left-hand or input variables, and that the right-hand nodes correspond to the right-hand or output variables, in order to maintain a correspondence between the ports of the network and the nodes of the flow graph. The voltage nodes will
5387:
I'm not sure what Pierre means by causality but I also see two uses. In one case it means that effects never precede their cause. In this sense, all the voltages and currents in a circuit are caused by the inputs. The other usage is cause and effect. A force on a mass causes acceleration. A
2907:
I think that the solution for this article is to declare the mish mash out of scope for this article with a note at the top that says this article is about xxx. Where xxx might be "signal flow graphs as described by Mason in 1953." Add a few lines about non-linearity and time dependent and then
2580:
The assertion of the text that needs a source for support is equivalent to: "Every SFG that leads to a particular equation set shares the same topology". Or something equivalent. Then the wording of the claims in the text needs adjustment so that it unambiguously states what the source supports.
5832:
It's clear that Mason and Kuo did not use the term "computational causality" as it had not been coined when their work was written, but it seems their notion of causality fits "computational causality" inasmuch as the signal-flow graph does have a connection to this form of causality but has no
5466:
Thanks for your comments. I am trying to understand the section on causality. Why is it there and what does it mean in plain language. It appears to be just a random collection of quotes and facts out of context that are hard to understand without the rest of the context. For example, what does
5067:
Iâm looking for a reason to include a section on causality and something to say about it that the general non-expert can understand and use. After reading through the various criticisms and those papers that are available I came up with what I wrote at the top of this section. SFGs, even when
2542:
In a system analysis workflow, the SFG is usually derived from system equations (perhaps representing a physical system). Many valid SFGs could be derived from such set of system equations. The process of building a SFG from system equations requires deriving each node function from one system
2223:
With this much complexity you lose the simplicity of the typical control system SFG. It looks to me like in the general form, it is about the same amount of work as solving the system by determinants. The complexity and the likelihood of making an error probably accounts for the method being
2175:
I just had another look at the example. I counted eight loops. With that many loops, it is easy to miss one. The system matrix for a typical control system is relatively sparse compared to a general set of linear equations. Going back to the example in Deo, which has three knowns and three
896:"Mason" was the first in a section on variants of signal flow graphs. This section would itemize Mason, Robichaud, Coates flow graph, and perhaps more. Another section to come should be the legacy of SFGs in which there would be a short presentation of bond diagrams and their origin in SFGs.
5213:
a simulation on an analog or digital computer. Implementation causality is a concern when implementing a computer simulation based on a SFG, whereby the input-output of the computer implementation blocks will follow the causality of the reference SFG (used as a blueprint for implementation).
3576:
Robichaud et al. wrote: "The signal flow graph contains the same information as the equations from which it is derived; but there does not exist a one-to-one correspondence between the graph and the system of equations. One system will give different graphs according to the order in which the
2482:
The claim is made in the article several times that a SFG topology is in one-to-one correspondence with its associated set of equations. Besides being unsourced, the concept of the topology of a set of equations is not explained or linked. In addition, we know there are multiple SFGs that can
5349:
So the SFG identifies "causes" (the "fundamental" variables of a particular strategy) without implying any physical causation. As a clarification intended for
Constant, it can be said that the processing at a node that sums various incident branches is "caused" by those inputs, which is an
5053:
The equations do determine the SFG, but sometimes the equations are not in SFG form and have to be manipulated. This ties into the solving linear equations section. The importance of that section is not that you can solve linear equations with SFGs but it tells you how to convert acausal
1326:
I'm not sure what the proposal is. It is not surprising at a flow graph and a di-graph mean the same thing. For me, a signal flow graph is a di-graph for which Mason's gain formula gives the correct results. If there was no MGF then the SFG would not be of interest to control engineers.
955:
4614:
I think the section on causality can be reduced to a couple of sentences in the introduction. Since a system of simultaneous linear equations can be made equivalent to a SFG, the SFG inherets the ability of linear equations to represent both causal and acausal; the is no controversy.
1604:
5457:
Looking at Newton's laws in an atmosphere. Gravity (force) on a mass causes acceleration which causes velocity which causes drag which reduces the force on the mass. The relationship is acausal (not strictly cause and effect), in the sense that acceleration pushes back against the
1674:
says "The nomenclature is far from standardized, and...no standardization can be expected in the foreseeable future." He uses 'flow graph' and 'signal flow graph' interchangeably (more often 'flow graph' as it is more compact, I guess) and defines the 'flow graph' like this:(p. 2)
3860:
I added additional quotes from severay authors. The Mason formula is an alternative to systemic reduction. Both methods are taught as ways to solve SFGs. Mason did not write that systemic reduction doesn't work. I will include how to solve the three linear equations in the wiki
1749:
5766:
has introduced two types of "causality" along the lines suggested by Pierre: "system causality" describing systems for which outputs at a given time are unaffected by inputs at future times, and "computational causality", a sequencing of equations for their sequential solution.
1424:
is not the same thing as a flow graph. A flow graph is a directed graph, but not all directed graphs are flow graphs. A flow graph introduces the meaning of an equation relating source and sink nodes representing variables, and the meaning of a transfer function to an edge.
4661:
Constant: I am with Pierre on this one for a different reason. That reason is that Kuo (a very influential text), Mason himself, Paynter, and
Willems stress causality, which means confusion reigns without a clear disclaimer that SFG has no necessary connection to causality.
867:
But you have now introduced a sub-section called 'Mason signal-flow graphs' under the main header 'Types of signal-flow graphs' suggesting that Mason graphs are a subset of signal flow graphs. Perhaps you could clear up this apparent conflict, and provide requisite sources?
5743:
The present intro uses the approach of
Choudhury, of Dorf & Bishop, and of Borutsky, and seems appropriate. The question arises whether the "cause and effect" comments that appear in the literature and are (IMO) misleading, need to be mentioned and put into perspective
881:
I have removed this section which appears misleading because of the headers attached to it that suggest a Mason graph and a signal-flow graph can be different things, and because the quote adds nothing new to the content of the article. The source already is cited earlier.
784:
Kou is unambiguous that the arrows in a signal flow graph represent cause and effect. A directed graph could represent acausal relationships, but it would not be a SFG. For example, in the documentation C++, some authors use the notation AâB to mean A is the child of B.
5239:
I understand physical causality, which in your example is simply the observation that when one thing consistently happens subsequent to another, the first is a "cause" of the latter. Closing a switch "causes" the current to flow. (Or, is the "cause" the desire for light?
1468:
Another important contributor to SFG theory and applications, Louis ROBICHAUD, ... Here the black halfânodes represent sources or inputs, the white halfânodes, sinks or outputs . Wholeânodes must then be always half-black/halfâwhite to assure causal compatibility during
5666:"The process of constructing a graph is one of tracing a succession of cause and effects through the physical system. One variable is expressed as an explicit effect due to certain causes; they in turn, are recognized as effects due to still other causes." (Section IV:
4021:(1) Some authors only consider as elementary transformations the summation of parallel-edges gains and the multiplication of series-edges gains, but not the elimination of loops (2) Other authors also include the elimination of self-loops as elementary transformations.
600:
a way to fudge it that's good enough if the application isn't too demanding. Scattering parameters are a relatively direct application of signal flow graphs with more intuitively meaningful results, e.g. S21 is the input to output voltage gain/attenuation of a 2 port.
5685:"The flow graph may be interpreted as a signal transmission system in which each node is a tiny repeater station. The station receives signals via the incoming branches, combines the information in some manner, and then transmits the result along each outpoint branch."
4722:
could be interpreted as saying force causes acceleration, it can be interpreted as saying acceleration is an indication of the presence of a force, or interpreted as how much acceleration corresponds to how much force. The math is neutral on the causal interpretation.
4253:
I've attempted to resolve this issue by quoting
Robichaud more carefully, indicating that he does not suggest that elementary operations are all that are needed. I have removed the template indicating a difference of opinion anticipating this matter is now resolved.
4205:
You can erase the whole SFG and replace it with one edge and put the gain on the edge equal to Mason's Gain
Formula and it would be equivalent to Gauss-Jordin. But you cannot make up a transformation rule just becasue it can be prooved mathemetically. That would be
3407:
Pierre: the new subsections you have introduced are premature and should be deleted until something of value to the reader can be produced. Please remove them and present these half-formed ideas on the talk page here until they have been improved and commented upon
5542:
used in the causality section of this article. If that were the meaning in use then there would be nothing to discuss. SFG's modeling real real physical systems would always be causal in that sense if they were an accurate representation of the physical system.
3845:
are forward cascades with no feedback. As a simple case, look at the example of a signal flow graph created by a system of three linear equations in three unknowns. The simplification rules cannot be applied to this case to connect inputs directly to outputs.
5859:
section ought to be greatly compacted by eliminating most of the quotes (but keeping them internal to the citation would be fine) and rewriting the section in plain declarative language that does not leave the reader with the need to infer all this for himself.
1933:
should treat all types of SFGs; since most content is about linear SFGs, a separate page on non-linear SFG would be near-empty. If the article becomes huge in the end, we should then consider creating one or more separate pages. If there is a separate page for
3110:
Although no purpose for this section has been presented on this talk page, I'm guessing that the goal is to generalize the presentation to go beyond linear systems. Perhaps a way forward would include sources for examples where this generalization is used?
4032:
5678:, for guiding a reader in the rapid construction of a signal-flow graph. As such it is not intended to suggest that physical cause and effect are part of the conception of a signal flow graph - only an interpretation sometimes useful for making a graph.
5574:
Brews, causal and acausal is being used in the sense that ohms law, V = IR, is an acausal relationship. It says that V and I have this relationship without saying that either is the cause or the effect. They could both be effects from some other cause.
653:
should point from V to θ. The SFG has more information than the equation. I do not have access to the reference, but assuming that the reference is correct, there is probably some requirement that the equations be in some sort of canonical form.
5048:= tachometer conversion gain constant,. There is one forward path (shown in a different color) and six feedback loops. The drive shaft assumed to be stiff enough to not treat as a spring. Constants are shown in black and variables in purple.
3502:
The bulleted points have yet to receive your attention. A full discussion isn't required. Just the general points of what the formula says and why it is useful and where the reader who finds these answers interesting can find more about them.
4389:
I apologize for only being here on weekends. I agree with Brews that the section, at this moment, has no factual errors or misleading statements. If we all agree with that, then let's stop this topic and start a new one about improving the
6106:
and simply replace the sections that we have discussed recently here. Some other editor may disagree and revert it. Don't let that bother you. It happens frequently. It means that we come back here to the talk page and find a consensus.
5220:
equations to be solved have been identified, any derived SFG will depend on the chosen association of equations to each of the dependent variables. There could be up to n! SFG possibilities. Loops represent cyclic dependencies in the set of
3067:
Most readers will be interested in the linear case, and in fact many published works assume the linear case, and some even restrict the subject to the linear case. So the linear case should be the focus, and the nonlinear case is an aside.
3216:
independent of linearity. These terms that do not depend on linearity of the flow graph need to be presented first anyway (ex. node, sink, source, path, etc...) Presenting these common concepts in the non-linear section would be awkward.
5799:
5811:
flow. Physically these are simply two concurrent aspects of one and the same physical phenomenon. Computationally, we may have to assume at times one position, and at other times the other." François
Cellier & Ernesto Kofman: §1.5
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the "standard" form. That info is indeed missing here, although part of the article elsewhere describes how to reduce clumsy SFGs. This omission doesn't make the section useless or easy to summarize in asides elsewhere in the article.
5338:
of the variables in terms of the others, and these algorithmic decisions, which are simply about solution strategy, then make the variables eliminated earlier in the solution "effects" of the remaining variables that are now "causes".
5449:
sense that you could compute MGF just as you could use Kramer's rule. But neither give you any intuitive feel for the real flow of cause and effect. When you look at that SFG, there is a branch from every node to every non-input node.
4269:
transfer function can be derived from a signal-flow graph by successively collapsing internal nodes until only the input and output nodes remain" is still misleading. I'll make my own attempt to make it correct and see how that sits.
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Building a signal-flow graph from equations is compatible with an acausal modeling approach: the signal flow graph, causal in nature, is only used as an artefact to solve the set of equations, not to imply a particular sequence of
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unknowns, I presume that for the general solution you would have to write MGF from each input to each output (nine in all) and use superposition to get the full expression for each unknown variables. It would be something like
4462:
This subsection is incomplete and erroneous as it stands. Block diagrams are more general than signal flow graphs and are not subject to the same rigorous mathematical requirements. I have removed the inaccurate lead sentence.
1856:
Sorry, I'm still not sure what you mean. Knowledge
Article naming has some fuzzy rules, but my interpretation is that the commonest name goes with the most common use rather than the most general use. So, this article named
2846:
indeed what a mishmash! Shu-Park Chan published in the
American Math Society : "Graph Theory and Some of its Applications in Electrical Network Theory" isbn:0821813226 this is probably an authoritative source on terminology
557:
The introduction paragraph says of an SFG that "its nodes are the variables of a set of linear algebraic relations." Can anybody provide an example application where the relations are, say, inequalities (e.g., less than)?
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The construction of the signal flow graph is basically a matter of following the cause-and-efect relationships through the system relating each variable to itself and to the others, using the basic building blocks of Fig.
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The 'standard' form for a linear set of equations described above always results in self-loops. Other forms for the equations do not always lead to self-loops. A diagram with self-loops is different from one without. See
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A variety of flow graphs exist, and some authors have chosen to refer to some of them as signal-flow graphs, for instance, Murota. This departure of meaning from Mason's signal flow graph appears to be a minority usage.
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In this quote it can be taken that Mason is suggesting a suitable but not a necessary or required perspective, and he proceeds to show how equations are related to this interpretation. The reader is free to assume that
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All well and good and maybe helpful in setting up an SFG for some kinds of system. But completely unnecessary. The equation set determines the SFG (or SFGs), and whether a causal argument can do it too is incidental.
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I think what needs to said is that a partial signal flow graph (a portion of s SFG lifted out of a larger SFG) does not express cause and effect but a complete SFG with input nodes specified does express cause and
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It occurs to me that your "implementation causality" describes how a computer program or algorithm can be arranged to solve a set of equations using various strategies. They differ in how they prioritize finding
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There appears to be no doubt that Mason introduced the term 'signal flow graph' and it is now referred to by many authors as he defined it. However, some authors have chosen to use the term in a different sense:
5350:"implementation" causality without any suggestion of physical causation. Different SFGs for the same system will identify different "causes", simply as a result of corresponding to different solution strategies.
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Acausal relationships cause loops in the SFG. Lots of acausal relationships cause lots of loops. SFGâs are lousy when there are a lot of loops. They are not obvious. Its easy to make an error when computing
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The title is one that readers are likely to look or search for and that editors would naturally use to link to the article from other articles. Such titles usually convey what the subject is actually called in
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that allows bilateral exchange between nodes. For feedback circuits, the Mason signal-flow graph is preferred to the Coates flow graph because it provides a more direct representation of the feedback process.
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that lead to the same equation set share the same topology? I am inclined to think that these statements of correspondence between SFG topology and that of its equation sets is a mistaken use of terminology.
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to itself. Every equation in the set makes assertions about the existence of nodes and branches between them. To me this is like a "the sky is blue" statement. Going the other way the SFG could imply both
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There are many types of block diagrams. The block diagram type that is illustrated in this section is as rigourous as SFGs. The lead sentence was actually representative of some authors. See for example
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This discussion of causality is meaningful when an SFG is used for the purpose of implementing an analog or digital computer simulation. The SFG is a causal representation derived from causal or acausal
993:
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It seems that the text description in Example 2 does not quite match up with the diagram it was supposed to describe. I could guess some corrections but isn't there an EE out there who can help us out?
3014:
Knowledge does not necessarily use the subject's "official" name as an article title; it prefers to use the name that is most frequently used to refer to the subject in English-language reliable sources
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Nowhere is it explained what "One system will give different graphs according to the order in which the equations are used" means. How does the order in which the equations are used change the graph?
1853:
which I see as a step back in the wrong direction. My intention was to expand on block diagrams and causality, and to keep linear flow graph discussions very separate from other types of flow graphs.
2505:, and maybe a particular signal flow graph defines what is meant by one particular topology of its equation set??? Now we need to show that all these signal flow graphs have the identical topology???
1607:, for example) and another that takes flow graph ⥠{subset of digraphs necessarily related to matrices or linear algebraic equations} so flow graphs include both Mason graphs and Coates graphs, and
3446:â˘Why does it belong in this article? Apparently signal flow graphs can be used to derive it, but is it proper topic to explore in an introduction? How come we need to bring up 'stability' etc, etc?
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As far as I can tell, the description is correct, but the example is almost too trivial. What he is saying is that the signal flow graph is for a system where the port voltages (V1 and V2) are the
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say: "Bond-graph literature uses the term computational causality, indicating the order of calculation in a simulation, in order to avoid any interpretation in the sense of intuitive causality."
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Constant: Indeed Robichaud uses a different example, but his is not the only example that demonstrates the point: algebraically identical sets of equations can be represented by different SFGs.
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A signal-flow graph contains the same information as the equations from which it is derived; but there does not exist a one-to-one correspondence between the system of equations and the digraph.
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are identical, and if one searches for a more inclusive term it is not to be found by redefining 'signal flow graph' to include things other than Mason graphs. More general classifications are
180:
Example 3 is a textbook example on control theory; it does, however, not show the forte of SFGs applied to circuits, nor does it clarify the possibility of cause-effect representation in SFGs.
3033:. To me that means that people who are actually looking for the linear time-invariant SFG although they don't know that there are non-linear and time varying versions are going to search for
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graph." It is not a statement about a general graph. On page 12 he says "An index-residual graph containing only sources and sinks besides index nodes cannot be reduced further without the
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This section is not needed at all. A simple example that shows the relation between the signal flow graph and a simple 3 equations with nimerical coefficient suffices. See the simple case in
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I did not see anything in the quote that would make me think Chen is referring to anything other than the well known fact that signal flow graphs can be solved by using Mason's gain formula.
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relationships into quasi-causal relationships. Using SFGs to solve a general system of linear equations is numerically similar to Kramerâs rule and probably has the same numerical problems.
3455:
Answering these questions requires a long discussion. Your source has many pages about it. I think all we need here is a See also link to a separate article that could handle the details.
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Perhaps the confusion comes from the fact that there are equations representing the SFG (one-to-one correspondence) and system equations representing the system (to be modeled in SFG form).
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I agree. The section is not remotely encyclopedic. It reads like a conversation. It could probably be reduced to one sentence in another section. The arrow does not imply causality.
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Pierre: Authority is not an issue. The trouble is that there is no standard. So the best that can be done is to adopt one approach and point out that there is confusion. That is done in
1678:"Flow graphs are a graphic representation of sets of linear algebraic or linear differential equations. Each vertex of a graph represents a variable of the equation...The coefficients
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variables, I take the term "implementation causality" as a way to introduce the term "causality" into a description of the noncausal SFG without any suggestion of physical causality.
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represent the same equations, so we need some theorem such as all such SFGs can be mapped into one another. We also need to relate this statement to the simplifications of SFGs that
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intends to show how to construct a signal flow graph that corresponds to a system of equations. You have suggested that an example would be the way to go. There is an example in the
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Circuit with two-port and equivalent signal flow graph. Notice that there are three loops in the signal flow graph. The larger loop goes from V1 to I2 to V2 to I1 and back to V1.
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I agree. The most common user of the article will be looking for the linear time-invariant SFG. He should not have to scroll through pages of text about obscure generalizations.
5507:. The simplest statement of causality is to say a causal theory professes that future events can be predicted using only present and past events. (A more general formulation is
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elementary reductions of a signal flow graph are shown". In other words he is not asserting that the five reductions shown are a complete set that allows any SFG to be solved.
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Constant: I haven't any ideas about how to introduce analog solutions to a set of equations into a discussion about "computational causality". And a source would be necessary.
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The idea of "implementation causality" is new to me. Supposing, as I think you agree, that the SFG is a representation of some set of algebraic and noncausal relations between
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between the matrix notation of a linear equation systemm instead of the Kronecker delta notation. My estimate is that the section will then be a third of the length. Opinions?
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Thanks for the comments; I reworked the section on synthesis. Is the intent clear now ? The section on analysis is very close to the cited source. Does it need improvement?
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Pierre: This subsection should be merged with any examples added into the subsection on nonlinear flow graphs. A general reformulation of the entire article isn't necessary.
821:
This section, as is, is incomplete. It does not show how to solve linear equations using graph transformation rules. To improve the section, please include the following:
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Most systems of general simultaneous linear equations have lots of acausal relationships. SFGâs are lousy for solving most systems of general simultaneous linear equations.
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variables simply have no causal connections. Possibly, if the gains are Laplace transforms of response functions these functions reflect causality, but not the SFG itself.
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For me, the two subsections under this topic are mumbo jumbo. They don' t explain how signal flow graphs help design. It seems the procedure would be the same without them
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as per Kuo. These claims contradict each other and both are false or at least misleading. That is the purpose of the section. You might have some ideas to make it clearer?
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includes analog computation. An amplifier may be said to compute its output from its input. A motor may be said to compute its position from its velocity. Or maybe not.
1541:
The question for me is: Should this subsection be added as it is for now? Of course, it can be added to or amended by anyone later to be more complete or better sourced.
5040:= motor torque constant (Nm/amp), T = torque, M = moment of inertia of all rotating components Îą = angular acceleration, Ď = angular velocity, β = mechanical damping, G
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Okay, here is one of the earlier cites I can find that summarizes this bijection. Even by 1967, this result was already known. See my cite to the SIAM journal article.
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The issue is that if, as claimed in the article, all SFG's can be solved with elementary transformations alone, then the claim needs a credible, unambiguous citation.
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The new section on "concepts" is not clear nor sourced. It doesn't clarify anything, and doesn't guide the reader to published discussions. I recommend its deletion.
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mean that the idea of causality is simply a crutch used to introduce directionality, and isn't really of any importance? Can this matter be explained more carefully?
2288:
I will add to the section on solving simultaneous linear equations in two blocks. The first will give setup and justification. The second will discuss computation.
1638:
if the directionality is removed. A network is a graph or digraph that associates a real number with each arc or edge. If the network is related to a graph, it is
1510:
it seems appropriate to have this application described in this article, although an extensive treatment would require a separate article (not yet present on WP).
4042:
Mauro Sonatros, Nuna Horta (2012). "Chapter 16: §4.1.2 Signal flow graphs algebra". In Mourad Fakhfakh, Esteban Tlelo-Cuautle, Francisco V. Fernåndez, eds (ed.).
3449:â˘What on Earth does the theorem say? The mathematical statement of the formula in the source is incomprehensible, of course. There is inadequate background here.
5436:
Response 1. In response to Brewâs comment âOne of your points is: The equation set one derives naturally for some systems using causality are not in SFG form.â
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What sort of clarification do you need? Every set of linear equations can be represented as a SFG and every SFG can be represented as a set of linear equations.
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I think links to software that can be used to solve (calculate transfer function) of signal flow graphs should be added to the article, here are a few examples
4643:
I favour keeping the extended critisism of SFG causality, since causality is a major point of differentiation from bond graphs (in which causality is explicit)
3879:
If you read few sentences in Robichaud beyond your quote, on page 10, just above fig 1-5 he says "These transformations are sufficient for the reduction of a
2725:
with the difference being the order of the terms. Of course if the variables are numbered like these, you can always insist the the terms be ascending order.
1865:. This article might have a note at the top saying that this article is about linear signal flow graphs. For non-linear signal flow graphs see <link: -->
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Response 2. In response to Brewâs comment âI need an example of a set of consistent equations that are outside the reach of this most general formulation.â
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I think this article is way too bloated. A wikipedia article should be nuch more concise. I suggest to rework it systematically, starting from the centre,
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Chen uses SFG and Mason graph as synonyms, and refers to Coates graph as simply flow graph. Others have other views. Maybe you disagree with the intro to
3613:
for flow graph for a simple set of 3 equations without self-loops. Then put these equations in standard form and make a new flow graph with self-loops.
5556:
What meaning do you think is being used? And, no, SFGs are acausal, regardless of causality in the system modeled. Because algebraic equations relating
3016:. Thus, if most English-language reliable sources use Signal Flow Graph to refer to the linear time invariant signal flow graph, then an article named
5289:. A stated benefit of acausal modeling is better reuse of models since equations do not specify Inputs and Outputs (explicit signal flow direction).
1382:, that's fine with me. If you want to add a section on something that is not a signal flow graph, I would suggest that it should have its own article.
940:
and rather than repeat what is in those articles just provide enough information to help the reader decide what might interest them in these articles.
6069:, I agree with greatly reducing the ""Systematic reduction to sources and sinks" section. And the section should probably be renamed "simplification."
1466:" Robichaud had a very good insight that led to bond diagrams, re in particular section 5.2 where there is a notation for explicit causality check "
1861:
should be about the linear signal flow graph. It might then have a paragraph about non-linear signal flow graphs and/or a link to an article called
1821:
Urgent: need to treat under a common heading all topicss pertaining to linear flow graphs from the rest. Why was this separation of concerns undone?
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Pierre: Your note remains a mystery to me. Maybe you can explain your use of 'artifact' here, and just what your causal-acausal concerns are about?
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should be moved here, and a new figure should present the basics . For example, source, sink, node, signal belong upfront. (separation of concerns)
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If nobody speaks up against it, I will replace example 3 by an example that does both in May 2010: the analysis of an opamp circuit with feedback.
3592:
it goes with the statement that there are n! SFGs for a given system of equation. I beleive it does not need context, maybe an example. Regards
2539:
A SFG can literally be transformed into a set of SFG equations of the form Xj = Fj(X1 .. Xn); equations in that form are easily mapped to a SFG.
2143:
Yes, it is a lucid example. Thank-you for pointing that out. I also read about the graph transformation rules. In particular the author said "
2051:
That section desperately needs an example of at least three equations and three unknowns. I do not understand what is written in that section.
1238:
PC Breedveld (2009). "§1.3.3 Bond graph notation". In Vincent Duindam, Alessandro Macchelli, Stefano Stramigioli, Herman Bruyninckx, eds (ed.).
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It appears that the Mason graph is a type of restricted bond graph, and that the Coates graph and the Mason graph are fundamentally the same (
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Also consider that a resister can be modeled as a voltage dependent current source. I.e.its current is proportional to the voltage across it.
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Well, Pierre, your distinction of two types of causality is a bit obscure to me, so let me try to restate what might possibly be your points.
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view in the parts of the article dealing with causality as only an interpretation of the SFG useful in some specific, limited applications.
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support massive adjustments to achieve a general formulation from the outset. That kind of rewrite is massive, and for almost no audience.
1649:. (p. 19) Graphs can be described by matrices, but the mapping of matrices to graphs is many to one. (p. 218) Also, see first paragraph in
1881:
I can relate to what you say Constant, given the state of inconsistencies in the papers and books. In his 1953 paper, Mason talks about
5629:"The SFG was introduced by SJ Mason for the cause-and-effect representation of linear systems that are modeled by algebraic equations."
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Response 4. In response to Brewâs comment â...you raise concerning the utility and the applicability of SFGs that might be valid... â
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Or is the problem about the meaning of topology? Two SFGs have the same topology if he have the same nodes and the same branch gains.
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is a set of vertices with a non-reflexive relation between pairs of vertices, named an 'arc' or 'edge'. (page 16) A digraph becomes a
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equation. A system equation can only be used once. This process was described in an earlier version of the page, but was deleted.
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SFG's can represent acausal relationships, but there are better tools. SFG's work best when most of the relationships are causal.
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Yes, this article is about Mason graphs (whether some do and some don"t call them signal flow graphs). And from the standpoint of
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Can we agree that a given SFG yields a unique set of equations not withstanding the order of the terms and order of the equations?
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linear FG. In his 1953 paper, he uses the term SFG twice (title and introduction); he uses the term "flow graph" about 48 times.
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These references present Mason's graphs as a specific type of signal flow graphs (i.e. Mason Graph and SFG are not synonyms).
4147:
I've seen elimination of self loops as an elementary transformation but not interlocked loops where neither contains the other.
5154:
A simple example would help the imagination. You seem to suggest a feedback loop is an example - maybe you could refer to the
5130:
Inasmuch as the SFG is readily representative of even the most general set of consistent algebraic relations between a set of
3258:
Electrical engineering: step-by-step construction of a signal-flow graph from physical model's equations needs to be condensed
5402:
Constant: I thought you had some disagreement with what had been said here, and I don't see how this remark bears upon that.
3909:
Here is an example of a SFG that cannot be reduced to a single edge from input to output by elementary graph transformations.
6087:
Sorry to ask a noob question: where is the proper place to write down the suggested new content for review? This page here?
5134:
variables, I need an example of a set of consistent equations that are outside the reach of this most general formulation.
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linear algebraic equations, but flow graphs are not. Nonetheless, the theorems about digraphs are useful for flow graphs.
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An example of a set of equations to be solved with at least 3 linearly independent equations with three unknown variables.
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This article is much better than it was a month or two ago, but it contains a lot of repetition and is poorly organized.
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Chan, Shu-Park âSection I â Circuitsâ, The Electrical Engineering Handbook, Ed. Richard C. Dorf, Boca Raton: CRC Press
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3. Your notion of "causal" doesn't fit with philosophy or science Maybe the clearest example of its use is in the
5342:
The discussion is referring to implementation by analog or digital computer simulations (not an analytical solver).
3631:
flow graph, not a flow graph and he says the SFG will be different it the equations are used in a different order.
5739:"Like block diagrams, signal flow graphs represent the computational, not the physical structure of a system."
4375:
Pierre: I believe the article now states Robichaud's position accurately, which I believe Constant agrees with.
3443:
OK: For a start let's look at the new section on the Shannon-Happ formula. Several points need to be clarified:
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3678:. If the quote is not explained and put in context, in the article, then it needs to come out of the article.
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3474:. I will add references and slight rework to show historical significance. Full treatment is not intended here.
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Evidently, Henley's 'flow graph' is not restricted to either the Mason or the Coates graph, but includes both.
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It seems to me that you are saying SFG â flow grap = di-graph and Pierre is saying SFG = flow graph â di-graph.
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Response 5. In response to Brewâs comment âI thought you had some disagreement with what had been said hereâ
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I'd say there should be no controversy, but several sources muddy the water, so a clear statement is useful.
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the same topology as all the other SFGs related to the same set, that discussion is useless without sources.
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I've made some minor additional changes and clarified that Robichaud's algorithmic reduction applies to his
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How about deleting Choma and Chen's quotes; with the paragraphs above, they seem redundant (no more useful).
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to do so. You can represent a voltage divider by a SFG, but it would not bring any insight to the analysis.
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I agree with your interpretations. In particular, I have reread Kou, sixth edition p. 77, he says â A SGF
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Are you trying to say that an arrow from node A to node B in a SFG does not guarantee that A is cause of B?
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Solving simultaneous linear equations is an example of the use of a signal flow graph. I moving it to the
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I've done some reorganization and rewording and added a few sources. No changes in substance, I believe.
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Later this week, I will add details on the rules to construct the sfg for its resolution by these rules.
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applies to all of linear flow graphs and not just to solving linear equations, so I propose to promote
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The Optimum Formula for the Gain of a Flow Graph or a Simple Derivation of Coates' Formula* C. A. DESOER
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by directed branches, (7-7) implies that the system equations may be portrayed by a signal flow graph.
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comments in-line instead of at the bottom. Did you see them? Perhaps I should move them to the bottom.
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I've rearranged the sections and subsections to put the causality-acausality issues all in one place.
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this point), they are not at all contradictory of what is said in the article so far. Do you agree?
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I hope that the new example provides the answer you are looking for. Have a look at the wikibook too
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3012:. There are many guidelines and some of them are in conflict, but I have focused on this sentence:
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The new section on causality will show two valid ways of looking at a SFG: causal and acausal.ÂÂÂÂ
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https://chrome.google.com/webstore/detail/signal-flow-graph/cdgiabknpabkdlahjgabbammnjfabkol?hl=en
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If quadri-pole flow graphs are not signal flow graphs then they should not be in this article.
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The equation set one derives naturally for some systems using causality are not in SFG form.
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Most circuits have lots of acausal relationships. SFGâs are lousy for solving most circuits.
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Constant: I see no ambiguity in the leading sentences of the quote. What ambiguity is there?
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In fact the way they are usually drawn is a signal flow graph with a little stylistic change.
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then any flow graph based on a set of equations that include that equation must have nodes X
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Signal flow graphs are useful for depicting and analyzing digital filters, especially IIR.
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causal and acausal relationships, unlike the bond graph in which causality is explicit."
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It looks as though some of the new sections are violations of copyright. In particular
630:, figure 3. It was retained. I still think it is a bunch of algebra signifying nothing.
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The removed sentence appeared to be a general statement, and therefore was misleading.
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Among the related diagrams often used in network analysis are the basically equivalent
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Mason and Coates should be presented as methods of resolving the gain in a flow graph
958:). Perhaps you understand where a Mason graph would prove easier to use? For example,
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digression explaining a different topic, but to clarify a relationship with the SFG.
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Never mind. I found the constraints on the equations and added them to the article.
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I don't know, but what is described is exactly what my text book has. That would be
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Pierre, it is not clear what you refer to. Is it something in a different article?
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Signal flow graphs and applications / Louis P.A. ... . Robichaud, Louis P. A., 1926-
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For me, the best explanation is the equivalence of these topological reductions to
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If there is any controversy on this point, I'll discuss it further. Is there any?
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2010:
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as referring only to the Mason flow graph, one among many possible flow graphs.
686:
I replaced by a sentence describing "acausal modeling" and a quote from Robichaud
218:
is the signal-flow graph notation based on some sort of authoritative standard? --
5151:
SFGs may not provide a system interpretation that satisfies causal requirements.
4361:
Constant's claim that it is misleading needs to be supported by a counterexample.
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The purpose of this section is to introduce SFGs in general, not separately from
1957:
All editors: please make sure that time-invariance is specified where relevant.
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The Long quote from Chen needs context and should probably be paraphrased. See
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What does Kuo mean when he says an SFG depicts a cause-and-effect relationship?
1241:
Modeling and Control of Complex Physical Systems: The Port-Hamiltonian Approach
5111:
It might help me to understand your remarks if I attempt to paraphrase them.
2360:
I meant artifact/artefact : a document produced along the way (an engineering
1527:
I can see some merit in such additions, but I have no interest in writing it.
1184:
J. R. Abrahams, G. P. Coverley (2014). "Chapter 1: Elements of a flow graph".
1153:
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5877:. It is now clearer, though perhaps not a short as you would like to see it.
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the motor current. We see a loop between these nodes which says in effect V
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One-to-one relationship with a system of linear equations. Reason to doubt.
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1. The notion of "SFG form" is vague. As the SFG corresponding to a set of
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Response 3. In response to Brewâs comment â...Newton's laws are causal...â
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For example, putting an equation in 'standard' form by adding the variable
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Is the word acausal in the introduction intentional or should it be causal?
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I gathered my scattered comments so that they are all here at the bottom.
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Louis P. A. Robichaud (1962). "§1.5 Reduction of the signal flow graph".
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Linear signal-flow graphs: Long Quote by Robichaud needs to be explained.
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Linear Signal Flow Graph, Long Quote needs to be paraphrased and explaind
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I have rewritten the material on causality in the subsection now titled
3953:|Control Systems|Signal Flow Diagrams|Examples of systematic reduction}}
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Systematic reduction of a linear flow graph to solve its gain - Disputed
3488:
the page belongs in the history section. Why did you move it, anonymous?
3125:
1992:
graph rather than a digraph would work just as well. Is that the case?
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should be about the linear time invariant signal flow graph. Also in
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I will add a section on Mason's explanation of SFGs as purely causal
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I'd like to see sourced commentary. I suggested one possible source.
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Example's 1 and 2 seem to have incorrect statements about causality.
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Maybe this is better; it shows a two-port in the context of a circuit
102:
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Satisfactory. Thank-you. Clarity is more important than brevity.
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4114:
Graph Theory with Applications to Engineering and Computer Science
3989:
listed each transformation rule at each step it would be clearer.
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Graph Theory with Applications to Engineering and Computer Science
1137:
If there is a distinction between this definition and that of the
393:
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One-to-one correspondence between SFG and associated equation set
1770:
155-1960 - IEEE Standards on Circuits: Definitions of Terms for
817:
Solving linear equations using graph transformation rules unclear
4718:
Yes. The SFG is a mathematical device, and just as Newton's law
3423:
willing to discuss; please be more precise about which section.
3183:
Brews, thanks. Will add as an example of a non-linear flowgraph
2830:
that tries to reach a balanced presentation of this mish-mash?
2403:
Solving simultaneous linear equations moved to Examples section
2097:
I can't do it because I don't understand what has been written.
5716:
It is noteworthy that no mention is made of cause and effect.
5694:
interpretation that leads to these equations is satisfactory.
5637:
What does Kuo mean by "cause-and-effect"? I submit that it is
1563:, and flow graphs and their connections? What do you all say?
15:
2794:
Mason's Graph, Coates Graph, Flow Graph, Signal flowgraph ...
4760:
is right, see Shannon's or Mason's original works. Example:
4165:
Question: If two equivalent sets of equations lead to (say)
2808:
GRAPHS: THEORY AND ALGORITHMS K. THULASIRAMAN Ă. N. S. SWAMY
2596:
The assertion seems obvious to me. If we have an equation X
148:
5674:
This passage can be taken as just heuristic, or a possible
1611:, and perhaps others. What is your view of the literature?
996:
which says Mason introduced the term signal flow graph, or
2316:
Pierre, did you perhaps mean artifice instead of artifact?
2065:
Within a few days I should be able to find time for this;
5681:
Mason also refers to the graph as a transmission system:
3266:. It should be placed after the telescope servo example.
2364:-- this could be CMMI jargon, sorry if it confused some )
1889:. Even Mason defines SFGs (unqualified) under a heading
1019:. This different meaning appears to be a minority usage.
4111:
Narsingh Deo (2004). "Reduction of signal-flow graphs".
1310:
This is a proposal. Comments and changes are solicited.
3262:
This should be limited to the circuit and the SFG. See
2441:
1851:
1459:
Robichaud's notations with half-circles for quadripoles
5731:
Again no reference to "cause and effect". And we have
5658:
Kuo suggests Mason introduced 'cause and effect', and
3092:
Recent addition of section "Basic flow graph concepts"
529:
http://www.mathworks.com/matlabcentral/fileexchange/22
446:
from Kou page 57 "... the branch directing from node x
5260:
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4783:
3147:. Some definitions currently defined in the section
4539:
refers to âthe above procedureâ which I think means
3810:
Page number is already there (page=x, i.e. roman 10)
2487:
in the course of using them to solve the equations,
2083:
Constant: Would you like to do that? It would help.
1866:. For other flow graphs see <different link: -->
1288:
Applied Graph Theory: Graphs and Electrical Networks
4045:
Design of Analog Circuits Through Symbolic Analysis
2426:this is *not* an example, it is part of SFG theory
1900:A BRIEF STATEMENT OF SOME ELEMENTARY PROPERTIES OF
1457:Robichaud's representation should have a paragraph
825:
Constraints, if any, on the equations to be solved.
5639:what Pierre has called "implementation causality"
5281:
4912:It has taken a while, but I think I see it now.
4858:
4807:
2994:Could we wait a few weeks before making that move?
1685:written alongside the branches are referred to as
5668:Illustrative applications of flow graph technique
2774:You are right. Let's have a source or remove it.
976:In any event, my understanding is that the terms
312:Sorry, I still do not know what you are wanting.
5156:SFGs provided for the negative feedback amplifer
4976:Angular position servo and signal flow graph. θ
4859:{\displaystyle x={\frac {z}{a}}-{\frac {by}{a}}}
3627:I do not that is it. He explicitly refers to a
1244:. Springer Science & Business Media. p. 16.
1224:. Springer Science & Business Media. p. 47.
5072:, the voltage across the motor inductance and I
3257:
1898:
1801:which needs some examples. Please take a look.
515:Signal Flow Graph Solver client side web page:
4541:4.3.1 Putting the equations in "standard form"
3380:Domain of application needs to be paraphrased.
3303:Agreed, will move and expand this in Wikibook.
1929:My opinion is that an article under a heading
1914:Mason, 1955 Technical Report 303 July 20, 1955
1171:has a different meaning in computer science.
521:Signal flow graph solver chrome application:
8:
4777:The first graph corresponds to the equation
3517:Agreed . Will add more in the next few days.
101:, which collaborates on articles related to
6029:Signal-flow_graph#Linear_signal-flow_graphs
2501:It would seem that every signal flow graph
1559:, that simply lays out definitions of SFG,
1086:Copyright: Public Domain, Google-digitized.
5985:
4555:up one level so that it is a sub-topic of
1221:Matrices and Matroids for Systems Analysis
706:
601:
47:
5259:
4841:
4828:
4820:
4782:
4084:CS1 maint: multiple names: editors list (
1276:CS1 maint: multiple names: editors list (
6023:Systematic re-write of the whole article
4769:
4761:
3916:
1768:There is also this withdrawn standard :
2908:stick to the linear time-invariant SFG.
1938:, it should be reflected in the title.
1693:. They are the operators that map node
831:A list of the knowns and the unknowns.
431:. Figure 2 unequivocally implies that I
49:
19:
5813:Simulation software today and tomorrow
5701:As an alternative description we have
4074:
4064:
4048:. Bentham Science Publishers. pp. 418
3782:-th equation introduces a self- loop.
1737:are functions of the Laplace operator
1266:
1256:
5854:y be defined ...â rather than âA SFG
4547:is in between those sections. Also,
1885:, and only qualifies them twice with
1051:appear to by quoted copyrighted text.
553:Example with a non-equality relation?
423:Figure 1 unequivocally implies that V
7:
5833:connection with physical causality.
5024:= voltage across motor inductance, I
2442:See this explanation of my reasoning
1555:Maybe a better idea is a stub, like
507:Software to Solve Signal Flow Graphs
435:is controlled by a weighted sum of V
157:This article is within the field of
95:This article is within the scope of
5698:and hence, to certain flow graphs.
5216:In an analysis workflow, after the
5016:= power amplifier output voltage, L
4815:, the second graph to the equation
4034:Signal Flow Graphs and Applications
2129:that seems to fit your suggestion.
1909:quantity called the node signal xj.
1781:. Notice "linear SFG" in the title
992:or perhaps some other designation.
517:https://github.com/ahmedkotb/sfg.js
38:It is of interest to the following
6146:Systems articles in control theory
6102:going to suggest that you be bold
5206:Comments: (I hope this will help)
4532:Some rearrangement of the sections
14:
4996:= motor velocity sense voltage, K
4117:. PHI Learning Pvt. Ltd. pp. 419
3947:Constant, please have a look in
3796:The citation needs a page number.
3362:Try it and we'll see how it goes.
1129:A definition of a flow graph is:
628:Ideal negative feedback amplifier
6031:and afterwards working outwards.
6007:So, what do you want to change?
5719:We have also Dorf & Bishop:
1778:DOI: 10.1109/IEEESTD.1960.81088
956:one can be mapped into the other
82:
72:
51:
20:
6141:Mid-importance Systems articles
5921:It might be worthwhile to note
1850:I was referring to this update
1630:uses a different vocabulary. A
135:This article has been rated as
6117:15:16, 24 September 2020 (UTC)
6097:14:28, 24 September 2020 (UTC)
6079:06:34, 24 September 2020 (UTC)
6061:06:23, 24 September 2020 (UTC)
6041:06:23, 24 September 2020 (UTC)
5638:
5500:2. Seems to be the same point.
4890:06:27, 24 September 2020 (UTC)
4876:06:00, 24 September 2020 (UTC)
4545:4.3.3 Systematic reduction ...
4189:reduction of linear equations.
4018:varies from author to author:
3452:â˘What is the theorem's value?
1994:Mason doesn't seem to think so
1370:to be less constrained than a
928:Perhaps a draft section, say â
354:and the port currents are the
1:
5949:15:52, 25 February 2015 (UTC)
5935:21:41, 24 February 2015 (UTC)
5901:21:26, 24 February 2015 (UTC)
5887:18:08, 24 February 2015 (UTC)
5869:11:48, 24 February 2015 (UTC)
5843:03:13, 24 February 2015 (UTC)
5828:01:43, 24 February 2015 (UTC)
5794:00:36, 24 February 2015 (UTC)
5777:00:31, 24 February 2015 (UTC)
5758:16:09, 23 February 2015 (UTC)
5654:02:26, 23 February 2015 (UTC)
5585:11:32, 24 February 2015 (UTC)
5570:21:36, 22 February 2015 (UTC)
5552:20:01, 22 February 2015 (UTC)
5529:15:56, 22 February 2015 (UTC)
5429:Gathered comments by Constant
5417:See Response 5 at the bottom.
5412:09:28, 22 February 2015 (UTC)
5398:22:26, 21 February 2015 (UTC)
5377:01:15, 24 February 2015 (UTC)
5363:18:14, 21 February 2015 (UTC)
5353:Is this what you are saying?
5325:01:15, 24 February 2015 (UTC)
5299:01:15, 24 February 2015 (UTC)
5231:00:10, 21 February 2015 (UTC)
5192:See Response 4 at the bottom.
5182:15:57, 19 February 2015 (UTC)
5162:See Response 3 at the bottom.
5138:See Response 2 at the bottom.
5124:See Response 1 at the bottom.
5102:12:04, 19 February 2015 (UTC)
5036:= current sense resistance, K
4959:03:03, 19 February 2015 (UTC)
4936:02:20, 19 February 2015 (UTC)
4733:16:36, 19 February 2015 (UTC)
4698:22:19, 18 February 2015 (UTC)
4672:16:02, 18 February 2015 (UTC)
4653:12:18, 18 February 2015 (UTC)
4639:03:43, 18 February 2015 (UTC)
4625:21:38, 17 February 2015 (UTC)
4604:18:36, 15 February 2015 (UTC)
4584:16:57, 15 February 2015 (UTC)
4569:21:17, 14 February 2015 (UTC)
4527:15:56, 14 February 2015 (UTC)
4505:03:44, 18 February 2015 (UTC)
4491:02:28, 18 February 2015 (UTC)
4473:16:13, 13 February 2015 (UTC)
4453:15:52, 13 February 2015 (UTC)
4439:15:09, 13 February 2015 (UTC)
4400:20:51, 14 February 2015 (UTC)
4385:02:03, 12 February 2015 (UTC)
4371:15:57, 11 February 2015 (UTC)
4325:13:51, 11 February 2015 (UTC)
4279:22:22, 10 February 2015 (UTC)
4264:17:31, 10 February 2015 (UTC)
4037:. Prentice Hall. pp. 12, 137.
1291:(2nd ed.). Elsevier. p. 172.
678:23:38, 31 December 2014 (UTC)
663:19:47, 31 December 2014 (UTC)
595:17:52, 31 December 2014 (UTC)
574:01:16, 28 February 2014 (UTC)
454:expresses the dependence of x
115:Knowledge:WikiProject Systems
6151:WikiProject Systems articles
5044:= motor back EMF constant, G
4249:21:52, 8 February 2015 (UTC)
4235:19:42, 8 February 2015 (UTC)
4220:18:04, 8 February 2015 (UTC)
4199:17:34, 8 February 2015 (UTC)
4179:13:54, 8 February 2015 (UTC)
4157:19:09, 7 February 2015 (UTC)
4141:14:58, 8 February 2015 (UTC)
4105:03:36, 5 February 2015 (UTC)
3999:02:26, 4 February 2015 (UTC)
3964:04:17, 3 February 2015 (UTC)
3934:16:47, 1 February 2015 (UTC)
3897:16:21, 1 February 2015 (UTC)
3871:00:11, 31 January 2015 (UTC)
3855:04:01, 30 January 2015 (UTC)
3820:01:00, 5 February 2015 (UTC)
3806:17:14, 1 February 2015 (UTC)
3792:04:43, 28 January 2015 (UTC)
3767:01:01, 28 January 2015 (UTC)
3752:03:04, 27 January 2015 (UTC)
3738:04:00, 26 January 2015 (UTC)
3712:01:09, 26 January 2015 (UTC)
3688:17:04, 25 January 2015 (UTC)
3661:00:58, 25 January 2015 (UTC)
3641:17:24, 24 January 2015 (UTC)
3623:07:07, 24 January 2015 (UTC)
3602:00:49, 24 January 2015 (UTC)
3587:23:42, 23 January 2015 (UTC)
3566:02:42, 28 January 2015 (UTC)
3551:07:08, 23 January 2015 (UTC)
3527:04:03, 30 January 2015 (UTC)
3513:03:06, 30 January 2015 (UTC)
3498:02:25, 27 January 2015 (UTC)
3484:23:03, 25 January 2015 (UTC)
3465:05:44, 23 January 2015 (UTC)
3433:01:52, 23 January 2015 (UTC)
3418:09:15, 22 January 2015 (UTC)
3398:02:30, 21 January 2015 (UTC)
3372:03:16, 23 January 2015 (UTC)
3358:02:38, 21 January 2015 (UTC)
3343:02:26, 21 January 2015 (UTC)
3313:13:25, 18 January 2015 (UTC)
3295:02:03, 18 January 2015 (UTC)
3276:23:57, 17 January 2015 (UTC)
3253:15:41, 17 January 2015 (UTC)
3232:14:45, 17 January 2015 (UTC)
3211:01:35, 17 January 2015 (UTC)
3193:04:54, 15 January 2015 (UTC)
3178:02:05, 14 January 2015 (UTC)
3164:23:27, 13 January 2015 (UTC)
3138:15:36, 13 January 2015 (UTC)
3121:15:27, 13 January 2015 (UTC)
3106:15:03, 13 January 2015 (UTC)
3078:11:58, 18 January 2015 (UTC)
3047:23:38, 17 January 2015 (UTC)
3004:14:58, 17 January 2015 (UTC)
2971:23:24, 17 January 2015 (UTC)
2957:00:59, 17 January 2015 (UTC)
2918:22:53, 16 January 2015 (UTC)
2887:09:30, 16 January 2015 (UTC)
2857:04:43, 15 January 2015 (UTC)
2840:06:33, 13 January 2015 (UTC)
2821:05:50, 13 January 2015 (UTC)
2784:02:21, 14 January 2015 (UTC)
2770:01:52, 14 January 2015 (UTC)
2751:23:10, 13 January 2015 (UTC)
2735:23:09, 13 January 2015 (UTC)
2591:14:51, 13 January 2015 (UTC)
2573:06:41, 13 January 2015 (UTC)
2553:05:33, 13 January 2015 (UTC)
2530:22:55, 12 January 2015 (UTC)
2515:15:46, 12 January 2015 (UTC)
2497:14:53, 12 January 2015 (UTC)
2468:04:04, 12 January 2015 (UTC)
2458:I acquiesce to the majority.
2454:23:38, 11 January 2015 (UTC)
2436:21:58, 11 January 2015 (UTC)
2421:15:04, 11 January 2015 (UTC)
2398:23:08, 25 January 2015 (UTC)
2326:03:46, 11 January 2015 (UTC)
2312:20:40, 10 January 2015 (UTC)
2298:17:31, 10 January 2015 (UTC)
2264:00:25, 10 January 2015 (UTC)
2234:17:00, 10 January 2015 (UTC)
2157:03:36, 10 January 2015 (UTC)
2075:00:25, 10 January 2015 (UTC)
2045:00:25, 10 January 2015 (UTC)
2011:00:25, 10 January 2015 (UTC)
1979:Pierre has added this note:
1967:23:39, 13 January 2015 (UTC)
1948:01:20, 14 January 2015 (UTC)
1877:23:45, 12 January 2015 (UTC)
1863:non-linear signal-flow graph
1846:03:51, 11 January 2015 (UTC)
1831:22:58, 10 January 2015 (UTC)
1791:00:56, 14 January 2015 (UTC)
1642:and if to a digraph it is a
922:19:00, 10 January 2015 (UTC)
811:23:29, 13 January 2015 (UTC)
696:03:12, 14 January 2015 (UTC)
293:21:33, 9 December 2010 (UTC)
274:21:09, 9 December 2010 (UTC)
249:21:06, 9 December 2010 (UTC)
118:Template:WikiProject Systems
4574:I think your change works.
2139:22:41, 9 January 2015 (UTC)
2107:21:54, 9 January 2015 (UTC)
2093:14:56, 9 January 2015 (UTC)
2061:23:21, 8 January 2015 (UTC)
2030:16:02, 8 January 2015 (UTC)
1811:19:09, 9 January 2015 (UTC)
1762:17:41, 9 January 2015 (UTC)
1662:16:23, 9 January 2015 (UTC)
1621:14:16, 9 January 2015 (UTC)
1589:23:23, 8 January 2015 (UTC)
1551:12:13, 8 January 2015 (UTC)
1537:02:17, 8 January 2015 (UTC)
1520:12:23, 8 January 2015 (UTC)
1499:04:40, 8 January 2015 (UTC)
1481:02:03, 8 January 2015 (UTC)
1435:02:03, 8 January 2015 (UTC)
1413:12:43, 8 January 2015 (UTC)
1392:04:31, 8 January 2015 (UTC)
1374:. If you want to say that
1354:01:57, 8 January 2015 (UTC)
1337:00:35, 8 January 2015 (UTC)
1320:19:11, 7 January 2015 (UTC)
1152:, and the rather different
1112:04:58, 7 January 2015 (UTC)
1098:04:07, 7 January 2015 (UTC)
1061:05:58, 6 January 2015 (UTC)
1049:Types of signal-flow graphs
1035:Possible copyright problems
1029:17:56, 7 January 2015 (UTC)
1010:17:13, 7 January 2015 (UTC)
972:17:04, 7 January 2015 (UTC)
950:16:54, 7 January 2015 (UTC)
906:12:40, 7 January 2015 (UTC)
892:16:52, 6 January 2015 (UTC)
877:03:04, 6 January 2015 (UTC)
862:Types of signal-flow graph?
857:03:57, 7 January 2015 (UTC)
841:20:28, 3 January 2015 (UTC)
795:18:22, 4 January 2015 (UTC)
779:20:27, 3 January 2015 (UTC)
760:02:40, 3 January 2015 (UTC)
427:is directly controlled by V
228:19:25, 9 October 2010 (UTC)
6167:
5008:= current sense voltage, K
4980:= desired angle command, θ
4458:Relation to block diagrams
3145:linear time-invariant SFGs
1953:Time-invariant linear SFGs
1420:-- Good intro. However, a
1362:to mean the same thing as
728:long dormant discussions.
626:It was actually example 2
501:03:52, 13 March 2011 (UTC)
485:03:45, 13 March 2011 (UTC)
207:18:39, 17 April 2010 (UTC)
141:project's importance scale
6046:Linear signal-flow graphs
6017:02:01, 9 April 2019 (UTC)
5782:Vichnevetsky & Miller
5631:Automatic Control Systems
5481:Follow-up by brews ohare:
5367:This is my understanding
4766:(a) Before path inversion
4016:elementary transformation
1902:LINEAR SIGNAL FLOW GRAPHS
1773:Linear Signal Flow Graphs
738:21:39, 9 April 2019 (UTC)
643:21:20, 9 April 2019 (UTC)
620:19:40, 9 April 2019 (UTC)
546:15:45, 6 March 2013 (UTC)
469:Automatic Control Systems
467:Kou, Benjamin C. (1967),
411:05:25, 4 March 2011 (UTC)
384:22:28, 3 March 2011 (UTC)
368:22:26, 3 March 2011 (UTC)
345:18:38, 3 March 2011 (UTC)
322:22:19, 3 March 2011 (UTC)
308:18:38, 3 March 2011 (UTC)
237:Automatic Control Systems
156:
134:
67:
46:
6136:C-Class Systems articles
5875:Interpreting 'causality'
5505:Kramers-Kronig relations
4774:(b) After path inversion
3611:Flow graph (mathematics)
3537:Dynamic systems analysis
3283:Flow graph (mathematics)
2875:Flow graph (mathematics)
2828:Flow graph (mathematics)
2636:and a branch with gain C
2381:can this whole Pierre's
1799:Flow graph (mathematics)
1557:Flow graph (mathematics)
1448:Nathan's representation
5808:computational causality
5114:One of your points is:
5000:= velocity loop gain, V
4988:= position loop gain, V
4808:{\displaystyle z=ax+by}
3470:this is in the section
3008:I have been looking at
2385:section be deleted now?
1750:Abrahams & Coverley
462:(but not the reverse).
5721:Modern Control Systems
5283:
5282:{\displaystyle V-RI=0}
5049:
5012:= current loop gain, V
4984:= actual load angle, K
4860:
4809:
4775:
4767:
3921:
2440:I agree with Pierre -
2035:will improve the note
1917:
1752:are in the same boat.
1726:is frequently used if
1075:Catalog Record Details
994:See this, for instance
746:Quote by Chen in intro
399:
153:
90:Systems science portal
28:This article is rated
5762:It can be noted that
5284:
5032:= motor resistance, R
5020:= motor inductance, V
4992:= velocity command, V
4975:
4861:
4810:
4773:
4765:
4537:4.3.4 Implementations
4014:The definition of an
3920:
3885:elimination of a loop
3778:to both sides of the
2485:modify their topology
1285:Wai-Kai Chen (2014).
1218:Kazuo Murota (2009).
1045:Domain of application
397:
152:
5705:Networks and Systems
5258:
5004:= current command, V
4819:
4781:
4590:State of the article
4553:Systematic reduction
4549:Systematic reduction
1971:
1187:Signal flow analysis
279:Clarification Needed
214:Notation a standard?
5800:provided by Cellier
5609:"The transmissions
5492:equations can have
5147:A second point is:
1687:gains, branch gains
1452:could be discussed.
1125:Related flow graphs
1120:Related flow graphs
930:Related flow graphs
580:Eliminate Example 3
98:WikiProject Systems
5992:PolychromePlatypus
5625:Another quote is:
5603:one quote from Kuo
5279:
5050:
5028:= motor current, R
4856:
4805:
4776:
4768:
4557:Linear Flow Graphs
4077:has generic name (
3922:
3149:Linear flow graphs
3126:Maybe this article
2224:somewhat obscure.
2016:So, does Pierre's
1931:signal-flow graphs
1817:Linear flow graphs
1442:Thulasiraman paper
1269:has generic name (
1190:. Elsevier. p. 1.
713:PolychromePlatypus
608:PolychromePlatypus
400:
330:Example 2 mismatch
154:
34:content assessment
6003:
5990:comment added by
5746:as attempted here
4854:
4836:
4424:Criticism of SFGs
3035:Signal flow graph
3018:Signal flow graph
1906:signal flow graph
1859:Signal-flow graph
1797:I've made a stub
1724:transfer function
1378:is a synonym for
1376:signal flow graph
1372:signal flow graph
1364:signal flow graph
1150:Coates flow graph
1143:signal flow graph
982:signal flow graph
724:
711:comment added by
622:
606:comment added by
564:comment added by
536:comment added by
210:
193:comment added by
176:Modify Example 3?
173:
172:
169:
168:
165:
164:
6158:
5288:
5286:
5285:
5280:
4865:
4863:
4862:
4857:
4855:
4850:
4842:
4837:
4829:
4814:
4812:
4811:
4806:
4131:
4089:
4082:
4076:
4072:
4070:
4062:
4038:
3954:
3757:change the SFG.
3403:Recent additions
3234:
2121:It appears that
1915:
1469:interconnection.
1301:
1281:
1274:
1268:
1264:
1262:
1254:
1234:
1214:
1200:
1000:. Do you agree?
576:
548:
472:
209:
187:
123:
122:
121:Systems articles
119:
116:
113:
92:
87:
86:
85:
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69:
68:
63:
55:
48:
31:
25:
24:
16:
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6126:
6125:
6048:
6025:
5614:
5599:
5431:
5256:
5255:
5245:
5244:
5204:
5091:
5088:is a cause of V
5087:
5083:
5080:is a cause of I
5079:
5075:
5071:
5047:
5043:
5039:
5035:
5031:
5027:
5023:
5019:
5015:
5011:
5007:
5003:
4999:
4995:
4991:
4987:
4983:
4979:
4910:
4843:
4817:
4816:
4779:
4778:
4611:
4592:
4534:
4515:
4460:
4426:
4128:
4110:
4083:
4073:
4063:
4059:
4041:
4030:
3948:
3842:
3776:
3704:203.189.142.161
3653:203.189.142.124
3615:203.189.142.124
3574:
3543:203.189.142.124
3539:
3457:203.189.142.124
3441:
3405:
3382:
3323:
3260:
3225:
3094:
2796:
2724:
2720:
2716:
2712:
2708:
2704:
2700:
2696:
2692:
2688:
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2676:
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2659:
2655:
2651:
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2643:
2639:
2635:
2631:
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2623:
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2615:
2611:
2607:
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2480:
2405:
2218:
2214:
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2206:
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2198:
2194:
2190:
2186:
2182:
1977:
1955:
1916:
1913:
1819:
1735:
1731:
1720:
1716:
1712:
1705:
1698:
1683:
1609:Murota's graphs
1577:
1358:Are you taking
1307:
1298:
1284:
1275:
1265:
1255:
1251:
1237:
1231:
1217:
1203:
1197:
1183:
1122:
1072:About this Book
1037:
864:
819:
767:
748:
650:
645:
582:
559:
555:
531:
509:
471:, Prentice Hall
466:
461:
457:
453:
449:
442:
438:
434:
430:
426:
418:
332:
281:
259:
257:Digital Filters
216:
188:
186:Any comments?
178:
120:
117:
114:
111:
110:
107:systems science
88:
83:
81:
61:
32:on Knowledge's
29:
12:
11:
5:
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5905:
5904:
5903:
5817:
5816:
5798:An example is
5741:
5740:
5729:
5728:
5714:
5713:
5687:
5686:
5672:
5671:
5662:, Mason says:
5635:
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5315:relationships.
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3718:
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3715:
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3695:
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3693:
3692:
3691:
3690:
3676:in the article
3666:
3665:
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3663:
3646:
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3644:
3643:
3605:
3604:
3573:
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3410:113.160.67.198
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3374:
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3319:
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3298:
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3259:
3256:
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3237:
3236:
3235:
3230:comment added
3196:
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3093:
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2847:(mathematics).
2810:
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2660:and a branch C
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1593:
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1590:
1586:
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1574:
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1570:
1566:
1562:
1558:
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1400:
1399:
1398:
1393:
1389:
1385:
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1377:
1373:
1369:
1365:
1361:
1357:
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1355:
1351:
1347:
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1338:
1334:
1330:
1325:
1324:
1321:
1317:
1313:
1309:
1308:
1304:
1302:
1299:
1297:9781483164151
1294:
1290:
1289:
1282:
1279:
1272:
1260:
1252:
1250:9783642031960
1247:
1243:
1242:
1235:
1232:
1230:9783642039942
1227:
1223:
1222:
1215:
1213:
1209:
1208:
1201:
1198:
1196:9781483180700
1193:
1189:
1188:
1181:
1180:
1176:
1172:
1170:
1169:
1163:
1162:
1158:
1155:
1151:
1146:
1144:
1140:
1132:
1131:
1130:
1127:
1126:
1119:
1113:
1109:
1105:
1101:
1100:
1099:
1095:
1091:
1088:
1085:
1084:
1083:
1077:
1074:
1071:
1068:
1065:
1064:
1063:
1062:
1058:
1054:
1050:
1046:
1042:
1034:
1030:
1026:
1022:
1018:
1013:
1011:
1007:
1003:
999:
995:
991:
987:
983:
979:
975:
973:
969:
965:
961:
957:
953:
951:
947:
943:
939:
935:
931:
927:
926:
923:
919:
915:
910:
909:
908:
907:
903:
899:
894:
893:
889:
885:
879:
878:
874:
870:
861:
859:
858:
854:
850:
842:
838:
834:
830:
827:
824:
823:
822:
816:
812:
808:
804:
800:
799:
796:
792:
788:
783:
782:
781:
780:
776:
772:
764:
762:
761:
757:
753:
745:
739:
735:
731:
726:
725:
722:
718:
714:
710:
703:
702:
697:
693:
689:
685:
684:
683:
682:
679:
675:
671:
667:
666:
665:
664:
660:
656:
647:
644:
640:
636:
629:
625:
624:
623:
621:
617:
613:
609:
605:
597:
596:
592:
588:
579:
577:
575:
571:
567:
566:74.71.235.237
563:
552:
547:
543:
539:
535:
530:
526:
524:
520:
518:
514:
513:
512:
506:
502:
498:
494:
489:
488:
487:
486:
482:
478:
470:
465:
464:
463:
444:
421:
415:
413:
412:
408:
404:
396:
389:
388:
385:
381:
377:
373:
372:
369:
365:
361:
357:
353:
349:
348:
347:
346:
342:
338:
329:
323:
319:
315:
311:
310:
309:
305:
301:
297:
296:
295:
294:
290:
286:
278:
276:
275:
271:
267:
262:
256:
250:
246:
242:
239:by Kuo,1967
238:
234:
233:
232:
231:
230:
229:
225:
221:
213:
211:
208:
204:
200:
196:
192:
184:
181:
175:
160:
151:
147:
146:
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138:
132:
129:
128:
125:
108:
104:
100:
99:
91:
80:
78:
75:
71:
70:
66:
60:
57:
54:
50:
45:
41:
35:
27:
23:
18:
17:
6066:
6049:
6026:
5986:â Preceding
5983:
5922:
5855:
5851:
5831:
5818:
5812:
5807:
5797:
5780:
5761:
5742:
5730:
5720:
5718:
5715:
5704:
5700:
5696:
5691:
5688:
5680:
5675:
5673:
5667:
5657:
5643:
5636:
5630:
5624:
5617:
5610:
5600:
5557:
5493:
5489:
5470:
5461:
5452:
5443:
5435:
5432:
5416:
5335:
5308:
5217:
5215:
5209:
5208:
5205:
5191:
5170:
5161:
5146:
5137:
5131:
5123:
5113:
5110:
4911:
4719:
4593:
4556:
4552:
4548:
4544:
4540:
4536:
4535:
4516:
4513:Changes made
4461:
4442:
4427:
4315:flow graph.
4312:
4187:Gauss-Jordan
4166:
4118:
4113:
4049:
4044:
4033:
4025:
4020:
4015:
4013:
3923:
3884:
3880:
3843:
3779:
3772:
3675:
3628:
3575:
3540:
3505:36.37.236.63
3471:
3454:
3451:
3448:
3445:
3442:
3439:Shannon-Happ
3406:
3386:WP:LONGQUOTE
3383:
3331:WP:LONGQUOTE
3327:WP:QUOTEFARM
3324:
3261:
3241:
3226:â Preceding
3167:
3154:
3148:
3144:
3128:could help?
3124:
3109:
3095:
3034:
3029:
3025:
3017:
3013:
2811:
2797:
2648:, a branch C
2579:
2576:
2561:
2500:
2481:
2408:
2406:
2388:
2382:
2362:work product
2361:
2144:
2127:cited source
2123:this section
2017:
2015:
1990:
1986:computation.
1984:
1978:
1973:
1956:
1935:
1930:
1928:
1905:
1901:
1899:
1890:
1886:
1882:
1862:
1858:
1820:
1775:
1772:
1769:
1738:
1727:
1723:
1708:
1701:
1694:
1690:
1686:
1679:
1666:
1644:
1639:
1631:
1597:Coates graph
1578:
1561:Coates graph
1554:
1540:
1526:
1467:
1462:
1450:Nathan paper
1419:
1379:
1375:
1371:
1367:
1363:
1359:
1287:
1283:
1240:
1236:
1220:
1216:
1211:
1206:
1202:
1186:
1182:
1178:
1177:
1173:
1167:
1164:
1160:
1159:
1147:
1142:
1136:
1128:
1124:
1123:
1081:
1048:
1044:
1040:
1038:
989:
985:
981:
977:
934:Coates graph
929:
895:
880:
865:
845:
820:
768:
749:
707:â Preceding
651:
627:
602:â Preceding
598:
583:
560:â Preceding
556:
538:41.46.219.11
532:â Preceding
510:
475:
468:
445:
422:
419:
401:
355:
351:
333:
282:
263:
260:
236:
217:
185:
182:
179:
136:
96:
40:WikiProjects
6109:Constant314
6071:Constant314
6009:Constant314
5941:Brews ohare
5927:Constant314
5923:computation
5893:Constant314
5879:Brews ohare
5861:Constant314
5835:Brews ohare
5820:Brews ohare
5786:Brews ohare
5769:Brews ohare
5750:Brews ohare
5703:Choudhury:
5646:Brews ohare
5577:Constant314
5562:Brews ohare
5544:Constant314
5521:Brews ohare
5404:Brews ohare
5390:Constant314
5355:Brews ohare
5174:Brews ohare
5094:Constant314
4951:Brews ohare
4928:Constant314
4882:Constant314
4758:Brews ohare
4725:Brews ohare
4690:Constant314
4664:Brews ohare
4631:Brews ohare
4617:Constant314
4596:Brews ohare
4576:Brews ohare
4561:Constant314
4519:Brews ohare
4497:Brews ohare
4465:Brews ohare
4445:Brews ohare
4431:Brews ohare
4392:Constant314
4377:Brews ohare
4317:Brews ohare
4313:generalized
4271:Constant314
4256:Brews ohare
4241:Constant314
4227:Brews ohare
4212:Constant314
4171:Brews ohare
4149:Constant314
4133:Brews ohare
3991:Constant314
3926:Constant314
3889:Constant314
3847:Constant314
3798:Constant314
3730:Constant314
3680:Constant314
3633:Constant314
3579:Constant314
3390:Constant314
3364:Constant314
3335:Constant314
3287:Brews ohare
3268:Constant314
3264:WP:NOTHOWTO
3245:Brews ohare
3203:Brews ohare
3170:Brews ohare
3130:Brews ohare
3113:Brews ohare
3098:Brews ohare
3070:Brews ohare
3039:Constant314
3026:Naturalness
2963:Constant314
2949:Brews ohare
2910:Constant314
2879:Brews ohare
2832:Brews ohare
2776:Constant314
2762:Brews ohare
2743:Constant314
2727:Constant314
2583:Brews ohare
2565:Brews ohare
2522:Constant314
2507:Brews ohare
2489:Brews ohare
2460:Constant314
2446:Brews ohare
2413:Constant314
2318:Constant314
2304:Brews ohare
2290:Constant314
2226:Constant314
2149:Constant314
2131:Brews ohare
2099:Constant314
2085:Brews ohare
2053:Constant314
2022:Brews ohare
1936:linear SFGs
1891:Linear SFGs
1883:flow graphs
1869:Constant314
1838:Constant314
1803:Brews ohare
1754:Brews ohare
1722:. The term
1654:Brews ohare
1613:Brews ohare
1581:Constant314
1575:Definitions
1565:Brews ohare
1543:Brews ohare
1529:Brews ohare
1512:Brews ohare
1491:Constant314
1405:Brews ohare
1384:Constant314
1380:Mason graph
1346:Brews ohare
1329:Constant314
1312:Brews ohare
1104:Constant314
1102:Good find.
1053:Constant314
1021:Brews ohare
1002:Brews ohare
990:bond graphs
978:Mason graph
964:Brews ohare
942:Brews ohare
884:Brews ohare
869:Brews ohare
833:Constant314
787:Constant314
771:Constant314
752:Constant314
730:Constant314
670:Constant314
655:Constant314
635:Constant314
587:Constant314
493:Constant314
477:Constant314
403:Constant314
376:Constant314
360:Constant314
314:Constant314
285:Constant314
266:Constant314
241:Constant314
189:âPreceding
6130:Categories
5369:Pierre5018
5317:Pierre5018
5291:Pierre5018
5223:Pierre5018
5221:equations.
4645:Pierre5018
4483:Pierre5018
4363:Pierre5018
4191:Pierre5018
4097:Pierre5018
3956:Pierre5018
3863:Pierre5018
3812:Pierre5018
3744:Pierre5018
3594:Pierre5018
3558:Pierre5018
3519:Pierre5018
3490:Pierre5018
3476:Pierre5018
3425:Pierre5018
3350:Pierre5018
3305:Pierre5018
3218:Pierre5018
3185:Pierre5018
3156:Pierre5018
2996:Pierre5018
2849:Pierre5018
2813:Pierre5018
2545:Pierre5018
2428:Pierre5018
2390:Pierre5018
2256:Pierre5018
2067:Pierre5018
2037:Pierre5018
2003:Pierre5018
1959:Pierre5018
1940:Pierre5018
1823:Pierre5018
1783:Pierre5018
1700:into node
1640:undirected
1605:RF Hoskins
1473:Pierre5018
1427:Pierre5018
1368:flow graph
1366:. I take
1360:flow graph
1210:. p. 418.
1168:flow graph
1154:bond graph
1090:Pierre5018
938:Bond graph
914:Pierre5018
898:Pierre5018
849:Pierre5018
803:Pierre5018
688:Pierre5018
5676:technique
5210:Causality
5202:Continued
4908:Causality
4609:Causality
4109:See also
4067:cite book
3951:Wikibooks
1972:Pierre's
1628:Chartrand
1259:cite book
1165:The term
450:to node x
416:Causality
6000:contribs
5988:unsigned
5764:Janschek
5733:Borutsky
5601:Here is
4390:section.
4075:|editor=
2944:WP:Undue
2411:section.
2409:Examples
1645:directed
1601:W-K Chen
1305:Comments
1267:|editor=
1017:see this
986:digraphs
960:see this
765:Acausal?
721:contribs
709:unsigned
616:contribs
604:unsigned
562:unsigned
534:unsigned
203:contribs
191:unsigned
5815:, p. 15
4026:Sources
3881:cascade
3472:history
3228:undated
3031:English
2207:+ MGF(Y
2195:+ MGF(Y
2183:= MGF(Y
1707:, i.e.
1647:network
1636:'graph'
1632:digraph
1422:digraph
1179:Sources
1139:digraph
1069:states:
1041:History
491:effect.
356:outputs
139:on the
112:Systems
103:systems
59:Systems
30:C-class
6089:Hanspi
6053:Hanspi
6033:Hanspi
5633:, p.48
5458:force.
4868:Hanspi
4208:WP:SYN
3629:signal
2664:from X
2652:from X
2640:from X
2001:issue.
1983:NOTE:
1887:signal
1776:, 1960
1672:Henley
1651:Hurary
458:upon x
352:inputs
337:Vonkje
300:Vonkje
220:Abdull
195:Hanspi
36:scale.
6104:WP:BB
5806:"The
5084:and I
4945:node.
3861:book.
3022:WP:NC
2697:and X
2632:and X
2215:) * Y
2203:) * Y
2191:) * Y
1904:-- A
1867:etc.
1161:Notes
439:and V
6113:talk
6093:talk
6075:talk
6057:talk
6037:talk
6013:talk
5996:talk
5945:talk
5931:talk
5897:talk
5883:talk
5865:talk
5839:talk
5824:talk
5790:talk
5773:talk
5754:talk
5650:talk
5619:7-1.
5581:talk
5566:talk
5548:talk
5525:talk
5509:here
5440:Yes.
5408:talk
5394:talk
5373:talk
5359:talk
5336:some
5321:talk
5295:talk
5227:talk
5178:talk
5098:talk
4955:talk
4932:talk
4917:MGF.
4886:talk
4872:talk
4729:talk
4720:F=ma
4694:talk
4668:talk
4649:talk
4635:talk
4621:talk
4600:talk
4580:talk
4565:talk
4523:talk
4501:talk
4487:talk
4469:talk
4449:talk
4435:talk
4396:talk
4381:talk
4367:talk
4321:talk
4275:talk
4260:talk
4245:talk
4231:talk
4216:talk
4195:talk
4175:talk
4153:talk
4137:talk
4123:ISBN
4101:talk
4086:link
4079:help
4054:ISBN
3995:talk
3960:talk
3930:talk
3893:talk
3867:talk
3851:talk
3816:talk
3802:talk
3788:talk
3763:talk
3748:talk
3734:talk
3708:talk
3684:talk
3657:talk
3637:talk
3619:talk
3598:talk
3583:talk
3562:talk
3547:talk
3523:talk
3509:talk
3494:talk
3480:talk
3461:talk
3429:talk
3414:talk
3394:talk
3384:See
3368:talk
3354:talk
3339:talk
3329:and
3309:talk
3291:talk
3272:talk
3249:talk
3222:talk
3207:talk
3189:talk
3174:talk
3160:talk
3134:talk
3117:talk
3102:talk
3074:talk
3043:talk
3000:talk
2967:talk
2953:talk
2914:talk
2883:talk
2853:talk
2836:talk
2817:talk
2780:talk
2766:talk
2747:talk
2731:talk
2717:+ C
2701:= C
2656:to X
2644:to X
2587:talk
2569:talk
2549:talk
2526:talk
2511:talk
2493:talk
2464:talk
2450:talk
2432:talk
2417:talk
2394:talk
2383:Note
2322:talk
2308:talk
2294:talk
2260:talk
2230:talk
2211:to X
2199:to X
2187:to X
2153:talk
2145:Some
2135:talk
2103:talk
2089:talk
2071:talk
2057:talk
2041:talk
2026:talk
2018:Note
2007:talk
1974:Note
1963:talk
1944:talk
1873:talk
1842:talk
1827:talk
1807:talk
1787:talk
1758:talk
1658:talk
1617:talk
1603:and
1585:talk
1569:talk
1547:talk
1533:talk
1516:talk
1495:talk
1477:talk
1431:talk
1409:talk
1388:talk
1350:talk
1333:talk
1316:talk
1293:ISBN
1278:link
1271:help
1246:ISBN
1226:ISBN
1192:ISBN
1108:talk
1094:talk
1082:...
1057:talk
1047:and
1025:talk
1006:talk
998:this
980:and
968:talk
946:talk
918:talk
902:talk
888:talk
873:talk
853:talk
837:talk
807:talk
791:talk
775:talk
756:talk
734:talk
717:talk
692:talk
674:talk
659:talk
639:talk
612:talk
591:talk
570:talk
542:talk
497:talk
481:talk
407:talk
380:talk
364:talk
341:talk
318:talk
304:talk
289:talk
270:talk
245:talk
224:talk
199:talk
105:and
6067:Yes
5692:any
5641:.
5243:âĚŻâ
4543:.
3224:)
2709:+ C
2689:+ C
2681:+ C
2673:= C
2628:, X
2616:+ C
2608:+ C
2600:= C
1732:, x
1689:or
988:or
131:Mid
6132::
6115:)
6095:)
6077:)
6059:)
6039:)
6015:)
6002:)
5998:â˘
5947:)
5933:)
5899:)
5885:)
5867:)
5856:is
5852:ma
5841:)
5826:)
5802::
5792:)
5775:)
5756:)
5748:.
5735::
5723::
5708::
5652:)
5613:kj
5605::
5583:)
5568:)
5550:)
5527:)
5494:n!
5410:)
5396:)
5375:)
5361:)
5323:)
5297:)
5265:â
5229:)
5180:)
5100:)
5006:IM
5002:IC
4994:ĎM
4990:ĎC
4957:)
4934:)
4888:)
4874:)
4839:â
4731:)
4696:)
4670:)
4651:)
4637:)
4623:)
4602:)
4582:)
4567:)
4559:.
4525:)
4503:)
4489:)
4471:)
4451:)
4437:)
4398:)
4383:)
4369:)
4323:)
4277:)
4262:)
4247:)
4233:)
4218:)
4197:)
4177:)
4155:)
4139:)
4121:.
4119:ff
4103:)
4071::
4069:}}
4065:{{
4052:.
4050:ff
3997:)
3962:)
3949:{{
3932:)
3924:.
3895:)
3869:)
3853:)
3818:)
3804:)
3790:)
3765:)
3750:)
3736:)
3710:)
3686:)
3659:)
3639:)
3621:)
3600:)
3585:)
3564:)
3549:)
3525:)
3511:)
3496:)
3482:)
3463:)
3431:)
3416:)
3396:)
3388:.
3370:)
3356:)
3341:)
3333:.
3311:)
3293:)
3285:.
3274:)
3251:)
3209:)
3191:)
3176:)
3162:)
3136:)
3119:)
3104:)
3076:)
3045:)
3028:â
3002:)
2969:)
2955:)
2916:)
2885:)
2877:.
2855:)
2838:)
2819:)
2782:)
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