1452:{{quote|text=State space representations originated in engineering and so an article like this is warranted in Knowledge. However, they are now also applied in other areas such as economic and business forecasting, where they often contain unit roots to cope with the non-stationary features of time series typically found in these disciplines. This gives rise to quite different classes of linear state space representations and to the need for more complex estimation methods than those based the traditional Kalman filter. My view is that a separate article is required, titled say "State Space Models in Economics and Business", to cover the issues missing from the current Knowledge article. There is now quite a large literature in this area, but two references cover many of its features:
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important) case. One should define "realization" first, noting that it isn't unique (see some of my previous contributions). "System variables" aren't defined (I'd just write "values" instead). In "linearly independent", linearly is superfluous, because linearity isn't required here. Finally, in "the minimum number of state variables is equal to the transfer function's denominator", it's equal to the denominator's degree, not to the denominator itself.
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908:. A much more precise and definitive argument is that feed-throughs are not realizable since information is moved instantaneously and this is not possible in physical systems, think of a mass which moves instantaneously and thus requires infinite energy. In fact we can demonstrate the problem by deriving (1) and applying limit to an instant
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variables (without their actual quantities/values) at a particular time? Does 'state' mean 'state variable quantities/values at time t'? It will be good for the article to define the meaning of a 'state' clearly - with very clear examples. Like, if 'state' means the same thing as 'state vector', then it needs to be indicated.
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As far as I know this does not mean the transfer function and State space model are not related as the transfer function consists of 9 parameters whereas the state space representation consists of 25 parameters and actually can hold more information. So when converting from state space to transfer
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Somebody seriously needs to start at the beginning, and define/explain the meaning of a 'state'. That is, what does a 'state of a system' actually mean? Does it mean actual set of values (1V, 5 degree C, 0.2 metres/sec) of state variables at a particular time? Or does it mean just the set of state
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I'm trying to learn some of the math from this article, so if I don't know what I'm talking about, that's why. That being said, I think there is some sort of error in the description of variables in the Moving Object
Example. In the second breakout "acceleration of the objection" it explains a
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I don't know if you want to restore more, so I prefer to ask you first. Section "State variables" is neither correct nor self-consistent, imo. State variables can be redundant (dependent); a state-space model with the number of state variables is a minimal realization, which is a special (yet
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I removed
CitationNeeded from "The state variables defined must be linearly independent; no state variable can be written as a linear combination of the other state variables or the system will not be able to be solved." because linear independence is a fundamental property of linear algebra
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makes the system acausal. This represents feed-through - for example, in a mechanical system if the feedback is by means of a magnetic actuator and the sensor is an inductive pick-up, it is possible for the sensor signal to contain a component due to the actuator field. This is causal and is
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it is not obvious for me why normal feedback is presented in detail here whereas state feedback, which is one of the advantages of a statespace model, is not even mentioned. State feedback is misused in the second feedback figure. this is not state feedback but ouput feedback (corrected)!
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The
Laplace transform of x'(t) is not sX(s), but sX(s)-x(0). I believe that the initial conditions term is usually assumed to be zero anyhow, to indicate no initial energy. I'm new to both controls and editing wikipedia, so I'll leave the actual editing to someone better equipped. :)
1475:: Ralph D. Snyder & Anne B. Koehler, 2008. "A View of Damped Trend as Incorporating a Tracking Signal into a State Space Model," Monash Econometrics and Business Statistics Working Papers 7/08, Monash University, Department of Econometrics and Business Statistics.
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function information gets lost and when converting from transfer function to state space there are many valid solutions. If the poles and zeros of the state space and transfer functon are the same the state space system below is one of these valid solutions
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August 2013 (UTC) The output equation in the observable canonical realization is wrong; It should be (as an illustration, the first state only depends on the input and itself; with , the output will be that from a 1st order system
186:==issue in the moving object example, if m tends to zero, and k1 (or k2) tends to infinity, then the system wont be controlable or observable, it is important to write this as it is the basis of nuclear physics
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I think, it would be good if someone add the
Observer Canonical Matrix just after the Controllable Canonical Matrix. That would make the article more complete (I do not have the time to do it anytime soon).
572:. What is represented in the article is the "disturbance" - that which interferes with our ability to control to the set point. I will let this sit for a few weeks before I edit the article.
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616:. In practical designs, one tries to avoid this by (for example) using a capacitative sensor, where the cross-talk is much smaller (perhaps even zero). It is true that with the inclusion of
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Also, state feedback was left out of the feedback section... might be good to include those tidbits. not a far stretch from what is already there, but it is entirely neglected.
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itself will have a frequency dependence, which is strictly proper but there seems to be no way to include this in the formalism. It would be possible to incorporate this into
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necessary for fully specified systems. I am not sure that it entire applies in this situation, so as opposed to a
Citation, perhaps it warrants removal for applicability.
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These programs can convert between transfer functions and state-space so I tried one to see how it matched to the page discussion. The coefficients are purely made up
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There seems to exist an alternative representation of the canonical realizations: (or at least another definition). Unfortunately I don't understand it completely.
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The transfer function, by definition, is the representation of the system in the s-domain with zero initial conditions. Perhaps the article could specify this?
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Hyndman, R. J., Koehler, A. B., Ord, J. K. & Snyder, R. D. (2008), Forecasting with
Exponential Smoothing: The State Space Approach, Springer-Verlag.
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321:. I reverted and attempted to restore edits made since then. Sorry if I missed some, but the amount deleted was wholly worth any loss since then. :/
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734:. That seems a preferable way to deal with the feed-through, with the behaviour of the transducers incorporated into the state space model
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The program is copyright, not the images created by it. Otherwise one could never publish any picture created with Paint, Photoshop etc.
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The 6-dof position and orientation (and corresponding rates) of an aircraft is not a euclidean space, but it is still the state space.
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Notice that in this general formulation, all matrices are supposed to be time-invariant, i.e. none of their elements can depend on time.
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Frank, it's debatable whether feed-throughs are causal or not since the information is output instantaneously with the input, that is
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the transfer function is proper (and not strictly proper. This is actually a deficiency with the formalism and presented. In reality,
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There also needs to either be a discussion about discrete time in this article or a link to another page which discusses that topic.
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may be slightly off. Inspecting its structure in comparison with the continuous counterpart the
Laplace transform, and studying
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We hope
Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.
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and thus we obtain an undetermined result. There is a good debate about this on the talk page of proper transfer functions. --
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Durbin, J., & Koopman, S. J. (2012). Time series analysis by state space methods (No. 38). Oxford
University Press.
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We believe Dr. Snyder has expertise on the topic of this article, since he has published relevant scholarly research:
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I'm tempted to put the template down in particular later subsections, the first section seems thoroughly covered.
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It looks like the canonical form on that page is the same as the one on this page (just with ordering reversed).
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is usually not left out just for the sake of simplification, but because it is zero in strictly causal systems.
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1738:{\displaystyle (z-1)\mathbf {X} (z)-z\mathbf {x} (0)=\mathbf {A} \mathbf {X} (z)+\mathbf {B} \mathbf {U} (z)}
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Your fix made it sound like the matrices *MUST* have a time dependence. They need not. I've fixed your fix. —
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I think another article on equilibrium is needed (phase diagrams, stabile points, unstable points, etc.).
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1620:{\displaystyle z\mathbf {X} (z)-z\mathbf {x} (0)=\mathbf {A} \mathbf {X} (z)+\mathbf {B} \mathbf {U} (z)}
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tells us. The problem arises with the definition of our feed-through in (1). Replacing (1) in (2) gives
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This is backwards; in the formulation shown the matrices do carry a time dependence. I corrected this.
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for the first difference forward, I cannot help but think that it should possibly read:
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There are two issues, which I would like to raise: I think it's incorrect to call
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systems do exhibit instantaneous variation, it is pretty much what the
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I noticed that the block diagrams on this page are created with
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Or make a prioritized plan for what needs to be cited inline?
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Where both S1 and S2 are given in state space representation.
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1311:Other Edits
1181:—Preceding
1818:Categories
1783:template?
1473:Reference
1318:J.H. Gorse
1505:Intellec7
1288:TedPavlic
1513:contribs
1501:unsigned
1204:Simulink
1183:unsigned
541:setpoint
378:setpoint
323:Cburnett
263:Cburnett
241:JMatopos
221:unsigned
1771:Remove
1352:Zfeinst
1337:Alorgen
1297:contrib
1223:Mesdale
503:Engelec
334:Engelec
289:--: -->
197:KorgBoy
150:on the
123:Systems
114:systems
70:Systems
41:B-class
47:scale.
1802:Mcint
1749:Redav
1410:-3.00
1407:-4.00
1380:tf2ss
1245:S243a
1806:talk
1753:talk
1509:talk
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1431:talk
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