State-Space Systems Open-loop Estimators Closed-loop Estimators Observer Theory (no noise)-Luenberger IEEE TAC Vol 16, No. 6, pp. 596-602, December 1971 Estimation Theory(with noise)-Kalman Copyright [2001 by JOnathan dHow
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Interpretations With noise in the system, the model is of the form =AC+ Bu+ Buw, y= Ca +U And the estimator is of the form =Ai+ Bu+L(y-9,y=Ci e Analysis: in this case: C-I=[AT+ Bu+Buw-[Ac+ Bu+L(y-gI A(-)-L(CI-Ca)+B
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Full-state Feedback Control How do we change the poles of the state-space system? Or, even if we can change the pole locations Where do we put the poles? Linear Quadratic Regulator Symmetric Root Locus How well does this approach work? Copyright [2001 by JOnathan dHow
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State-Space Systems e Ful-state feedback Control How do we change the poles of the state-space system? Or, even if we can change the pole locations Where do we change the pole locations to? How well does this approach work?
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This is a bit strange, because previously our figure of merit when comparing one state-space model to another(page 8-8)was whether they reproduced the same same transfer function Now we have two very different models that result in the same transfer function
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State-Space Systems What are the basic properties of a state-space model, and how do we analyze these? e Time Domain Interpretations System Modes Copyright 2001 by Jonathan How
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Controllability Definition: An LTI system is controllable if, for every a*(t d every T>0, there exists an input function u(t),0
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In going from the state space model i(t)=A.(t)+ Bu(t y(t)= Ca(t)+ Du(t) to the transfer function G(s)=C(sI -A)-B+D need to form the inverse of the matrix(sI- A)-a symbolic inverse- not easy at all For simple cases, we can use the following
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Topic 8 16.31 Feedback Control State-Space Systems What are state-space models? Why should we use them? How are they related to the transfer functions used in classical control design and how do we develop a state- space model?
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16.31 Feedback Control State-Space Systems What are state-space models? Why should we use them? and how do we develop a state-space mode( &ased in classical control design How are they related to the transfer functions What are the basic properties of a state-space model, and how do we analyze these?
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