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Goal: Design a controller K(s so that the system has some desired characteristics. Typical objectives Stabilize the system( Stabilization) Regulate the system about some design point(Regulation Follow a given class of command signals(Tracking) Reduce the response to disturbances(Disturbance Rejection Typically think of closed-loop control > so we would analyze the
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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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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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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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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 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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Closed-loop system analysis Robustness State-space -eigenvalue analysis Frequency domain- Nyquist theorem Sensitivity Copyright 2001 by Jonathan How
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MIMO Systems Singular Value Decomposition Multivariable Frequency Response Plots Copyright 2001 by Jonathan How
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Bounded gain There exist very easy ways of testing(analytically) whether S Gu)< SISO Bounded Gain Theorem: Gain of generic stable system
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Weighting Matrix Selection a good rule of thumb when selecting the weighting matrices Rxx (or Ru and R uu is to normalize
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