Fall 2001 16.313-1 Introduction Root locus methods have Advantages k Good indicator if transient response k Explicity shows location of all closed-loop poles Trade-offs in the design are fairly clear Disadvantages k Requires a transfer function model(poles and zeros) k Difficult to infer all performance metrics k Hard to determine response to steady-state(sinusoids
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?
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
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
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?
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
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?
Model Uncertain Prior analysis assumed a perfect model. What if the model is in correct= actual system dynamics GA(s)are in one of the sets Multiplicative model G,(s=GN(s(1+E(s)) Additive model Gp(S)=GN(S)+E(s) where
