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
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
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
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
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?
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
MG!∈R- ORDER5)sT6As RREL丹T(0sHP5 BETWEEN1MER6soN5毛 TAST∈P兵 ND THE POLE LOCAT(0NS心EK ALCULATE0 FoR A SECOND-ORDER SYSTEM GuES60工 NSIGHTS AcTuALLy Gooo APPRoXIMATIONS foR MAwy HIGHER- ORDER SYSTEMS BECAUSE THEIR
