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?
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
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
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