Optimal Transient Response Shaping for the       Discrete-Time Servomechanism Problem
Professor Edward J. Davison

Systems Control Group

Department of Electrical and Computer Engineering

University of Toronto

Toronto, Ontario

Canada M5S 3G4


Abstract – The problem of finding an “optimal controller to solve the servomechanism problem, which results in a closed loop system which has a desired transient response, with negligible cross-channel interaction, without necessarily using high-gain control methods, is considered in this talk for the case of discrete LTI systems.  Subject to fundamental limitations on achievable performance, this objective is achieved by introducing a new cheap-control quadratic performance index that has the desired transient response characteristics embedded within it.  A study of the fundamental limitations for error tracking/regulation are then carried out to obtain explicit expressions for the limiting performance cost associated with the servomechanism problem as the weight on the control energy tends to zero.  These limitations can be characterized by the system order, the number of the outputs, the number of the system’s transmission zeros, and the location of the system’s non-minimum phase transmission zeros.  Application of the new performance index to various industrial system examples are given.


Friday, February 14, 2003

3:30 – 4:30 p.m.

1500 EECS