Optimization and Systems Theory Seminar
Tuesday, June 26 2007, 11.00-12.00, Room 3721, Lindstedtsvägen 25

Shinji Hara
University of Tokyo, Japan
E-mail: Shinji_Hara@ipc.i.u-tokyo.ac.jp

When is a linear system easy or hard to control?

Our focus in this talk is to characterize easily controllable plants in practical
control applications rather than to design an optimal or a robust controller for
a given plant. It is well known that the fundamental requirement of closed-loop
stability provides intrinsic performance limitations such as the Bode integral
formula on the sensitivity gain.

We first provide closed-form expressions for the best achievable H2 control
performances in two typical optimal control problems, namely tracking and regulation.
The results clearly show the performance limitations caused by gain characteristics
as well as unstable poles, non-minimum phase zeros, time-delays of the plant.
They also reveal and quantify how the lightly damped poles, the anti-resonant zeros,
and the bandwidth of the plant affect the performance even if the plant is
minimum-phase. We then show how to apply those analytical expressions of control
performance limitations to practical applications including control of magnetic
bearing systems.

In our second result, we derive a quantitative result that relates the gain/phase
property of the plant to the achievable control performance in H
Calendar of seminars
Last update: May 4, 2007 by Marie Lundin.