17th International Symposium on
Mathematical Theory of Networks and Systems
Kyoto International Conference Hall, Kyoto, Japan, July 24-28, 2006

MTNS 2006 Paper Abstract

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Paper TuA06.5

Hämäläinen, Timo (Tampere Univ. of Tech.), Pohjolainen, Seppo (Tampere Univ. of Tech.)

A Self-Tuning Robust Regulator for Infinite-Dimensional Systems

Scheduled for presentation during the Mini-Symposium "Distributed Parameter Systems-II: Control of Infinite-Dimensional Systems" (TuA06), Tuesday, July 25, 2006, 12:05−12:30, Room G

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on June 23, 2024

Keywords Control of distributed parameter systems, Robust adaptive control

Abstract

It is well known that a low-gain controller of the form $C_eps(s) = sum_{k=-n}^n eps K_k/(s - miomega_k)$ is able to track and reject constant and linear combinations of sinusoidal reference and disturbance signals, asymptotically for stable plants $P$ in the Callier-Desoer algebra, and in the $L^2$ sense for exponentially stable well-posed systems.

In this paper we allow the scalar gain $eps$ to depend on time, $eps = eps(t)$, but assume the matrix gains $K_k$ to be fixed constants. The tuning method generalizes the one given by Miller and Davison for finite-dimensional systems with constant reference and disturbance signals.

The tuning method constructs a sequence of times $t_0 = 0 < t_1 < dots < t_k < cdots$ such that the gain is a constant $eps_k$ in each interval $(t_k, t_{k+1}]$. It is also shown that there is a time $t_{ss} > 0$ and a constant $eps_{ss} > 0$ such that $eps(t) = eps_{ss}$ for $t ge t_{ss}$. Hence the gain is tuned in finite time.