A Self - Tuning Robust Controller for Distributed Parameter Systems

Abstract

The main purpose of a robust controller is to stabilize the closed loop system and regulate the measurements in spite of a class of perturbations and system parameter variations. The controller may be tuned on the basis of measurements made directly from the process. The existing robust control theory gives the structure of the controller and leaves some freedom to assign the controller parameters. The final tuning includes the selection of a tuning parameter ε ∈ TR + , which typically will be fixed experimentally, using simulation or direct experiments with the plant. In this paper the selection of control parameters to improve and optimize the time responses are discussed. Using the well knowr Parseval's formula a connection between time domain and frequency domain can be established. The main advantage in the frequency domain is that the criterion to be optimized can be defined with the aid of the frequency response, which can be measured from the process. The final criterion, which gives a good performance and is sufficiently simple for optimization and stability analysis, was selected to be min ε max ω 1 ω 2 α tr I+ ε G j ω I+ ε G j ω ∗ − 1 . The possibility for an automatical optimization of control parameters will result in a self - tuning robust controller. At a specified steady state the frequency response can be measured and the feedback robust controller may be tuned. As an example the method will be applied to control a heat exchanger. The final controller consists of two parts: a nonlinear feedforward controller and a robust feedback controller. The feedforward controller determines the steady state in which the robust controller will be tuned.