Design of PID controllers for uncertain plants

Abstract

This thesis presents several design methods of proportional-integral-derivative (PID) controllers for uncertain plants. It is considered the case in which the plant to be controlled is modeled by a family (finite or infinite) of linear time-invariant (LTI) single-input-single-output (SISO) plants. The control design problem is a rich problem that should be taken into account several aspects, such as, disturbance attenuation, reference tracking, measurement noise, and changes in the plant dynamic. The frequency domain approach provides very useful tools to deal with such problems. In particular, this thesis uses Quantitative Feedback Theory (QFT) developed mainly by Isaac Horowitz and the Parameter Space Approach. The control design problems are formulated as constrained optimization problem and they are solved by using numerical optimization techniques. The results of this thesis comprise several design methods applicable to different kinds of models. Firstly, some parametric model (integrator time-delay and first-order time-delay) with interval uncertainty are considered. After that, a method applicable to a model consisting of a family of frequency responses is presented. This kind of model is very general. On the one hand, it is possible to obtain a frequency response from any LTI system. On the other hand, experimental frequency response data can be used directly. An alternative approach to model the uncertainty in this thesis has been the use of probabilistic models. In this way, an unknown-but-bounded parameter is modeled by a uniform random variable. Finally, a novel relay autotuning method is presented through its application to an industrial pH control system.