Mixed H2/h∞-based Pid Control via Genetic Algorithms: an Experimental Evaluation

As is pointed out in [2], the so-called mixed H2/H∞ control designs are quite useful for robust performance design for systems under parameter perturbation and uncertain disturbance. However, as is also pointed out in [2], the conventional output feedback designs of mixed H2/H∞ optimal control are complicated and not easily implemented. By these reasons, it is quite common to fix the structure of the controller in order to express mixed H2/H∞ control in terms of a tractable numerical optimization problem in the parameter vector space. The real parameter vector obtained as a solution to the optimization problem corresponds then to a particular fixed-structure controller which satisfies the specified control problem. The Proportional Integral Derivative control (PID control) law is a very succesful industry-oriented fixed-structure controller. As far as numerical optimization techniques are concerned, evolutionary computing [5] offers some powerful tools. In particular, Genetic Algorithms, initially inspired from the processes of natural selection and evolutionary genetics, have been succesfuly applied in control and signal processing design (see for instance [11]). We are interested here in the experimental evaluation of a PID mixed H2/H∞ control methodology based on the application of a standard genetic algorithm. With this objective in mind, we follow the procedure described in [2] to obtain the gains of a PID controller which solves a positioning control problem. The concerned plant is an experimental DC servosystem affected by a disturbance acting on the output. The paper is organized as follows: