New Criteria for Tuning PID Controllers

We propose a new approach to the problem of tuning and optimizing the parameters of aPID controller based on reducing the problem to an optimization problem. In this case, theperformance of the controller is evaluated by a quadratic criterion of the system output: the PIDcontroller is tuned against the uncertainty in the initial conditions so that the system output isuniformly small; in this case, a given degree of stability of the closed-loop system is additionallyguaranteed. A gradient method for finding the PID controller parameters is given. Numerousexamples show that the recurrent procedure proposed is very efficient and leads to PID controllersthat are quite satisfactory in terms of engineering performance indices. The article continues aseries of papers by the present authors devoted to synthesizing feedback in control problems fromthe standpoint of optimization.