PID tuning using extremum seeking: online, model-free performance optimization

Extremum seeking (ES) tunes PID controllers by minimizing a cost function that characterizes the desired behavior of the closed-loop system. This tuning method is demonstrated on four typical plants and found to give parameters that yield performance better than or comparable to that of other popular tuning methods. Additionally, ES produces favorable results in the presence of actuator saturation. The ES method thus has an advantage over model-based PID tuning schemes in applications that exhibit actuator saturation. However, since ES requires initial values of the PID parameters, the method can be viewed as a complement to another PID parameter design method. Furthermore, the ES cost function can be chosen to reflect the desired performance attributes.