PID controller tuning based on the covariance matrix adaptation evolution strategy

This paper deals with a PID control problem with constraints on sensitivity and complementary sensitivity functions, and proposes a PID controller tuning method based on the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Since the original CMA-ES is developed for an optimization problem without constraints, the PID control problem is transformed into an optimization problem without constraints by using a penalty method. Numerical examples are given to show the effectiveness of the proposed method.