Multi-objective optimal design of online PID controllers using model predictive control based on the group method of data handling-type neural networks

Abstract

In this paper, model predictive control (MPC) is used for optimal selection of proportional-integral-derivative (PID) controller gains. In conventional tuning methods a history of response error of the system under control in the passed time is measured and used to adjust PID parameters in order to improve the performance of the system in proceeding time. But MPC obviates this characteristic of classic PID. In fact MPC tries to tune the controller by predicting the system's behaviour some time steps ahead. In this way, PID parameters are adjusted before any real error occurs in the system's response. For this purpose, polynomial meta-models based on the evolved group method of data handling neural networks are obtained to simply simulate the time response of the dynamic system. Moreover, a non-dominated sorting genetic algorithm has been used in a multi-objective Pareto optimisation to select the parameters of the MPC which are prediction horizon, control horizon and relation of weight of Δ u and error, to minimise simultaneously two objective functions that are control effort and integral time absolute error of the system response. The results mentioned at the end obviously declare that the proposed method surpasses conventional tuning methods for PID controllers, and Pareto optimal selection of predictive parameters also improves the performance of the introduced method.