Design of balanced proportional–integral–derivative controllers based on bilevel optimisation

Abstract

A bilevel optimisation framework is proposed to find the proportional–integral–derivative (PID) controller with balanced performance in terms of transient response, actuator preservation and robustness. In the lower level problem, the transient performance is optimised so that the balanced controller can be designed with minimal controller output variation in the upper level problem, where the requirement on transient performance is relaxed to a pre-specified extent. The robustness of the system is guaranteed by constraints on the maximum sensitivity in both problems. The trade-off between transient performance and actuator preservation is controlled uniformly for diverse process dynamics by a single parameter, which characterises the uniformness of relaxation in transient performance. By choosing different values of this parameter, tuning rules are provided for first order plus time delay (FOPTD) processes for set point following and load disturbance rejection, respectively. The efficiency of these tuning rules is demonstrated by examples covering the whole plant family set.