Nash tuning for optimal balance of the servo/regulation operation in robust PID control

In this paper we propose a multi-objective optimization approach for the tuning of one degree-of-freedom proportional-integral-derivative controllers where both the trade-off between the servo and regulation operation modes and the trade-off between performance and robustness are considered. After having quantified the loss of performance that occurs when robustness is taken into account in the optimal design of the controller a tuning rule is proposed based on the Nash solution. A balanced robust tuning is obtained simply starting from a first-order-plus-dead-time model of the (self-regulating) process.