Tuning of PID controllers based on simplified single parameter optimisation

Abstract

A simple method to design PID controllers in the frequency domain based on a simplified constrained optimisation is proposed. The method is based on the use of a single tuning parameter, defined as the quotient between the final crossover frequency and the zero of the controller. The tuning procedure is based on the maximisation of the controller gain subject to an equality constraint in the phase margin and an inequality constraint in the gain margin. The main advantage of the proposed method is that, even though the maximisation of the controller gain is straightforward, since there is only one parameter to be tuned, the solution is close to the optimal tuning obtained with direct numerical optimisation methods. Moreover the method is applicable to any linear model structure, including dead time and non-minimum phase systems.

Keywords:

• PID
• tuning
• frequency domain design
• gain margin
• phase margin
• integral gain maximisation