Simultaneous design of proportional–integral–derivative controller and measurement filter by optimisation

Abstract

A method for optimisation of proportional–integral–derivative controller parameters and measurement filter time constant is presented. The method differs from the traditional approach in that the controller and filter parameters are simultaneously optimised, as opposed to standard, sequential, design. Control performance is maximised through minimisation of the integrated absolute error caused by a unit step load disturbance. Robustness is achieved through constraints on sensitivity and complementary sensitivity. At the same time, noise attenuation is enforced by limiting either the or norm of the transfer function from measurement noise to control signal. The use of exact gradients makes the synthesis method faster and more numerically robust than previously proposed alternatives.