Robust, optimal PI-controller tuning for integrator plus delay plants with varying parameters based on randomised algorithms

In this paper we consider the problem of tuning a PI-controller for robust, optimal performance with an integrator plus delay plant with varying plant parameters. The integrated absolute error for set-point tracking is considered as the performance index to be minimised by tuning. To this end, classical worst case and mean value based techniques for robust, performance optimal controller tuning are discussed. It is shown that these techniques require the consideration of an infinite amount of possible plant parameters in the optimisation step and are thus infeasible. To overcome this, we adopt randomised algorithms that allow an approximation of the original problem with a finite number of plant parameter samples in every step. Furthermore, we show that the minimisation problems to be solved in the randomised algorithm are convex and can thus be solved to their global minimiser, using readily available iterative algorithms. This is shown to introduce convexity of the set of stabilising controller parameters as a necessary condition, which is proven to hold for the problems considered here. Application of the proposed algorithm is shown for the tuning of a level controller in a continuous stirred tank heater demonstrator plant.