Robust tuning of low-order controllers via uncertainty model identification

A tuning method for a controller of given structure is proposed, with particular emphasis on low-order compensators. The method consists of the processing of experimental results and prior information on the plant to be controlled, in order to obtain a plant uncertainty model, composed of a nominal model and a bounded perturbation representing the modelling error. The number of poles and zeros of the controller being fixed, a procedure is described which allows one to obtain the so-called robust Q set. This is the set of the controller parameter values for which the desired closed-loop performance specifications are satisfied, whatever plant is considered within the previously estimated uncertainty model. Given a designed controller, the worst-case performances, i.e. the performances that can be guaranteed for all systems belonging to the uncertainty model, are derived. This way the designer can tune the controller parameters to suitably balance the closed-loop performances. Moreover, the performances guaranteed by applying the designed compensator to the actual plant can be evaluated.