Robust continuous-time controller design via structural Youla–Kučera parameterization with application to predictive control

This paper addresses the continuous-time control of uncertain linear SISO plants and its nominal and robust stability and nominal and robust performance objectives. A specific application of the Youla–Kučera (Q) parameterization concept leads to a new development of observer-like controller structures. This method is combined with a nominal design of continuous-time generalized predictive control suitable for both minimum-phase and non-minimum-phase plants. The subsequent design procedure consists of two steps. Firstly, the nominal stability and nominal performance of the control system are established by using an analytical design methodology, based on a collection of closed-loop prototype characteristics with definite time-domain specifications. And secondly, a generic structure of the controller is enhanced by suitable Q-parameters guaranteeing that the control system has the required robustness properties. The proposed structural (reduced-order) Q-parameterization relies on an observer structure of controllers, which can be easily enhanced with certain filters necessary for control robustification. To reduce the complexity of the resulting robust controllers, we suggest using a structural factorization, which allows for simple forms of robustifying (phase-lag) correctors of low order, easy for implementation, and convenient for optimization and tuning. Two numerical examples are given to illustrate the composed technique and its practical consequences.