An off-line methodology was proposed for enhancing the robustness of an initial Generalized Predictive Control (GPC) by convex optimization of the Youla parameter. However, this procedure of robustification is restricted with the case of the systems affected only by unstructured uncertainties. This paper proposes an extension of this method to the systems subjected to both unstructured and structured polytopic uncertainties. The main idea consists in adding supplementary constraints to the optimization problem which validates the Lipatov stability condition at each vertex of the polytope. These polytopic uncertainties impose a set of non convex quadratic constraints. The globally optimal solution is found by means of the GloptiPoly3 software. Therefore, this robustification provides stability robustness towards unstructured uncertainties for the nominal system, while guaranteeing stability properties over a specified polytopic domain of uncertainties. Finally, an illustrative example is given

One of the most critical issues in the fast and large step change in the speed control of an induction motor is the excessive generated current command, and consequently, if the speed controller does not have output magnitude limiter, this might end up damaging the power electronics converter and the motor itself. This paper is devoted to overcoming the speed controller saturation phenomenon. Firstly, predictive controllers in polynomial form are designed for the speed control loop and for the two inner currents control loops. Then, the outer predictive speed controller is retuned by convex optimization of the Youla parameter considering temporal and frequency constraints, so that the resulting controller assures that the speed response to the reference remains in an imposed template with a minimal current command in transient periods and, in other hand, it keeps the closed loop features obtained by the initial predictive controller. Simulations results show the speed control performance of the proposed control system for various operating conditions of the motor.

In the induction motor indirect vector control system, because of its physical limitations, the large step change in the speed command and/or load would eventually cause the so-called “integral windup phenomenon” which causes unexpected behavior of the system. To counteract this problem, an anti- windup generalized predictive speed control method is proposed by using the Youla parametrization. As first step, the design of an initial GPC controller based on its polynomial equivalent structure is required. Then, thanks to the Youla parametrization, this controller is retuned considering two specifications. The first is a frequency specification on the quadratic component of stator current response to the speed reference. And the second is a time domain constraint on the measured speed response to the speed reference. These constraints are formulated within a convex optimization framework. The simulation results proved the efficiency of the present design method.