ROBUST MODEL PREDICTIVE CONTROL FOR A MAGNETIC LEVITATION SYSTEM EMPLOYING LINEAR MATRIX INEQUALITIES

With the evolution of computational technology, the implementation of predictive control techniques in systems with fast dynamic became viable. In this formulation, the control action is obtained on line by the minimization of a constrained quadratic performance index within a receding horizon. The main advantage of these techniques is the possibility to deal with input/output constraints explicitly. The standard model predictive control (MPC) scheme does not consider model uncertainties, which can be caused by modeling simplifications or system faults. Among the formulations proposed to address this problem, linear matrix inequalities (LMI) techniques have become very popular. This work employs an LMI-based robust MPC approach for regulation of a magnetic levitation system with gain uncertainty. In order to achieve offset-free regulation, the plant model was augmented with an additional state associated to the accumulated error. However, such modification, which amounts to including integral control action, can cause windup problems that substantially increase the settling time. To circumvent this inconvenience, an anti-windup scheme was proposed. For this purpose, the error integrator is reset when the plant state approaches the boundaries of the feasible region. A modification was also introduced to allow the inclusion of an overshoot constraint in the MPC formulation. This is not possible in the basic LMI technique, which only handles symmetric output constraints. The proposed approach was evaluated by using a simulation model of a magnetic levitation system. The results show that the use of a robust MPC formulation may be indeed necessary to prevent constraint violations in the presence of uncertainties such as gain mismatch between the design model and the plant. Moreover, it was notice that the proposed anti-windup scheme is capable reducing the settling time without introducing steady-state errors.