Two Case Studies of Robust Multi-parametric Model Predictive Control Algorithm

This paper presents case studies of robust algorithm of multi-parametric model predictive control (mpMPC). For discrete-time linear parameter-varying (LPV) systems, the robust algorithm is investigated based on the solution of the mpMPC problem for discrete-time linear time-invariant (LTI) systems. The algorithm provides a controller design method, adaptable to parameter changes of a LPV system. By this controller the performance of the controller LPV system is improved in terms of robustness particularly for slowly varying parameters in the system. Thus the design method is applicable to systems suffering from slow parameter variations due, for example, to aging or degradation. The paper illustrates two control problems, one of which is disturbance rejection problem while the other is reference tracking problem. Each control problem is studied by computer simulation. Particularly for the reference tracking problem the robust mpMPC technique not only reduces the tracking error but renders a system stable while the nominal mpMPC could not.