Controllability of the predictive model and its effect on the stability of the model predictive controller

It is shown that the existing methods of designing stable predictive controller fail to stabilize the closed loop system for processes with repetitive unstable poles (minimum or non-minimum phase) even though the required conditions are satisfied. We show that the main reason, that has stayed unnoticed in the previous works, is the decrease of controllability of the predictive model (not the model of the process) in the controller. In consequence, a GPC control design method is proposed in which some of the cost function weightings are used to compensate for weakness in the predictive model controllability. The remaining weightings are set to guarantee the stability of the closed loop system. By studying different examples it is shown that using the proposed method, the closed loop stability of minimum or non-minimum phase processes with repetitive unstable poles are achieved.