Robust Precision Position Tracking of Planar Motors Using Min-Max Model Predictive Control

In this article, a min-max model predictive control (MPC) method of planar motors is proposed for the first time to achieve robust precision position tracking, which has a low computational burden and strong capability to deal with the problems of stability, robustness, optimization, and input constraints. A state-space model with a homogeneous state equation is built to describe the dynamics of the time-varying reference trajectory. Combining the state-space model of the reference trajectory and that of the planar motor, an augmented state-space model is established to obtain an error state formulation. Then, using the error state formulation, a min-max optimal control problem subject to the constraints on bounded uncertainty, stability, and control input is developed. Moreover, applying the theory of asymptotically stable invariant ellipsoids and employing the nested invariant ellipsoids, the explicitly linear state-feedback control laws are obtained using a linear-matrix-inequalities based offline control algorithm. Finally, the min-max MPC is applied to a planar motor system developed in the laboratory for an experimentally comparative study. The results demonstrate the effectiveness of the proposed min-max MPC of planar motor for robust precision position tracking applications.