Hybrid model-predictive-control for mechanical system with backlash

The hybrid model-predictive-control for mechanical system with backlash is studied. The operation model of a mechanical system with backlash is distinguished into the"backlash mode"and the"contact mode", and a piecewise affine(PWA) model of the mechanical system with backlash is built. For controlling this constrained PWA system, the optimal control law is derived by using the model predictive control(MPC) method; the offline solution of which is obtained by using the dynamic programming and the multi-parametric quadratic programming method. Finally, a piecewise quadratic(PWQ) Lyapuno function for the stability of the closed-loop system is found by transforming its searching process to a semi-definite programming. Experiments in tracking a reference speed signal demonstrate that the hybrid MPC gives desirable performances for the mechanical system with backlash, satisfying the real-time control requirements for systems with small sampling time.