Abstract:

The mechanical system with backlash is distinguished between a “backlash mode” and a “contact mode”. The inherent switching between the two operating modes makes the system a prime example of hybrid system. For eliminating the bad effect of backlash, a piecewise affine (PWA) model of the mechanical servo system with backlash is built. The optimal control of constrained PWA system is obtained by taking advantage of model predictive control (MPC) method, and the explicit solution of MPC in a look-up table form is figured out by combining the dynamic programming and multi-parametric quadratic programming, thereby establishing an explicit hybrid model predictive controller. Furthermore, a piecewise quadratic (PWQ) function for guaranteeing the stability of closed-loop control is found by formulating the search of PWQ function as a semi-definite programming problem. In the tracking experiments, it is demonstrated that the explicit hybrid model predictive controller has a good traction control effect on the mechanical system with backlash. The error meets the demands of real system. Further, compared to the direct on-line computation, the computation burden is reduced by the explicit solution, thereby being suitable for real-time control of system with short sampling time.