RETRACTED: Hybrid Time-Optimal Predictive Control for Mechanical Systems with Backlash Nonlinearity (Retracted Article)

The mechanical system with backlash nonlinearity is distinguished between a "backlash mode" and a "contact mode". The inherent switch between the two operating modes makes the system a prime example of hybrid system. In this paper, a PieceWise Affine (PWA) model of the mechanical system with backlash nonlinearity is built. A constrained time-optimal predictive control problem based on the hybrid PWA model is formulated for solving the optimal control problem of mechanical system with backlash nonlinearity. The proposed constrained time-optimal predictive control strategy consists of two parts, that is, control invariant set computation and constrained time-optimal control law computation. For the purpose of reducing computation of online implementation, the control law is precomputed offline for the range of model states and references by combining dynamic programming strategy with the reachability analysis for the PWA model. In the simulation of tracking the reference speed, it is demonstrated that the constrained time-optimal predictive control approach has better tracking control effect and less computation time compared with the constrained finite time optimal control approach. The resulting control law achieves that for any reference the tracking error remains within a small bounded set, furthermore, the online implementation becomes simpler by the offline computation in the former step, thereby reducing computation burden and being implemented on low-cost hardware for systems with small sampling time.