Abstract: A constrained time-optimal predictive controller based on the piecewise affine (PWA) model is designed for solving the computation complexity of optimal control problem for mechanical system with backlash. For reducing computation burden of online implementation, the control law is computed offline for the range of states and references tracking speed by dynamic programming. In the experiments of tracking the reference speed, it is demonstrated that the constrained time-optimal predictive controller has better tracking control performance and reduces the computation time about ten times when compared with the constrained finite time optimal controller, therefore, the proposed approach and controller are suitable for real-time tracking control for systems with small sampling time.