This paper proposes a discrete-time nonsmooth internal model control （NSIMC） approach for mechanical transmission systems described by so-called sandwich system with backlash. In this method, a dynamic compensator is introduced to compensate for the effect of the input linear subsystem. Thus, the sandwich systems with backlash can be simplified as a pseudo-Hammerstein system with backlash. The corresponding NSIMC strategy is designed to control this system. The design procedure of the controller is presented based on the analysis on the robust stability by considering the model errors involved with the effect of backlash as well as the compensated error of the input linear subsystem. Moreover, as the model is switched among the different operating zones, the robust filters are proposed to guarantee the robust stability and satisfactory control performance of the system.
Backlash-like hysteresis is one of the nonsmooth and multi-valued nonlinearities usually existing in mechanical systems. The traditional identification method is quite difficult to be used to model the systems involved with such complex nonlinearities. In this paper, a nonsmooth recursive identification algorithm for the systems with backlash-like hysteresis is proposed. In this method, the concept of Clarke subgradient is introduced to approximate the gradients at nonsmooth points and the so-called bundle method is used to obtain the optimization search direction in nonsmooth cases. Then, a recursive algorithm based on the idea of bundle method is developed for parameter estimation. After that, the convergence analysis of the algorithm is investigated. Finally, simulation results to validate the proposed method on a simulated mechanical transmission system are presented.
