Modeling and robust control of worm-gear driven systems

Abstract

This paper investigates modeling and control issues associated with worm-gear driven systems. In the modeling part, both static and dynamic analyses are conducted to investigate the characteristics of the worm-gear. The static analysis reveals not only the non-backdrivability but also the dependency of break-in torques on the loading torque, direction of motion as well as crucial system parameters. The dynamic analysis generates four linear equations of motion, of which , at any particular instant, only one applies. The applicable equation at any given instant depends on the direction of motion and the relative magnitude between the input torque and the loading torque. In the control part, a sliding controller is designed based on the modeling results. The controller can provide robustness against variations of system parameters caused by the speed-dependent nature of the coefficient of friction. Because the dependency of the dynamic equation on the operating condition may render the controller ill-defined in some scenarios, a lemma is proved and can be used to select proper control parameters to guarantee the well-definedness of the controller. The proposed control scheme is applied to a worm-gear driven positioning platform. Experimental results indicate the proposed control system achieves 20% of the tracking error of a conventional PID control.