Robust adaptive control and applications to friction and backlash compensation

In this dissertation two common problems that arise in servo-mechanical applications are addressed. The problems of friction and backlash are especially evident when gears are used. In the first part of the dissertation, a nonlinear robust adaptive controller is proposed for friction compensation. The design has been performed for a six parameter dynamic model of friction. The advocated control design does not utilize any knowledge of these six parameters and requires just an upper bound on the static friction level, which can be easily obtained experimentally. Furthermore, the controller is robust to dynamic uncertainties in the friction model. Therefore, a robust cancellation of friction effects is achieved. The results are further extended to the case where drive compliance is present and friction is present both on the motor and the load side. This is a challenging problem that arises in many applications. In this case, the controller is robust to dynamic uncertainties and can compensate the effects of friction which is separated from the control input through drive compliance. Results of extensive simulation and experimental studies highlight the efficacy of the proposed scheme.; In the second part of the dissertation, an adaptive nonlinear controller is proposed to control systems with backlash. A similar solution is utilized to solve the problem of backlash when it occurs at the input of a plant as an actuator nonlinearity. A new model for backlash inverse is developed and used in conjunction with a PD-controller in order to minimize the effect of backlash. The backlash inverse model is a compact dynamical model and is simpler to implement than existing schemes (1-3). The backlash parameter is assumed to be unknown and an adaptive update law estimates its value. The stability of the closed-loop system is shown using Lyapunov arguments. Simulation results show that the control methodology greatly improves tracking performance over a PD type controller.; In the third part of the dissertation, the combined effects of friction and backlash on systems are considered. A variable structure controller in conjunction with an adaptive backlash inverse is used to reduce the effect of friction and output backlash. In the case of input backlash, a variable structure controller is shown to achieve global asymptotic tracking and regulation. Simulations of a second-order system with friction and backlash are presented.