Fuzzy modelling and robust control with applications to robotic manipulators

In this thesis, fuzzy modelling of a class of nonlinear systems has been investigated based on fuzzy logic and linear feedback control theory, and a few robust variable structure control schemes for nonlinear systems have been developed. A number of robustness and convergence results with dramatically reduced control chattering are presented for variable structure control systems with applications to robotic manipulators in the presence of parameter variations and external disturbances. The major outcomes of the work described in this thesis are summarised as follows. A robust tracking control scheme is proposed for a class of nonlinear systems with fuzzy model. It is shown that a nominal system model for a nonlinear system is established by fuzzy synthesis of a set of linearised local subsystems, where the conventional linear feedback control technique is used to design a feedback controller for the fuzzy nominal system. A variable structure compensator is then designed to eliminate the effects of the approximation error and system uncertainties. Strong robustness with respect to large system uncertainties and asymptotic convergence of the output tracking error are obtained. A sliding mode control scheme using fuzzy logic and Lyapunov stability theory has been proposed. It is shown that a sliding mode is first designed to describe the desired system dynamics for the controlled system. A set of fuzzy rules are then used to adjust the controller's parameters based on the Lyapunov function and its time derivative. The desired system dynamics are then obtained in the sliding mode. The sliding mode controllers with fuzzy tuning algorithm show the advantage of reducing the chattering of the control signals, compared with the conventional sliding mode controllers. A robust continuous sliding mode control scheme for linear systems with uncertainties has been presented. The controller consists of three components: equivalent control, continuous reaching mode control and robust control. It retains the positive properties of sliding mode control but without the disadvantage of control chattering. The proposed control scheme has been applied to the tracking control of a one-link robotic manipulator with fuzzy modelling of the nonlinear system. A robust adaptive sliding mode control scheme with fuzzy tuning has been presented. It is shown that an adaptive sliding mode control is first designed to learn the system parameters with bounded system uncertainties and external disturbances. A set of fuzzy rules are then used to adjust the controller's uncertainty bound based on the Lyapunov function and its time derivative. The robust adaptive sliding mode controller with fuzzy tuning algorithm show the advantage of reducing the chattering and the amplitude of the control signals, compared with the adaptive sliding mode controller without fuzzy tuning. Experimental example for a five-bar robot arm is given in support of the proposed control scheme. Finally, a new adaptive sliding mode controller has been developed for trajectory tracking in robotic manipulators. This controller is able to estimate the constant part of the system parameters as well as adaptively learn the uncertain part of the system parameters by the Gaussian neural network. It is shown that under a mild assumption, the proposed control law does not require measurement of acceleration signals. This new control law exhibits the good aspects of Slotine and Li's (1987) and keeps the chattering to a minimum level. An experiment of a five bar robotic system was done and the results have confirmed the effectiveness of the approach.