Abstract

Control of under-actuated mechanical systems (robots) represents an important class of control problem. This thesis studies several related control problems associated with an under-actuated robot, Pendubot, from the point view of fuzzy logic control. To swing up the Pendubot from a rest position to the upright configuration, a fuzzy algorithm is proposed from non-complete sets of linguistic rules that link some mechanism states to the sign of a single control action. Therein, a simplified Tsukamoto's reasoning method and quasi-linear-mean aggregating operators are used to derive and analyze the controller input-out mappings. In order to balance the Pendubot at the unstable upright top configuration after swinging up, another simple fuzzy controller is derived according to its joint states: This combining fuzzy algorithm for swinging-up and balancing is successfully applied to the Pendubot. This thesis also investigates the case that the Pendubot tracks a desired signal and a corresponding fuzzy scheme is proposed, which combines the linear regulator theory with the Takagi-Sugeno fuzzy methodology. The stability and stability conditions for this fuzzy scheme are analyzed. Numerical simulations for all the above controllers are carried out to validate the theoretical analysis by using SIMULINK. Finally, the hardware experiments in the Pendubot have successfully been conducted in the Robotics and Mechatronics Laboratory.