Maneuver control and active vibration suppression of a two-link flexible arm using a hybrid variable structure/Lyapunov control design

This paper deals with maneuver control and vibration suppression of a two-link flexible arm with embedded smart materials. First, by using extended Hamilton’s principle and assumed mode method, equations of motion of the two-link flexible arm with PZT patches as sensor and actuator are obtained. Inspecting the resulting equations reveals that the dynamics of the flexible structure that encompasses the vibrations of the links and their rigid in-plane maneuver takes place in two different time scales. Consistent with this characteristic, a slow subsystem associated with rigid motion dynamics and a fast subsystem associated with link flexible dynamics are identified by using the singular perturbation theory. Then, a hybrid controller is proposed as a combination of two distinct controllers for these subsystems and their stability is studied using the Lyapunov approach. The controller consists of a variable structure control (VSC) for maneuvering control of the slow subsystem and a Lyapunov based controller for vibration suppression of the flexible structure. According to the numerical simulation results it can be concluded that the proposed hybrid controller has a suitable and efficient performance for maneuver control and suppressing the transverse vibrations of the structure.