Output Feedback Finite-dimensional Repetitive Learning Control on Virtual Force for Flexible-base Flexible-link and Flexible-joint Space Robot

Motion control and flexible vibration synchronous suppression of base, links and joints for flexible space robot are studied. By combining linear spring, torsion spring, simply supported beam and hypothetical modal method, and using Lagrange equation, the dynamic model of flexible-base, flexible-link and flexible-joint space robot is established. Then, by using singular perturbation method, the model is decomposed into a joint motion slow subsystem and joint flexible vibration fast subsystem. In order to control the rigid motion of the base and joints in the slow subsystem and suppress flexible vibration of links, according to the concept of virtual control force, an output feedback repetitive learning algorithm based on the finite-dimensional Fourier series analytical periodic signal is proposed. The algorithm uses virtual force to suppress the flexible vibration of the robotic links. The output feedback method is designed so that the controller can be implemented based on position measurement only. It is proposed that the repetitive learning algorithm can effectively compensate for repeated errors in periodic tasks and improve the control quality of the system. The Lyapunov direct method confirms the stability of the above controller. In addition, in order to suppress the flexible vibration of the base and joint in the fast subsystem, the linear quadratic optimal control method and the joint flexible compensator are used to indirectly increase the joint equivalent stiffness, so that the control algorithm cannot be limited to solving the weak nonlinear problem. Simulation results show that the proposed controller can effectively suppress the vibration of multiple flexible components of the system, and achieve high-quality tracking of the desired signal.