Discrete-time repetitive optimal control: Robotic manipulators

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This paper proposes a discrete-time repetitive optimal control of electrically driven robotic manipulators using an uncertainty estimator. The proposed control method can be used for performing repetitive motion, which covers many industrial applications of robotic manipulators. This kind of control law is in the class of torque-based control in which the joint torques are generated by permanent magnet dc motors in the current mode. The motor current is regulated using a proportional-integral controller. The novelty of this paper is a modification in using the discrete-time linear quadratic control for the robot manipulator, which is a nonlinear uncertain system. For this purpose, a novel discrete linear time-variant model is introduced for the robotic system. Then, a time-delay uncertainty estimator is added to the discrete-time linear quadratic control to compensate the nonlinearity and uncertainty associated with the model. The proposed control approach is verified by stability analysis. Simulation results show the superiority of the proposed discrete-time repetitive optimal control over the discrete-time linear quadratic control.