Design of the MRAC scheme with PID controllers for robotic manipulators
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A traditional steepest descent MRAC scheme, applied for the two-link manipulator, provides satisfactory tracking only for a certain desired input. The MRAC scheme is inaccurate when the required planned trajectory is complex, for example when both links are maneuvering in the different directions with the high speed. This phenomenon can be explained by strong disturbances caused by interactions between the links. This thesis investigates the proposed steepest descent MRAC with the PID controllers scheme. Stability of the PID-controlled robotic manipulator is investigated and adaptive regulators are derived. The robustness of the control system is increased with the help of the PID controller parameter and MRAC weighting factor optimization. The simplex algorithm and the time-squared weighted performance index is utilized for optimization. The worst trajectory and structure of the two-link manipulator when the disturbances are strongest is introduced. Simulations confirm that the steepest descent MRAC with the PID controller gives good tracking in the presence of any disturbances.