Tuning the PID parameters for robot manipulators with compliant bases by using grey theory

This research focuses on the issue of dynamic modeling and controlling a robotic manipulator attached to a compliant base. Such a system is known under the name macro-micro system, characterized by the number of control actuators being less than the number of state variables. The motion of equations for a two-link planar elbow arm mounted on an oscillatory base has presented in this investigation. In order to study the sensitivity of tuning the PID parameters to achieve the desired performance, the grey relational analysis has been proposed. Therefore, the optimization parameters of the output feedback PID controller by using grey theory have first investigated for such structure in this research. The experimental results of the proposed methodology also show that it is technically and economically feasible to develop a low-cost, reliable automatic, less time consuming controller for robots mounted on oscillatory bases