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 equations of motion for a two-link planar elbow arm mounted on an oscillatory base has been 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 first been proposed. Therefore, the aim of this work is to apply Grey theory to optimize parameters for partial states feedback of a PID controller for such a structure. 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 robotics mounted on oscillatory bases.
