Trajectory Tracking Control for a 3-DOF Parallel Manipulator Using Fractional-Order $hbox{PI}^{lambda}hbox{D}^{mu}$ Control

摘要

In this paper, a 3-degrees-of-freedom parallel manipulator developed by Tsai and Stamper known as the Maryland manipulator is considered. In order to provide dynamic analysis, three different sequential trajectories are taken into account. Two different control approaches such as the classical proportional–integral–derivative (PID) and fractional-order PID control are used to improve the tracking performance of the examined manipulator. Parameters of the controllers are determined by using pattern search algorithm and mathematical methods for the classical PID and fractional-order PID controllers, respectively. Design procedures for both controllers are given in detail. Finally, the corresponding results are compared. Performance analysis for both of the proposed controllers is confirmed by simulation results. It is observed that not only transient but also steady-state error values have been reduced with the aid of the $hbox{PI}^{lambda}hbox{D}^{mu}$ controller for tracking control purpose. According to the obtained results, the fractional-order $hbox{PI}^{lambda}hbox{D}^{mu}$ controller is more powerful than the optimally tuned PID for the Maryland manipulator tracking control. The main contribution of this paper is to determine the control action with the aid of the fractional-order $hbox{PI}^{ lambda}hbox{D}^{mu}$ controller different from previously defined controller structures. The determination of correct and accurate control action has great importance when high speed, high acceleration, and high accuracy needed for the trajectory tracking control of parallel mechanisms present unique challenges.