Analysis of Nonlinear Control Systems

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 PIλDμ controller for tracking control purpose. According to the obtained results, the fractional-order PIλDμ 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 PI λDμ 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.

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

As the demand increases for machines of high accuracy, high speed, and high stiffness, programmable closed-loop linkages emerge in the development of modern machinery. A mechatronic design methodology is proposed for the integrated design of mechanical structure and control algorithm for a programmable closed-loop mechanism system. This design methodology suggests a negative mass-redistribution scheme, which follows the principle of a shaking force/shaking moment balancing scheme, for the modification of an existing four-bar mechanism, with the aim to obtain a simple system dynamic model and, thus, to facilitate controller design. In consequence, motion tracking performance and vibration behavior of the linkage system are significantly improved by simply applying a conventional PD control algorithm. The effectiveness of the proposed methodology has been verified by simulation studies.

Integrated design of mechanical structure and control algorithm for a programmable four-bar linkage

The performance of an electromechanical system not only depends on its controller design, but also on the design of its mechanical structure. In order to achieve the excellent performance of the four-bar-link mechanism byemploying the simple PD control, we redesign the structure of the four-bar-link mechanism by a mass-redistribution scheme to simplify the dynamic model. Theoretically, we analyze the stability of the closed-loop system consisting of the PD controller and several kinds of four-bar-link mechanisms, and discuss the relations between the performance of the PD controller and its gains and the mechanical design. The obtained results show that the performance of the PD controller may be significantly improved by using the methodology of Design For Control (DFC). The effectiveness of the proposed methodology has also been verified by some simulation studies.

Jian Tao

Papers

Constant speed control of a motor driven mechanism system