Fractional Order PI~λ Controller Design And Experiment For Level Control System

Fractional order calculus is a subject of ancient and modern. The applications in information science of fractional order calculus are just the rising research in recent years, especially in the system control field, which is a familiar and strange mathematical tool. Fractional order calculus-integral equations could be used to describe the control system of fractional order precisely, and on this basis, one could analyze the dynamic and steady-state performances.In this paper, taking the THJS-1type three tank experiment platform as the engineering background, the theoretical foundation of fractional order calculus, the structure of fractional order control systems, the feature of time-delay systems are discussed. Based on the discussion, using a graphical stability criterion applicable to fractional-order time-delay systems, the stabilizing region and tuning of PIλ controller for first order and second order time-delay systems are studied, the entire region of the controller parameters that meet the requirement is given, which is compared with the effectiveness of the integral order PI controller, and the superiority of fractional order controller is verified. The main works of this dissertation are as follows:(1)According to the three tank experiment device and working principle, we establish the approximate integral order models of single-tank and double-tank, and test the correctness and effectiveness of the models.(2)For the first-order and second-order time-delay systems, the fractional order PI and the integral order PI controllers are designed, and the stabilizing region is determined according to the graphical stability criterion. The stability margin is considered in stabilizing region. Then, selecting the parameters in the stabilizing region, and comparing the control effectiveness with the PI control, the simulations shows that the fractional order controller can ensure a better dynamic performance.(3)With the selected controller parameters, we input them into the experiment equipment, for the level closed-loop control experiment, which verifies that the performance of the fractional order controller is more excellent than the integer order controllers.The innovation of this dissertation is applying a graphical stability criterion to the practical first order and second order time-delay systems. Using the criterion, the parameter stabilizing region of the fractional order PI controller and the design of the system performance are studied, which provides a simple and useful means for fractional order time-delay systems’analyze and design.