α-β Fractional Order Pi Controller Design And Experiment

The theory of fractional order calculus can be traced back to300years ago, it takes calculus order to fractional even complex, extends the description ability of the well known integer calculus. With the in-depth understanding of fractional order calculus and the development of computer technology, the fractional calculus has been widely used in many fields. In recent years, the fractional order calculus and applications have become a more popular research interest in control community; more and more scholars begin to study in this field and have obtained certain achievements.In this dissertation, taking the THJS-1type three tank experiment platform as the engineering background, we introduce the basic theory of fractional order calculus, the structure and properties of fractional order control system, a-(3fractional order PI controller, the graphical tuning of α-β fractional order PI controller, the digital controller design of the computer control system as well as the fractional calculus dieselization, and verify the superiority of a-P fractional order PI controller over the conventional fractional order PI controller by experiment. The main works of this dissertation are as follows:(1) According to the THJS-1type water tank experiment equipment and working principle, we establish the mathematical model of the water tank, and through the MATLAB simulation software to verify the accuracy and effectiveness of the model.(2) In view of the established model of the water tank, using graphical stability criterion which can be applied to the fractional order system, we study the stability region of α-β fractional order PI controller, and discuss the influence of parameter α,β on the shape and size of the stabilizing region. Then, in the stabilizing region, we design the gain margin and the phase margin. The simulation results show that through the above design choices of α-β fractional order PI controller parameters the designed controller can obtain better dynamic performance compared with the traditional fractional order parameters of PI controller.(3) Through designing the digital controller, discrediting the α-β fractional order PI controller and programming the control algorithm, we put the control algorithm and controller parameters of the selected to experiment equipment. The water tank experiment proves that the α-β fractional order control performance of PI controller is superior to the fractional order control performance of PI controller.The innovation of this dissertation is that it adds an adjustable parameter on the basis of the original fractional order PI controller and obtains a new α-β fractional order PI controller. Graphical stability criterion is used to study the stability domain of α-β fractional order PI controller parameters and performance design of the system. The use of MATLAB simulation and water tank experiment verify that the controller has advantages in control performances.