Fractional-order PI~λD~μ Controller Design And Fealization

Fractional-order calculus is the theory of arbitrary differential-order and integral-order and the generalization of the integer-order calculus theory. Although it is an old topic in the field of mathematical research, however, it is an emerging research in modern control science. Fractional-order systems can be described by fractional-order differential equations more accurately. Through the establishment of the fractional-order mathematical model and the design of fractional-order controller, the control system can achieve better control effect. At present, under the efforts of many scholars and engineers, the study of the fractional-order PIλDμ controller has developed significantly.In this paper, taking the water tank model as an engineering background, we introduce the theoretical foundation of fractional-order calculus, the structure of the fractional-order PIλDμ control systems, the graphical tuning of PIλDμ controller, the digital controller design of the computer control system as well as the fractional calculus dieselization, verify the superiority of the fractional PIλDμ controller over the integral PID controller by experiment. The main works of this paper are the following.(1) According to the THJSK-1 type tanks integrated control system hardware and software environment, using the equipment working principle, we establish the mathematical model of the water tank, and verify the accuracy and validity of the model through MATLAB simulation.(2) For the tank model established, applying a graphical stability criterion fit for fractional-order system, we determine the stabilizing regions of the factional-order PIλDμ controller in integral-gain and derivative-gain plane, and we also draw the stabilizing regions in the three-dimensional space of proportional-gain, integral-gain and derivative-gain. Then, in the stabilizing region, we design the gain margin, the phase margin, the relative stability and the optimization of the stabilizing region with respect to parameters λ and μ. The simulation results show that the factional-order PIλDμ controller parameters selection through the above procedure can achieve better control performances.(3) Through designing the digital controller, discrediting the fractional-order PIλDμ controller and programming the control algorithm, we use the MCGS software to validate the control effect. The result shows that the dynamic performance with fractional-order PIλDμ controller is better than that with the integer-order controller, and thus, we prove the feasibility of the application of fractional-order PIλDμ controller to the practical control systems.