Design Of Fractional Order PI~λD~μ Controller For Multivariable System

Multivariable systems are often encountered in industrial practice. The research on multivariable control system has been a hotspot and a difficult spot in the field of process control. At the same time, with the higher request of system stability, anti-jamming, robustness and control performance, the research on multivariable system control theory and method is very significant to improve the system control performance.The application of fractional order PIλDμcontrollers is a new field and a new research hotspot in control system. So it is wery meanful and valuable for multivariable system to research how to design fractional order PIλDμcontrollers.The design method and design theory of fractional order PIλDμcontroller is researched deeply in this paper. The z domain discretization methods are analyzed in this paper. Three kinds of program based on z domain discretization methods are wrote with the use of Matlab. The advantages and disadvantages of these methods are given by simulation analysis. It is a theoretical foundation for the design and application of fractional order controllers. The parameters setting method of fractional order PIλDμcontroller based on Particle Swarm Optimization (PSO) is proposed in this paper. Compared with other methods, this method has high search capability in the earlier stage and high development ability to accelerate the convergent rate in the later stage. Apart form the characters analysis of the fractional order controller, the influence of fractional order PIλDμcontroller parameters on the performance of closed-loop control system is also researched. In addition, the robust stability check problem of fractional order PIλDμcontroller for uncertain variable systems is solved by boundaries of eigen-clusters. This method is proved to be practical and effective. The design method of decentralized controllers for multivariable system is researched in this paper and the simulation results are analyzed. Based on the fixed calculus orders of the fractional order PIλDμcontrollers, we obtain fractional order PIλDμcontrollers for multivariable system with using improved genetic algorithm. The overall performance of multivariable system is optimal with using these controllers. From the sinulation analysis, better performance can be obtained with using PIλDμcontrollers based on improved genetic algorithm.The design theory of fractional order PIλDμcontrollers is fundamental to the design of fractional order PIλDμcontrollers in industrial process. It is important for the development and application of control theory.