Decoupling PID Control Design For Multivariable System With Time Delays

With the improvement of contemporary technology, coupling multivariable system widely exists in various fields such as metallurgy, electric power, chemical production. Multivariable systems always contain complex coupling relationship among multi-input multi-output. In recent years, the research of control methods for multivariable systems is getting more and more attention.This article first briefly introduced the basic theory of fractional calculus, by extending the description of integer order to the fractional order system, transfer function expression of fractional order system is obtained. By frequency domain analysis of a typical fractional order transfer function, the Nyquist diagram shows the excellent characteristics of fractional order system is superior to the integer order system.Due to the description of fractional order system is more accurate to the real process than integer order system, this paper introduces the concept of fractional order calculus to the order reduction procedure of complex higher order integer system. Using fractional order system to approximate the original EOTF (Effective Open-loop Transfer Function) achieve better description of the original dynamic characteristics. Based on the fractional order systems, the fractional order controllers can be used to in the design of the multivariable systems’decentralized controller. The simulation results demonstrate the effectiveness of the decentralized fractional controller.For serious coupling involved in multivariable systems, a two-step analytical design method for centralized PI/PID controller based on equivalent model is proposed. Firstly, divide the decoupling function module and controlling module of centralized controller with centain principle. Then, design controllers with control function based on the equivalent model obtained. Finally, get the decoupling controllers through some basic mathematic deduction and the complete centralized controller is obtained.The proposed method could effectively eliminate the interaction between loops. Furthermore, the proposed method can be used conveniently for both square and non-square systems. Simulation results demonstrate the effectiveness of the proposed method.