The Inverted Decoupling Based Fractional Order Multiple-input-multiple-output Internal Model Control

In recent years,the appearance of modeling problems in complex physics,mechanics,biology and engineering has made integer order models no longer applicable.However,fractional order models will show more characteristics when it is used to describe the system.For now,researches on fractional order system control have obtained a lot of results.However,most of the fractional order controller design methods focus on single-input-single-output processes.As we all know,most of the actual process is multiple-input-multiple-output system.It is necessary and meaningful to study the control method of fractional order multiple-input-multiple-output system.In this paper,a fractional order IMC controller with inverted decoupling is proposed to handle non-integer order multiple-input-multiple-output system with time delay.This thesis includes the following main innovations:1.For integer order multiple-input-multiple-output system,there are three decoupling method:ideal decoupling,simplified decoupling,inverted decoupling.Ideal decoupling is to construct a decoupling matrix to make the generalized transfer function matrix ideal.Simplified decoupling is to construct a simplified decoupling matrix to make the off-diagonal elements of the generalized transfer function matrix 0.Inverted decoupling has special structure which makes the generalized transfer function matrix and the decoupling matrix simplified.According to the three methods,based on fractional order multiple-input-multiple-output system,we derived the expression of the decoupler.And the realizability of the decoupler has been discussed.2.Based on fractional order multiple-input-multiple-output time delay system,this paper combines multivariable internal model control methods with fractional multivariable systems and proposed a fractional order IMC controller with inverted decoupling to handle non-integer order multiple-input-multiple-output system with time delay.The Maximum sensitivity function is used to tune the parameters.Simulation results show the proposed controller provides ideal performance for both set point-tracking and disturbance rejection.3.Based on fractional order multiple-input-multiple-output time delay system and the proposed method,we deduced the general conditions of the stability of the closed-loop system.