Research On Designing Of Fractional-order TI~?D~? Controller Based On The Method Of Internal Model Control

Fractional-order control theory is a new studying field that combines Fractional order calculus with the traditional control theory.The main advantages over the traditional control theory,the fractional-order calculus can be more delicate to portray complex system and more accurate to describe the characteristic of system properties.Fractional-order controllers are used to instead of the traditional integer controllers can obtain better control performance.Internal model control is a control strategy among the fixed model based control schemes.System disturbance and parameters uncertainty problem can be overcome with this control strategy.Researchers have found that large and complex calculation can be overcome when internal model control is introduced to the parameter tuning of fractional order controller,and this combination can improve the system control quality.Fractional calculus operator numerical implementation is the basis of the fractional-order system.Now,most researchers use Oustaloup indirect discretization to fit the fractional order operators,but when using Oustaloup algorithm to fit the fractional order operators would make relatively large error at the two-stage of the frequency range.In this paper two problems are researched deeply.One is that brings the IMC strategy into the parameters tuning of fractional order controller,the proposed scheme can overcome the complex of parameters tuning of fractional order controller,and also can improve the system control quality.Two is that in order to improve the accuracy of rational approximation for the fractional order operators,Oustaloup algorithm is used to seek better coefficients of transfer function of rational approximation with CPSO algorithm.This paper is organized as follows:(1)A design method of Internal Model TI?D?(IMC-TI?D?)controller is proposed for a kind of Integer-order system and Fractional-order system respectively.Firstly,the original Fractional-order model is approximated to the second-Fractional-order delay time model,then the method of Internal Model control is introduced to the approximate model,and the IMC control Gc(s)is designed.Finally,comparing the Gc(s)with TI?D? controller,we can find the correspondence between parameters,then we can get the parameters of TI?D? controller.The advantage of IMC is brought into the designing of Fractional-order controller,achieving the rapid parameter tuning of the Fractional-order controller,and the control quality of the whole system is improved.Simulation results show the proposed controller(TI?D?)controller has good control quality and robustness.(2)For fractional calculus operators with the feature of infinite dimensional,which is unable to realize the value directly,the optimization problem of the rational approximation function is discussed in this paper.Oustaloup algorithm is used for fractional operators to obtain rational approximation function,then the structure of the rational transfer function is determined.CPSO algorithm is used to seek for optimal coefficients of the transfer function in order to improve the accuracy of the rational function approximation for fractional operators.Lastly.the simulation results show that using the proposed method can get more accuracy of the rational function approximation for fractional operators.(3)In order to further verify the effectiveness and practicality of the improved Oustaloup algorithm,the designed TI?D? controller is realized its value with the improved Oustaloup and Oustaloup algorithm respectively.By further comparison,Fractional internal model TI?D? controller can obtain better dynamic characteristic with the improved Oustaloup algorithm.