Research On Advanced Control Strategies For Fractional Order System And Application

With the growing demand for quality control of engineering more and morestrict, Inorder to obtain more accurate control effect, Mathematical model of the industrial systemdescribes needs to be more accurately. Currently, Industrial systems use integer-ordermodel to describe. But this only partially reflects the characteristics of the system, cannot achieve the desired accuracy. As for the use of fractional-order systems described,order by way of a weighted fractional calculus contains the whole characteristic functioneffectively improve the way people describe the system features precision. In recentyears, Fractional theory is gaining more and more attention, and effectively applied toindustrial control systems, physical systems, bio-engineering and other fields. Fractionalcalculus has the following advantages:(1)Fractional derivatives have global relevance, beable to describe the function of the system changes during the entire time, but the integerorder partial derivatives only reflects the characteristics of the system;(2)Fractionaldescribed system effectively avoids the integer-order system consistent with thetheoretical model problem of inaccurate;(3)Compared to the non-linear system model,fractional calculus has more concise presentation, and clearer physical meaning whiledescribing complex engineering problems.For fractional-order systems control problems, studies show that compared to theinteger order controller, fractional controller system can obtain a more satisfactorycontrol precision. But Fractional controller structure is complex, multi-controllerparameters, parameter tuning becomes more difficult, currently only in the research stage,there is no uniform method. To solve this problem, this paper on the basis of a detailedstudy of the fractional-order system features advanced control method is proposedfractional-order systems, the main work done in this article include:(1) In the paper, the development, the basic content and the features of fractional theoryare described in detail. In addition, the fractional characteristics, exhibited betweenmechanics and actual engineering systems, are expounded combined with the actual.(2) Dynamic matrix control algorithm is a predictive control method based on the stepresponse of the system, which has no fixed requirements to the form of specificmathematical model of the system, just needs the step response of the system. In thispaper, the DMC algorithm is applied to the fractional control system. On the one hand,the parameter tuning of PIλDμcontroller is simplified. On the other hand, the stepresponse coefficients of fractional systems are obtained in a method, as in which the stepresponse coefficients of integer order system are obtained. Finally, the performance of theDMC algorithm in the fractional system is verified though simulating the system.(3) Internal model control(IMC) algorithm is a method to design the controller based on system model. In the paper, the design and parameters tuning method of PIλDμcontrollerapplying the IMC principle for several typical fractional thermodynamic processes areresearched based on a detailed understanding of the IMC principle. By using the IMCalgorithm, the PIλDμcontroller parameters are simply, to solute well the issue of tuningPIλDμcontrol parameter difficultly. Simulation results show that fractional system can becontrolled effectively by PIλDμcontroller designed by IMC algorithm.(4)In order to solve the problem in the fractional system of taking into account twoaspects, set points tracking and disturbance rejection, in the paper, the design methodsuitable for fractional systems of two-degree-freedom fractional-order internal modelcontrol algorithm is given. The controller designed in this method has only twoadjustable parameters. By adjusting the controllers parameters, the system can obtain theideal setpoint tracking features, characteristics and robustness to interference, to makeup for fractional internal model controller design deficiencies.(5) H2performance control system design allows the system to get a good dynamic andstatic characteristics, H∞performance design can solve the problem of the robustness ofthe system effectively. In this paper, the performances of the H2and H∞design areexpanded to the fractional system, and the PIλDμcontroller parameter tuning method areproposed, which is based on H2/H∞fractional hybrid optimization system. Simulationexperiments show that the fractional PIλDμcontroller which is optimized by this methodcan achieve the desired requirements to track setpoint tracking capability,anti-interference capability and robustness properties.