Design And Application Of Fractional Order Model Reference Adaptive Controller Based On Hyperstability Theory

Model Reference Adaptive Controller(MRAC)is widely used in the engineering practice.So it's of theoretical and practical significance to extend the control strategy to the field of fractional calculus for better performance.According to the problems existing in present.design methods of fractional order MRAC,such as non-steady,limited range of application and complex control strategy,a particular design method of fractional order MRAC based on Popov hyperstability is given in this paper and applied in a class of nonlinear system through a transformation method of Nonlinear Feedforward/State Feedback(FF/FB).At the same time,the study is applied to the thermal management system of Proton Exchange Membrane Fuel Cell(PEMFC).Firstly,based on the theory of Popov hyperstability and the properties of fractional calculus,it's demonstrated that model reference adaptive control system would satisfy the hyperstability theorem if the integral order of control law changed.Also,The design method of fractional order MRAC similar to integer order's is given,which is using the state variable or input and output signals of system.Secondly,the FF/FB transformation method is proposed by classifying the disturbance using relative order concept of differential geometry theory,which is effective for linearization of a class of MIMO nonlinear system with measurable disturbance.Thereby,the scope of applying fractional order MRAC is expanded.Thirdly,a temperature model of PEMFC thermal management system is built by analyzing the 5kW water cooled PEMFC power generation system,and linearized through FF/FB transformation method.Also,in order to meet the requirements of the accuracy and robustness of the temperature control,a fractional order MRAC of the thermal management system is given.The dynamic performance and anti-interference ability of the control system is improved.