Research On Dynamic Matrix Control Algorithm For Fractional Order Systems

The fractional order calculus is a generalization of the order of calculus from the conventional integer domain to the real number field and even the complex range.Most dynamic systems in practice are of fractional order and the integer order differential equation model can only describe part of dynamic characteristics of the control system.However,the inherent characteristics of these systems can be characterized by the fractional order differential equations more precisely because of the number of arbitrary orders and the distinctive memory feature of fractional order calculus.So it is of great theoretical significance and engineering value to study the control problem of fractional order system.As a representative algorithm in the predictive control,there are low requirements for the model,strong robustness,simple processing delay in dynamic matrix control(DMC),and it is suitable in the process with large time delay and strong coupling,also in which cannot establish accurate mathematical model.However,there are some limitations in this method,such as the enormous online computation,the sampling period which should not be too small and so on,which makes it difficult to achieve the desired control effect in the control system with uncertainty in the model order,environmental disturbance and nonlinear etc..In this paper,the traditional dynamic matrix control method is improved,and it is applied to the control of fractional order system.The main work of this thesis can be divided into three parts:the first part serves as an introduction to two kinds of improved dynamic matrix control methods and compares them with the traditional dynamic matrix control in the simulation examples of stable gasoline vapor pressure control,which shows the advantages of the improved DMC method based on the PID control structure on the overall performance.In the second part,the PID-type dynamic matrix control method is applied in a class of single input and single output fractional order linear systems,and the control performance of the method is verified by the simulation examples of the temperature control of the heating furnace.The last part is that since the PID-type dynamic matrix control is introduced to the distributed control structure,an improved distributed dynamic matrix control method is obtained considering a class of multivariable fractional order systems.And it is utilized in the control of a class of multivariable fractional order systems.Finally,the feasibility and effectiveness of the proposed method are verified by MATLAB simulation.