Fractional-order Identification And Controller Design For Nonlinear Systems

One of the most important characteristics of nonlinear systems is that they cannot be analyzed using the principle of superposition,which determines the complexity of the study of such systems.One of the most important problems of nonlinear systems is to determine the mathematical model of the system.Fuzzy neural network has attracted the attention of many scholars because of its characteristics of autonomous learning and rapid search for optimal solutions to problems,and has excellent performance in system identification,which can be seen in biology,chemistry,physics and other fields..Nevertheless,a large number of research data show that fuzzy neural network still has room for improvement in identification speed and model accuracy.In order to obtain a better system model,it is of great significance to study fuzzy neural network.At the same time,the design of the system controller is also a top priority.Considering that the fractional-order PID controller has a good performance in the control field,a suitable controller can improve the stability of the system.Although the fractional-order controller has better performance,it has stricter requirements for the design of its parameters.At the same time,some adaptive algorithms have good advantages in processing optimization problems,so it is of great significance to study the adaptive algorithms of fractional-order controllers.The main work of this paper is as follows:For discrete nonlinear systems,considering the characteristics of high precision and fast identification speed of fuzzy neural network,combined with fractional gradient descent algorithm,a fuzzy neural network model based on fractional gradient descent method is proposed.Using the memory characteristics of fractional calculus,the past information can be used more reasonably and effectively,and more effective parameter iterative formulas can be designed,so as to identify more accurate models.And through simulation experiments,it is verified that the proposed learning algorithm has excellent performance in parameter identification.For complex nonlinear systems,the U model is combined to reduce the complexity of the model.On this basis,considering the fast convergence of the fractional-order PID controller,a fractionalorder PID controller based on the U model is proposed.The mathematical analysis of complex nonlinear systems is difficult,so there are certain difficulties in the design of the controller.The advantage of the U model is that it reduces the complexity of the system and can optimize the nonlinear model into an approximate linear model.The linear model is more Conducive to analysis,so as to design a better controller.At the same time,the introduction of fractional calculus optimization controller can improve the control effect of the controller and make the system converge faster.Through simulation experiments,it is verified that the proposed controller has excellent control effect.For the parameter adjustment of the controller,by considering the advantages of the fuzzy adaptive algorithm and the coyote optimization algorithm in the optimization problem,a fractionalorder PID controller based on the fuzzy algorithm and a fractional-order PID controller based on the coyote optimization algorithm are proposed.The fuzzy adaptive algorithm can modify the parameters of the controller according to the feedback of the error during the operation of the controller,so that the parameters can converge to a better value at a faster speed and improve the effect of the controller.The coyote optimization algorithm is to first optimize the individual coyote within a certain range,and obtain the best individual coyote through continuous iteration,that is,the optimal controller parameters,and further control the system.And through simulation experiments,it is verified that the proposed adaptive algorithm has excellent effect on the selection of controller parameters.