Research And Application Of Design Method Of Fractional PID Controller

With the continuous development and progress of artificial intelligence and control theory,the research and application of fractional calculus in the field of control is also constantly enriched.Because the fractional order PI?D? controller has certain advantages over the traditional controller in terms of system response speed,control accuracy and anti-interference ability,fractional order PI?D? controllers are widely used in aerospace,industrial process control,servo control,and various mechanical control fields.For the design of fractional orderPI?D?controllers for the system,there are many tuning parameters and difficult tuning,etc.Based on the theory of fractional order control theory,this paper studies the design method of fractional order PI?D? controller and applies the fractional order PI?D? controller to the concrete example of permanent magnet synchronous motor.The main research work of this article is as follows:(1)In order to solve the problem that the fractional order PI?D? controller has many controller parameters and is difficult to set in engineering applications,this paper studies the particle swarm optimization algorithm to optimize the controller parameters.In order to solve the problems that the particle swarm optimization algorithm is easy to fall into local optimization and low convergence accuracy,the improved particle swarm optimization algorithm is studied,mainly by adjusting its inertia weight factor to balance the global and local search capabilities.In addition,for the iterative process of the improved particle swarm algorithm,its learning factor will also affect the local and global cognitive ability of the particle,and improper value will affect the search performance and convergence accuracy of the algorithm.This paper further proposes an adaptive parameter adjustment strategy,studies the improved adaptive particle swarm optimization algorithm to optimize the parameters of the fractional order PI?D?controller and derives the adaptive weighting factor and adaptive learning factor to improve the individual optimal search and global optimal search capabilities.Finally,simulation experiments are used to verify that the improved adaptive particle swarm optimization algorithm designed in this paper has small steady-state error and strong anti-interference ability.(2)In order to solve the problem of complicated parameter setting when designing fractional orderPI?D?controllers for high-order systems,this paper adopts internal model control strategy in controller design to design fractional order internal model PI?D? controllers.Firstly,the model of higher-order system is reduced by improving the adaptive particle swarm optimization algorithm,and then a controller with unique adjustable parameters is designed based on the internal model control idea.The parameter expression of the controller is given according to the maximum sensitivity method,and finally the simulation experiment is performed to verify.The results show that the fractional-order internal model PI?D? controller designed for higher-order systems can reduce the complexity of its parameter setting and make it have good control performance and robustness.(3)Based on the design of the fractional order PI?D? controller in this paper,the application of the fractional order PI?D? controller to the permanent magnet synchronous motor is studied.The design of the fractional order PI?D? controller is mainly aimed at the speed loop of the motor,and the control performance is compared with the integer order PId controller through simulation experiments.The results show that the fractional order PI?D?controller designed in this paper can improve the control performance of permanent magnet synchronous motors under no-load,sudden load and sudden changes of speed.