For fractional order PID controller, a parameter tuning method based on particle swarm optimization is presented.
Firstly, the initial three parameters Kp, Ki and Kd are roughly determined by the engineering tuning method (critical scale method); secondly, the optimal parameters of PID controller are obtained by using particle swarm optimization algorithm; finally, the response curve of the system is given by simulating the PID parameter optimization system with SIMULINK software.
As the earliest practical controllers, PID (proportion), integration and differentiation) controllers have a history of nearly 100 years, and are still the most widely used industrial controllers. PID controller is easy to understand and widely used in life. The level of industrial automation has become the primary way to measure the level of modernization.
After three stages of classical, modern and intelligent control theory, the development of control theory has gradually matured. The control system includes a controller, a sensor, a transmitter, an actuator and an input-output interface. The output of the controller is added to the controlled system through the output interface and the executing mechanism, and the controlled quantity of the control system is sent to the controller through the input interface through sensors and transmitters. Different control systems have different sensors, transmitters and actuators.
Group behavior is the possession of all living organisms in nature, thermostatic element and one of the main research fields of artificial life is to explore the group behavior of natural organisms, so as to construct its group model on computer. Scientists have been devoting themselves to the study of the swarm behavior of birds and fish. Craig Reynolds, a biologist, proposed a very influential swarm aggregation model in 1987.
Particle swarm optimization (PSO) is a new swarm intelligence optimization algorithm, which originates from the study of the swarm behavior of birds and fish. It is a new branch of evolutionary computing.
Its main characteristics are simple principle, fewer parameters, fast convergence speed and less knowledge in the field. The algorithm has attracted the attention of many scholars, and has been widely used in function optimization, neural network training, combinatorial optimization, robot field, and achieved good results.
Fractional-order PID, which is based on the traditional PID, introduces the idea of fractional-order, and is a subject worthy of study [4,5]. Because the fractional order PID controller has two adjustable parameters (integral order lambda and differential order mu) on the basis of the traditional PID controller, it can control the controlled object more flexibly and achieve good control effect and robust performance.
For the traditional PID, it is the adjustment of parameters, but for the fractional order PID, it is also the adjustment of parameters, only two more parameters, which can overcome the non-linearity of PID control, the complexity of time-varying uncertainties of parameters and the difficulty of establishing accurate mathematical models [6,7]. However, the application of fractional order PID controller can effectively adjust the above problems and make the system more perfect. Fig. 1 shows the principle block diagram of fractional order PID control system, which consists of analog fractional order PID controller and controlled object.
The closed-loop control system of fractional order PID controller is shown in Figure 1. The controller is mainly a feedback and closed-loop control system composed of fractional order PID and controlled object model. According to the error E (t) between the given input value Input and the actual output value Output, the fractional order PID controller controls the plant of the controlled object model by controlling the error nonlinearity to form the control quantity u (t), so as to achieve the desired output. Among them, Kp is the proportional coefficient, Ki is the integral time constant, Kd is the differential time constant, lambda > 0 is the integral number, and Mu > 0 is the differential number. If the end condition is reached (a good enough solution or the maximum number of iterations), then the end is achieved, otherwise the step is changed. The flow chart of PSO is shown in Figure 2. Simlink in MATLAB is used to simulate integer-order PID model and fractional-order PID model.
The results are shown in Figures 3 and 4, respectively.
From the following figure, it can be seen that the fractional order PID control effect based on particle swarm optimization is obviously better than the integer order PID control effect. Firstly, the basic control principle of fractional order PID controller is given. Secondly, the parameter tuning method based on particle swarm optimization is given. Particle swarm optimization is used to optimize the parameters of fractional order PID controller, and the optimal parameters of PID controller are obtained. Finally, the integer order and fractional order PID parameter optimization system are simulated by SIMULINK software, which shows that the fractional order PID control effect is obviously better than the integer order PID.