Abstract: A BP neural network is used to adjust the three parameters of a PID controller online, and a GRNN neural network is used as an identifier to identify the sensitivity information of the control output to changes in the control input object online, thereby improving the control accuracy of the system. A MATLAB program is then developed for simulation. The algorithm is tested by simulation, and the results show that it has good control effect and strong robustness. Keywords: BP neural network, GRNN neural network, PID 1 Introduction In industrial control, traditional PID control still dominates, especially for deterministic control systems where mathematical models can be established. However, many industrial processes often have nonlinear, time-varying, and uncertain factors, making it difficult to establish accurate mathematical models. In addition, the parameters in the PID controller are usually manually tuned, and since these parameters obtained by one-time tuning are difficult to guarantee that the control effect is always optimal, the control effect and control accuracy of conventional PID controllers are limited. Neural networks have advantages such as self-learning, self-organizing functions, associative memory, and parallel processing, making them widely used in complex industrial control [1,2]. Currently, the most widely used neural network is the multilayer feedforward neural network based on the BP algorithm. This type of network reflects the static input-output mapping relationship of the system. Reference [3] proposes a control system based on a diagonal recurrent neural network (DRNN). Compared with static networks, this recurrent network has a better ability to handle dynamic problems. Since it only requires fewer neurons and weights, the recurrent network is more suitable for handling time-varying input and output processes [4]. Based on the above characteristics of the recurrent neural network, this paper uses the DRNN network to design a PID controller whose proportional, integral, and derivative parameters can be learned online, and applies it to the heating control system in daily life. A control simulation based on the MATLAB environment is established. 2 PID algorithm based on BP neural network control The PID parameters kp, ki, and kd are adjusted online using a multi-layer feedforward neural network-BP network, as shown in Figure 1. In order to fully reflect the characteristics of the input controller signal, combined with the controller structure, the number of neurons in the input layer of the network is selected as 4, and the number of neurons in the output layer is 3. The activation function of the output layer neurons is: g(x) = . The activation function of the hidden layer neurons is: f(x) = . The input of the network input layer is: O[sub]j[/sub]（1）=x（j）,1,2,3,4. The input and output of the hidden layer are net[sub]i[/sub]（2）（k）=,…8. In the formula, w[sub]ij[/sub]（2） is the weighting coefficient of the hidden layer; the activation function of the hidden layer neuron is f(x)=. The input and output of the network output layer are: net[sub]l[/sub]（3）（k）= In the formula, w[sub]li[/sub]（3） is the weighting coefficient of the output layer. The superscripts (1), (2), and (3) in the above formulas represent the input layer, hidden layer, and output layer, respectively. The activation function of the output layer neuron is g(x)=. The performance index function is e(k)=1/2error[sup]2[/sup]（k）. The network weight coefficients are corrected by gradient descent, and an inertia term is added to make the search quickly converge to the global minimum: is the learning rate; is the inertia coefficient. Since the unknown is used, the sign function sgn() is used as an approximation. The resulting inaccuracy in calculation can be compensated for by adjusting the learning rate. From the above introduction, the incremental equation of PID is as follows: u(k) = u(k-1) + kp(e(k) - e(k-1)) + kie(k) + kd(e(k) - 2e(k-1) + e(k-2)). From this, we can obtain: The learning algorithm for the weights of the network output layer is: l = 1, 2, 3, 4. Similarly, the learning algorithm for the weights of the hidden layer is: i = 1, 2, ..., q. [align=center] Figure 1 Control System Structure Diagram[/align] 3 DRNN Recognition Network The DRNN neural network is a type of regression neural network. The network structure has three layers, with the hidden layer being a regression layer, so it can effectively recognize dynamic systems. The structure of the DRNN neural network is shown in Figure 2. [align=center] Figure 2 DRNN Neural Network Structure Diagram[/align] 4 BP Neural Network PID Algorithm Based on DRNN Identification The structure of the BP neural network PID control system based on DRNN identification is shown in Figure 3. The controller consists of three parts: (1) Classical PID controller, which directly performs closed-loop control on the controlled object process, and its three parameters k[sub]p[/sub], k[sub]i[/sub], k[sub]d[/sub] are tuned online by self-learning. (2) DRNN identification network, which is used to establish the identification model of the controlled object so as to dynamically observe the sensitivity of the output of the controlled object to the control input and provide it to the BP neural network. (3) BP neural network, which adjusts its own weight coefficients to adjust the PID control parameters in order to achieve the optimal performance index. [align=center] Figure 3 Control System Structure Diagram[/align] The BP neural network PID control algorithm based on DRNN identification is as follows: (1) Determine the BP neural network structure and give the initial values ​​of the weight coefficients of each layer w[sub]ij[/sub] (2) (0) and w[sub]li[/sub] (3) (0), learning rate η, inertia coefficient α ;k=1;（2）Assign small random values ​​to the weights of the input layer, regression layer, and output layer of the DRNN network, and set the learning rate and inertia coefficient of each layer of the network;（3）Sampling to obtain y（k） and r（k）, calculate e（k）, and assign zero initial values ​​to pj（k） and q[sub]ij[/sub]（k）;（4）Calculate the input and output of each layer of neurons of the BP network in the forward direction; calculate the output u of the PID controller and send it to the controlled object and the DRNN identification network to generate the output yout(k) of the controlled object;（5）Real-time correction of the weights of the DRNN network, and identify the output y[sub]m[/sub]out(k);（6）Correct the weight coefficients of the BP network using the iterative algorithm of the BP network;（7）Let k=k+1 to return to the first step and continue to execute step by step. 5 Simulation Implementation The sine wave input response curve diagram shows that the two curves basically overlap and the error is very small. The tracking ability of the model is satisfactory. It can be seen that the identification network composed of the DRNN neural network has a fast convergence speed and high accuracy. [align=center]Figure 4 Sine Tracking Curve[/align] Due to the unavoidable existence of uncertain disturbances in the centralized heating process, random disturbances were added to the above model for testing, and the adaptive control of the system under an external random disturbance at a certain moment was tested. Figures 5-6 show the simulation curves when the system is suddenly disturbed. As can be seen from the figures, even with a disturbance error over a certain period of time, the BP neural network PID control algorithm based on DRNN identification still shows good control capability, and the sine tracking curve remains basically unchanged, demonstrating a very good and strong suppression capability against sudden dynamic disturbances. [align=center]Figure 5 Sine Tracking Curve with Added Disturbance Figure 6 Sine Tracking Error Curve with Added Disturbance[/align] 6 Innovation Points The BP neural network is used as the controller, and the DRNN network is used as the identifier, which is applied to the PID controller. This is used to control the temperature model of a centralized heating heat exchange station with slow time-varying coefficients, large nonlinearity, and disturbances. Simulation results show that the second control method, which integrates three control strategies, has good control effect and strong robustness. References Jin Yihui, Process Control. Tsinghua University Press, 1993, 4 Mao Heng, Wang Yongchu. Application of Neural Networks in Process Control. Fujian Computer, 2003, (9) Liu Jinkun. Advanced PID Control and its MALAB Simulation. Electronic Industry Press, 2003, 1 Zhao Changzhan, Research and Application of Incomplete Differential PID Control Algorithm. Computer and Digital Engineering, 2007, 8 Liu Jinkun, Intelligent Control. Electronic Industry Press, 2005, 5 Wu Weibing, Neural Network PID Control Based on RBF Online Identification and Its Application Metallurgical Automation, 2006, 4 Rao J Rural.Neural nerwork architeure for parameter estimation of dynamical systems .IEEE Pror-CTA 1996,143(4):387-393. J JH opfield,DWTank.Neural Computation of Decisions Optimization Problem.Biological Cybernetics.1985,52:141-152