Abstract: A PID parameter self-tuning control system based on an improved CMAC cerebellar model neural network is established. The PID parameter tuning method is a rule-based tuning method, which does not require precise identification of the mathematical model of the controlled object. It only needs to input the feature values ​​of the time characteristics of the system error into the CMAC network, and then the CMAC will derive the corresponding change in the PID parameter based on the input feature values, thereby realizing the self-tuning of the PID parameter. Keywords: CMAC neural network; PID; parameter self-tuning; [b][align=center]Research on Method of the Auto-tuning of PID Parameters Based on CMAC Neural Network ZHANG Yong-tao, ZHANG Shi-jie, DONG Han-bo[/align][/b] Abstract: Constitute a system of auto-tuning of PID parameters based on CMAC neural network. The method of auto-tuning is rule-based and does not require an accurate mathematical model of the object. We only need to send the eigenvalue of system error e to the CMAC neural network, and then we can get the change quantity of PID parameters. Key words: CMAC neural network; PID; auto-tuning of parameters; 0 Introduction The parameter tuning of the controller is achieved by adjusting the PID controller parameters (K[sub]P[/sub], K[sub]I[/sub], K[sub]D[/sub]) to make the system's transient process meet satisfactory quality requirements. Tuning PID parameters generally requires experienced engineers, which is both time-consuming and labor-intensive. Furthermore, the wide variety of actual systems and factors such as hysteresis and nonlinearity make PID parameter tuning challenging, resulting in many PID controllers not being tuned well. Such systems naturally cannot operate in a satisfactory state, hence the development of self-tuning PID controllers. Combining the determination of process dynamic performance with the calculation method of PID controller parameters can achieve PID controller self-tuning [1,2]. This paper designs a PID parameter self-tuning control system based on a CMAC (Cerebellar model articulation controller) neural network, thereby achieving rapid PID parameter tuning and ensuring a certain level of accuracy in PID parameter tuning. 1 CMAC Neural Network CMAC (Cerebellar model articulation controller) is a neural network model simulating cerebellar function proposed by JS Albus in 1975. CMAC is an associative network where only a small number of neurons (determined by the input) are associated with each output. Its association has local generalization ability, meaning similar inputs will produce similar outputs, while distant inputs will produce almost independent outputs. CMAC is similar to a perceptron. Although the relationship between each neuron is linear, it is suitable for a nonlinear mapping in terms of the overall result. Therefore, CMAC can be regarded as a table system for expressing nonlinear mappings (functions) [3]. Since its adaptive adjustment (learning) is in the linear mapping part, its learning algorithm is a simple algorithm, the convergence speed is much faster than BP, and there is no local minima problem [4]. The structure of the CMAC neural network is shown in Figure 1. [align=center] Figure 1 CMAC structure[/align] 2 System principle The working principle of the system is as follows: When the closed-loop control system is disturbed, the time characteristics of the system error are pattern recognized. First, the peak value and time of the system error curve are obtained, as shown in Figure 2. [align=center] Figure 2 Error e(t) curve when the given value changes by step[/align] Then, according to the following formula, the multiple characteristic parameters ei (i=1,2,3) of the response curve of the process are obtained as follows: overshoot σ, damping ratio ζ and damped oscillation period T. The three identified characteristic parameters are input to the CMAC parameter tuning network. After calculation, the corresponding change in PID parameters is obtained, and the obtained parameters are then sent to the PID controller to achieve PID parameter self-tuning. The PID parameter self-tuning system is shown in Figure 3. [align=center] Figure 3 PID parameter self-tuning control system[/align] In this CMAC neural network, three characteristic parameters in the system error characteristic curve are obtained. Each characteristic parameter becomes a characteristic parameter level according to the table division. When the size of the characteristic parameters in each region is determined, a characteristic parameter pattern is formed. When the obtained characteristic values ​​change, the corresponding pattern also changes. Therefore, the input of the CMAC network established in this paper is a vector composed of three components, that is, the three selected characteristic values ​​(damping ratio, overshoot percentage, and damped oscillation period) can also be called characteristic parameter patterns. Since the PID controller needs to tune three parameters, the output of the CMAC network is a vector composed of three components. Each element corresponds to one parameter to be tuned in the PID controller. 3 Improvement and Implementation of CMAC Neural Network [5] 1) Arrangement and Total Number of Basis Functions 2) High-Order Basis Functions When the initial CMAC network uses binary basis functions, its output is piecewise continuous, that is, continuous within each grid and discontinuous at the input axis nodes. To make the network have continuous output, the output of the basis function must be 0 at the boundary of its domain. In this design, represents distance, represents single variable function, and infinite factor basis function is used to achieve continuous output. When calculating distance using infinite factor, the output of the basis function at the boundary of the domain can be 0, and the output at the center of the domain can be 1/ρ. In the one-dimensional case, other output values ​​are linear interpolations between these two extreme values. In the two-dimensional input space, the basis function output is pyramid-shaped. 3) Memory Scattering Technique The memory requirement of the CMAC network is proportional to an exponential multiple of , so it is very large. For high-dimensional input, the number of basis functions can be approximately calculated by formula (5). Since the number of basis functions is required to be less than the number of grids (p < 0), 4. CMAC Neural Network Training The main parameters of the CMAC neural network include: quantization precision of the input variables, generalization parameters, and the types of basis functions. The three inputs of the CMAC neural network are quantized separately: the damping ratio ζ is divided into 23 levels, the overshoot percentage σ into 12 levels, and the damped oscillation period Tc into 20 levels, resulting in 23 * 12 * 20 = 5520 training patterns. 2000 patterns are selected from these 5520 as training samples for the CMAC parameter tuning network. Then, 1620 feature parameter patterns are selected from these 2000 as the training set to train the network. A mapping from input to physical storage space is established, as well as the relationship between physical storage space and output. The generalization parameter is set to 32, and an error correction algorithm is used for the learning algorithm. The learning rate β is 0.6, and the spline function SPLINE is used instead of the traditional ALBUS function as the basis function of the CMAC neural network. The ALBUS function outputs only 0 and 1, so the output curve is segmented and continuous only between internal nodes, often discontinuous at the boundaries of internal nodes. Spline functions, on the other hand, can better solve this problem. The corresponding memory usage is 300. After training convergence, the weights reflect the relationship between the feature parameters and the parameters to be tuned in the PID controller. Figure 4 shows the training error curve of the CMAC neural network for 1620 feature parameter patterns. [align=center] Figure 4 CMAC training error curve[/align] Figure 5 shows the number of training data in each error interval after the 1620 sets of training data are fed into the CMAC neural network for training. It can be seen that more than 90% of the training data has high error accuracy, i.e., error accuracy < 0.1. [align=center] Figure 5 Numbers of training data in different section of error[/align] The remaining 380 sets from the selected 2000 feature parameter modules were used as the test set to test the trained CMAC parameter tuning network. The output control parameter change value was compared with the expected result of the learning sample. The error rate was 7.8%, indicating that the CMAC network training was relatively successful and had a certain generalization ability. Figure 6 shows the test error curve of the CMAC neural network. Figure 7 shows the number of test data in different error intervals. [align=center] Figure 6 CMAC test error curve Fig.6 Testing error curve of CMAC Figure 7 Numbers of testing data in different error intervals[/align] 5 Simulation Results The controlled object is selected as: , and the original controller's control performance for this object meets the requirements. The step disturbance curve is shown as line 1 in Figure 8. When PID parameter self-tuning is performed, the response curve after tuning is line 2 in Figure 8. The feature parameters are fed into the CMAC parameter tuning network, and the tuned parameters are . From the simulation figure, we can see that the PID parameter tuning effect is relatively ideal, and the training time for the CMAC neural network to reach stability is also relatively short. [align=center]Figure 8 Response curves before and after tuning[/align] 6 Conclusion Simulation results show that the characteristics of the CMAC neural network make it suitable for use in PID parameter self-tuning. The adjustment of the CMAC neural network weights is local, with fast learning speed and good convergence, and the tuning effect of the PID parameters also meets the tuning requirements. The innovation of this paper is that in the pattern recognition-based PID parameter self-tuning system, the tuning rules are directly obtained using the CMAC network, avoiding the need for establishing a large amount of traditional expert tuning experience. References: [1] Pan Wenbin. Research on self-tuning PID method based on pattern recognition and its application [D]. Zhejiang: Zhejiang University, 2006 [2] Duan Peiyong. CMAC neural computation and neural control [J]. Information and Control, 1999, 9 (3): 23-25 ​​[3] Chen Hui. Determination of cerebellar model CMAC network structure and related parameters [J]. Computer Engineering, 2003, 29 (2): 252-254 [4] Su Gang. Theory and application of cerebellar model joint controller (CMAC) [J]. Journal of Instrumentation, 2003, 24 (4): 269-271 [5] Zhu Hongchao. Research and implementation of ball mill measurement and control system based on CMAC [D]. Nanjing: Southeast University, 2006