Modern radar servo systems mostly use PID control, while traditional PID control has some limitations under the non-linear system, time-varying system and large inertial system. Aiming at the complex mathematical model of radar servo system, a method of designing a fuzzy PID controller based on radial basis function neural network improved by genetic algorithm is proposed, which makes the PID controller have the characteristics of self-adaptability, strong robustness and stability. The system is applied in radar servo system to improve its sensitivity response. The simulation results show that the design of the fuzzy PID controller based on the improved radial basis function neural network with genetic algorithm has certain advantages and is effective and feasible in practical application. Real-time tracking of radar servo system through radar antenna is an important part of radar system. The quality of servo system directly affects the measurement accuracy of radar system. The traditional radar servo system usually adopts PID control, which mainly controls the control object by adjusting the three parameters of P (proportion), I (integral) and D (differential). It shows the influence of control deviation and the calculation and adjustment of control error, error change and error accumulation. Conventional PID controller is widely used in the field of control because of its simple structure and easy realization. However, in the face of non-linear problems, complex battlefield environment and interference factors, the conventional PID controller needs to adjust the parameters of P, I, D manually in real time to meet the needs of the system, which is unrealistic. Therefore, how to optimize the PID controller has become the focus of attention. In order to improve the capability of the PID controller system, a fuzzy-PID controller based on improved radial basis function neural network (RBF-NN) is proposed. The PID controller system combines the self-learning, self-organizing and self-adapting abilities of neural network, the principle of eliminating the fittest of genetic algorithm and the strong reasoning ability of fuzzy control. It is more suitable for solving the problems of complex non-linear systems [3-7].
In this paper, the RBF neural network, genetic algorithm and T-S fuzzy control are analyzed and calculated in detail, and the correctness and effectiveness of the proposed method are verified by the simulation application of MATLAB. Radial Basis Function Neural Network (RBF Neural Network) is a three-layer feedforward neural network with single hidden layer proposed by Moody and Darken in the late 1980s. It generally includes input layer, hidden layer and output layer, as shown in Figure 1. In the formula, WJ is the connection weight from the hidden layer node HJ to the output layer node; Mu is the learning rate; u (k) is the control input value. The parameters Kd, Kp and Ki of PID control e (k) by adaptive tuning of RBF neural network online algorithm. MATLAB provides two commands, newrb and newrbe, to design RBF neural network. Newrb controls the error standard by increasing the number of RBF neurons for long-term training; Newrbe controls the error quickly by constructing the network. In the learning algorithm of RBF neural network, the central vector Cj and the width parameter BJ of each node in the hidden layer are determined according to the input samples, and then the connection weight WJ [12] is obtained. Genetic algorithm (GA) is an estimation scheme based on the “survival of the fittest” mechanism of nature and can obtain the optimal solution by exchanging information. It is an efficient method to solve the optimization problem. Especially for some function optimization problems of non-linear modules, it can quickly and conveniently achieve the best result of function optimization.
Compared with other optimization algorithms, such as simulated annealing algorithm, it shows better global search ability, fast convergence speed, and does not fall into the problem of local optimal solution. The algorithm is mainly composed of chromosome coding method, fitness evaluation, genetic operator and operation parameters of basic genetic algorithm. After the initial population is generated, genetic algorithm generates offspring by using replication, crossover and mutation operators, replacing part of the old population, and forming a new population superior to the old one. With the continuous optimization of the population, genetic algorithm finds the best individual to approach the optimal solution gradually, and finally achieves the purpose of solving the optimal solution problem.
The design of genetic operators is crucial because these are all processes that simulate the reproduction, hybridization and mutation of natural species, so that individuals with high adaptability can be retained to form new populations, and new populations can inherit and outperform the previous generation, which is a very important process [13]. In the process of replication, the selection of individuals in a population depends on their fitness. Individuals with higher fitness will have more chances to reproduce, that is to say, they will have more chances to survive in the next generation. The main selection methods are ranking selection method, fitness ratio selection method and league tournament selection method. The basic idea of this paper is to select a certain number of individuals randomly from the existing groups, and keep the individuals with the greatest adaptability [14]. This process is repeated until the next generation of individuals can fill the mating pool. Reproduction operations only select individuals with high adaptability from previous generations, but can not create new chromosome individuals. Cross-over operations can achieve this process. The global search performance of genetic algorithm is mainly determined by crossover operator. Crossover operator refers to the parent chromosome with strong adaptability to reproduce as parents in order to get better next generation.
The range of crossover probability is generally 0.6-1. If the position of the parent chromosome is close to each other, the newly generated chromosome will also be closer to the parent chromosome. Therefore, search will become more random. The mutation operator is performed after the crossover operation.
In the process of mutation, new chromosomes are added to the population. Variation is a process in which chromosome information changes randomly and slightly. This process does not occur in all chromosomes. The main purpose of mutation is to improve the local search ability of genetic operators and to enhance the diversity of population.
The uniform mutation operator is mainly used in this paper.
RBF neural network is a kind of feedforward neural network with excellent performance. It has the ability to approximate any nonlinear function with arbitrary precision, and has compact topology and fast convergence speed. However, due to the complexity of the system structure and the increase of the amount of data, RBF neural network can not completely avoid falling into the problem of local minimum. Especially, the selection of the center value and width of the hidden layer node has an important influence on the function approximation ability of RBF neural network [15]. In this paper, the global search ability of genetic algorithm is used to optimize the center and width of hidden layer in RBF neural network to ensure that the optimal solution of weight can be found.
On the premise of fixed structure of RBF neural network, genetic algorithm is used instead of RBF network learning algorithm to train network weights and optimize their weights. Until the performance requirements are met, a set of optimized weights are obtained. The optimal parameters of the PID controller are obtained by tuning the RBF neural network optimized by genetic algorithm. This process mainly includes the selection of variable symbols and the adjustment of fitness function. The parameters tuning elements of the PID controller include proportional gain Kp, integral gain Ki and differential gain Kd. This method of directly expressing the tuning variables first greatly reduces the storage space of the computer for the number of population. Therefore, the parameter value is obtained by optimizing the PID controller by the improved RBF neural network program based on genetic algorithm. The above parameter representation method is the evaluation result of maximizing the non-negative fitness function, and the fitness function value is linearly related to the objective function value. Therefore, the objective function F (Kp, Kd, Ki) can be used as a criterion for the evaluation of parameter settings, while the fitness function is established by the relevant criteria of the objective function. The purpose of formula (5) is to increase the value of 1/F so that the fitness of chromosomes can be carried out in a relatively larger range. The PID controller tuned by RBF neural network takes the error and error rate as input. After optimization by genetic algorithm, the output parameters of Kp, Kd and Ki are obtained. In order to minimize the error, the population with higher adaptability is usually selected for replication, crossover and mutation operations.
The genetic algorithm is used to optimize the center value of hidden layer nodes, the width of hidden layer nodes and the output linear weights to ensure that the RBF neural network can find the global optimal solution. In the formula: A and B are fuzzy sets in the preceding part; X and y are input variables; f (x, y) are exact functions of the latter part; the fuzzy sets of each variable are represented by its corresponding membership functions. Compared with the Mamdani fuzzy system model, the output of T-S fuzzy control is not a fuzzy variable, but an exact constant or linear function [16]. The core of T-S fuzzy system is formed by a set of such rules. In this paper, the parameters of PID controller under various operating conditions are determined by S-T fuzzy system.
The real-time optimization of PID parameters is accomplished by T-S fuzzy controller. Among them, error E and error rate EC are input parameters, while Kp, thermostatic element Kd and Ki are output values. Seven fuzzy subsets are defined in the domain of error E and error rate of change ec, which are {negative large (NB), negative medium (NM), negative small (NS), zero (ZO), positive small (PS), positive medium (PM) and positive large (PB)}. Their membership functions are selected as the orthomorphic form of complete overlap. The input and output parameters of the PID can be optimized by the improved RBF neural network based on genetic algorithm. The optimal control parameters corresponding to the combination of input value E and EC in each optimization process can be used as the control rules of the fuzzy PID controller to participate in the final parameter setting process of the PID controller. Based on each combination form of E and ec, the corresponding optimal values of Kp, Kd and Ki are given by RBF neural network improved by genetic algorithm. For the fuzzy logic toolbox (FIS) editor, the input of the fuzzy control is defined as error E and error rate ec, and the output is processed to obtain the optimized parameters Kd, Kp, Ki of the PID. According to the actual situation, the range of error E is – 6. As can be seen from Figure 7, compared with the traditional PID controller, the improved fuzzy PID controller has greatly improved the overshoot and the stability of the system, and the response time is shorter. The improved PID controller can play a good role in the control of radar servo system. Compared with the traditional PID regulation, this control method can respond to the setting of servo system more quickly and stably. In order to more accurately reflect the effect of the improved fuzzy PID controller in more complex systems, noise interference and non-linear influence factors of saturation zone are added to the original simulation model. Firstly, the interference factor of white noise is added to the system, as shown in Figure 8. The output results of the traditional PID control and the improved fuzzy PID control have some fluctuations, but the improved fuzzy PID controller can be more quickly stabilized in the noise environment, and has good ability to deal with complex environment. Secondly, in the output part of the system, the non-linear influence factors of dead zone and saturation zone as shown in Figure 9 are added to obtain the output signal of the system under the PID control and the improved fuzzy PID control, as shown in Figure 10. From Fig. 10, it can be seen that the improved fuzzy PID controller can suppress the non-linear factors of the system better after adding the non-linear disturbance to the system control input.
At this time, the traditional PID controller has been distorted and divergent, and the control performance has been seriously degraded. In the design of radar servo system, traditional PID controller encounters difficulties in solving practical non-linear and complex problems, so it is necessary to improve the PID controller. In this paper, genetic algorithm, S-T fuzzy logic control and radial basis function neural network are combined to improve the optimal parameters of the PID controller.