**Abstract**

In the recent years, researchers have sophisticated the synthesis of neural networks depending on the wavelet functions to build the wavelet neural networks (WNNs), where the wavelet function is utilized in the hidden layer as a sigmoid function instead of conventional sigmoid function that is utilized in artificial neural network. The WNN inherits the features of the wavelet function and the neural network (NN), such as self-learning, self-adapting, time-frequency location, robustness, and nonlinearity. Besides, the wavelet function theory guarantees that the WNN can simulate the nonlinear system precisely and rapidly. In this chapter, the WNN is used with PID controller to make a developed controller named WNN-PID controller. This controller will be utilized to control the speed of Brushless DC (BLDC) motor to get preferable performance than the traditional controller techniques. Besides, the particle swarm optimization (PSO) algorithm is utilized to optimize the parameters of the WNN-PID controller. The modification for this method of the WNN such as the recurrent wavelet neural network (RWNN) was included in this chapter. Simulation results for all the above methods are given and compared.

**Keywords:** BLDC motor, particle swarm optimization (PSO), wavelet neural network (WNN), speed control

### **1. Introduction**

Brushless DC (BLDC) motors have a wide application in our life due to their high-power density and high dynamic response. In addition, the BLDC motor is utilized with constant loads, varying loads, and position applications with high accuracy. This motor is generally controlled utilizing electronically commutation by three-phase power semiconductor bridge inverter with rotor position sensors that are required for starting and providing proper firing sequence to turn on the power devices in the inverter bridge. Based on the rotor position, the power devices are commutated sequentially every 60° [1, 2]. The mathematical model and the Simulink model of BLDC motor to control the speed of a BLDC by using conventional methods are introduced in Refs. [2–6]. The DC-DC converter technique is utilized to control the speed of the motor [5, 6].

In the past decade, artificial intelligence techniques such as neural networks, fuzzy-neural networks, and wavelet neural networks control have been utilized to control the speed of the BLDC motor [7–10]. Since BLDC motor is a multivariable and nonlinear system, it is complex to obtain high performance by applying classical PID control. The main objective of this chapter is to develop wavelet neural networks (WNNs) to control the speed of the BLDC motor, and the recurrent wavelet neural network (RWNN). These methods lead to an enhanced dynamic performance of the system of motor drive and are resistant to load perturbations. The learning strategy for the wavelet neural network and PID controller is developed based on PSO algorithm.
