**6.2 Speed control based on proposed recurrent WNN-PID controller**

The RWNN that is proposed here is similar to that of feedforward WNN with feedback connections. The RWNN consists of three layers, with two inputs in the

**Figure 11.** *Position stair signal of BLDC motor with WNN-PID controller.*

**Figure 12.** *Torque-speed characteristics of BLDC motor with feedforward WNN-PID controller.*

**Figure 13.** *Phase current ia of BLDC motor with feedforward WNN-PID controller.*

input layer, the hidden layer has four neurons, with one output in the output layer and feedback connection for each layer. In this section, the feedback connection is called "Fully feedback." Besides, the RWNN contains a number of delay samples in the input and output layers as shown in **Figure 16**. The translation and dilation factors, weights and PID parameters are learning on-line to utilize PSO method in

*Wavelet Neural Networks for Speed Control of BLDC Motor DOI: http://dx.doi.org/10.5772/intechopen.91653*

**Figure 14.** *Phase back-emf ea voltage for BLDC motor with WNN-PID controller.*

**Figure 15.** *Line voltage vab for BLDC motor with feedforward WNN-PID controller.*

#### **Figure 16.**

*Simulink model for a proposed recurrent WNN-PID controller.*

the same manner used in the previous subsection and the results are given in **Tables 4–6**. The output of WNN is described by Eqs. (7) and (8).

The BLDC motor drive system with RWNN-PID controller is simulated in Matlab/Simulink program as shown in **Figure 6**. The time period that is assumed in


#### **Table 4.**

*PID parameters tuned using PSO for RWNN-PID controller.*


#### **Table 5.**

*RWNN parameters tuned using PSO.*


**Table 6.**

*Feedback parameters of RWNN tuned using PSO.*

this model is 1 s. The WNN-PID controller can be utilized for speed control in a wide range between 0 and the rated value, with better performance and more flexibility in the controller. **Figure 17** depicts the step change in speed of the BLDC. The motor is started at a speed of 500 rpm and then is changed in step to 500 rpm each 0.2 s. The actual speed of the motor is tracking the desired speed with a good response. The system starts at no load and suddenly a torque 2 N m (full load) is added at *t* = 0.4 s. **Figure 18** shows the speed response of the BLDC motor at 2000 rpm during no load and load conditions. The developed torque during no load and load conditions is shown in **Figure 19**. The position signal, the torque-speed characteristics, the phase current *ia*, Phase Back-emf *ea* voltage and line voltage *vab* are given in **Figures 20–24**, respectively.

**Figure 17.** *Step change in speed of BLDC motor with RWNN-PID controller.*

*Wavelet Neural Networks for Speed Control of BLDC Motor DOI: http://dx.doi.org/10.5772/intechopen.91653*

**Figure 18.** *Speed response of the BLDC motor with RWNN-PID controller.*

**Figure 19.** *Development torque of BLDC motor with RWNN-PID controller.*

**Figure 20.** *Position stair signal of BLDC motor with RWNN-PID controller.*

**Figure 21.** *Torque-speed characteristics of BLDC motor with RWNN-PID controller.*

**Figure 22.** *Phase current ia of BLDC motor with RWNN-PID controller.*

**Figure 23.** *Phase back-emf ea voltage of BLDC motor with RWNN-PID controller.*

*Wavelet Neural Networks for Speed Control of BLDC Motor DOI: http://dx.doi.org/10.5772/intechopen.91653*

**Figure 24.** *Line voltage vab for BLDC motor with RWNN-PID controller.*
