2.7.2. Modeling and Simulation of PID Control System

The simulation model of the fuzzy PID control system was established in the simulation module. The input signal was a saving signal of 2. The simulation process was as

follows: input a step signal with amplitude of 2 at the time of t = 0, set the simulation time as 60 s, input variables of fuzzy controller as fuzzed error e (k) and error change rate ec (k). The fuzzy controller output the PID parameter compensation value after fuzzing and optimized the initial parameters through the compensation value. Finally, the control system simulation waveform was obtained [9]. The simulation waveform is shown in Figure 11. Figure 11 shows that the response time of fuzzy PID control was 7.21 s, and the overshoot was 0.035.

**Figure 11.** Simulation waveform of fuzzy PID control model.

2.7.3. Modeling and Simulation of BPNN–PID Control System

The simulation model of the BPNN–PID dominant system was established in the Simulink simulation module, and the input signal was also a step signal with an amplitude of 2. In the simulation process, the import amplitude step signal with an amplitude of 2 was time t = 0. Simulation time was disabled at 20 s. The input variables of the fuzzy regulator were the error e (k) and error rate of change ec (k) processed by the neural network, and the BPNN-PID regulator output compensation values of PID parameters after calculating KP, KI, and KD through BPNN. Initial parameters were optimized through compensation values, and the control system simulation waveform was obtained.

The built BPNN–PID control system model is displayed in Figure 12, while its simulation waveform is shown in Figure 13.

**Figure 12.** BPNN–PID control system model.

**Figure 13.** Simulation waveform of BPNN–PID control model.

As shown in Figure 13, the reaction time of the BPNN–PID control was 6.97 s, the overshoot was 0.03, and there was some oscillation before the system ran stably. Compared with the classical PID control, the overshoot increased by 0.011, while the system response time decreased by 1.63 s. Compared with the fuzzy PID control, the overshoot decreased by 0.005, while the system response time decreased by 0.24 s.
