Optimizing the Cascade Deep Neural Network Parameters Using an Egret Swarm Optimisation Algorithm: An Application to PID Tuning for the AVR with Shallow Controller

Voltage regulation of synchronous generators remains a significant and complex challenge in the field of engineering, particularly under varying load conditions. Although various control strategies have been applied to Automatic Voltage Regulator (AVR) systems for managing the terminal voltage of synchronous generators, Proportional–Integral–Derivative (PID) controllers continue to be one of the most fundamental and widely used approaches due to their simplicity, reliability, and robust structure. The tuning process, which involves determining the optimal values of the three fundamental parameters of a PID controller—namely the coefficients for the proportional, integral, and derivative terms (KP, KI, and KD)—is essential to achieving the desired controller performance. While tuning can be performed through simple trial-and-error methods, such approaches often fail to yield satisfactory results. In this study, the tuning of a PID controller, which provides automatic voltage regulation for 1 kW stand-alone synchronous generator constructed as a real physical experimental setup, was performed using a novel hybrid method named ESOA-CDNN, which combines the Egret Swarm Optimization Algorithm (ESOA) and a Cascade Deep Neural Network (CDNN). The ESOA is utilized to optimize the number of hidden layer neurons, the weights, and the biases of the CDNN. Furthermore, since the PID controller can be readily implemented through a standard Programmable Logic Controller (PLC) within the proposed approach, there is no need for additional hardware in the control system. The PID controller tuning was conducted using four different methods: tuning via PLC, tuning using CDNN, tuning using CDNN optimized with Particle Swarm Optimization (PSO-CDNN), and the proposed ESOA-CDNN approach. Experimental results demonstrate that the PID controller tuned with the ESOA-DNN method significantly outperformed the others in terms of settling time and overshoot reduction. The experimental results under sudden load application (0–500 W, 0–1000 W, and 0–550 VA) and sudden load rejection (500–0 W, 1000–0 W, and 550–0 VA) demonstrate that the PID controller tuned using the ESOA-DNN method significantly outperformed the others in terms of settling time and overshoot reduction.