different PID optimizers (GA, GWO, GA-GWO)

PID tuned using GA, GWO, and Hybrid GA→GWO; compares step response, disturbance rejection, and hardware-like discrete simulation.

Title: PID Controller Optimization Comparison (GA vs GWO vs Hybrid GA→GWO)

Aim:

To optimize PID controller gains for a second-order system using Genetic Algorithm (GA), Grey Wolf Optimizer (GWO), and a hybrid GA→GWO approach, and to compare their performance in terms of step response, disturbance rejection, and hardware-like discrete implementation.

Learning Outcomes:

After completing this project, you will be able to:

1. Understand and implement PID controllers for second-order systems.
2. Apply metaheuristic optimization algorithms (GA and GWO) to tune controller gains.
3. Analyze and compare controller performance using step response and disturbance rejection.
4. Simulate hardware-like effects, including sampling, quantization, and actuator saturation.

Key Steps:

1. Plant Definition: Second-order system with specified damping and natural frequency.
2. PID Gain Optimization:

• GA: Optimizes PID gains using population-based evolution.
• GWO: Optimizes PID gains inspired by grey wolf hierarchy.
• Hybrid: Initializes GWO with GA’s best solution for refinement.

1. Controller Creation: Constructs pid objects from optimized gains.
2. Closed-loop Analysis:

• Step responses (Figure 1) for all controllers.
• Disturbance rejection simulation using hybrid controller (Figure 2).
• Hardware-like discrete response considering sampling, quantization., and actuator limits.

Outputs:

• Optimized PID gains and corresponding cost.
• Comparison plots illustrating continuous vs hybrid vs hardware-like responses.