Golden Eagle Algorithm–Optimized PID Controller
- lms editor
- 19 hours ago
- 3 min read
👋 Introduction
Golden Eagle Algorithm (GEA)–optimized PID controller implemented using MATLAB/Simulink. The primary objective of this work is to optimally tune the PID controller parameters (Kp, Ki, and Kd) for a given plant using a nature-inspired metaheuristic optimization technique known as the Golden Eagle Optimizer (GEO).
🎯 Problem Statement
Conventional PID tuning methods often fail to provide optimal performance for nonlinear or complex systems. Improper tuning can lead to:
❌ High steady-state error
❌ Large overshoot
❌ Slow settling time
✔️ To overcome these limitations, Golden Eagle Algorithm–based optimization is applied to determine the best PID gains that minimize the system error.
🧩 System Configuration
The Simulink model consists of:
⚙️ A simple plant model
🎛️ A PID controller
🔁 A closed-loop feedback system
📌 The plant output is continuously compared with a reference signal, and the resulting error is used to evaluate controller performance.
🦅 Golden Eagle Optimization Algorithm (Concept)
The Golden Eagle Optimizer is a nature-inspired metaheuristic algorithm developed based on the hunting behavior of golden eagles.
🔍 The algorithm mimics:
🌀 Spiral flight motion of golden eagles
🎯 Prey selection strategy
⚔️ Attack and cruise mechanisms
Based on these behaviors, mathematical equations are formulated to balance:
🔎 Exploration (global search)
🎯 Exploitation (local refinement)
📚 This algorithm was introduced and validated in the journal Computers & Industrial Engineering, where it was tested using several benchmark optimization functions.
🧠 Application of GEA for PID Tuning
In this work, the Golden Eagle Algorithm is used to tune:
🔧 Proportional gain (Kp)
🔧 Integral gain (Ki)
🔧 Derivative gain (Kd)
📌 Each candidate solution (eagle) represents a set of [Kp, Ki, Kd] values.
⚙️ Optimization Setup
The key parameters used in the optimization process are:
👥 Population size: 50
🔁 Maximum iterations: 100
🎯 Number of variables: 3 (Kp, Ki, Kd)
📏 Lower and upper bounds defined for each gain
⚔️ Attack and cruise factors set according to GEO theory
These parameters control the convergence speed and accuracy of the optimization.
📐 Objective Function Definition
The performance of each PID parameter set is evaluated using an objective function.
🎯 Objective function used:
Mean Absolute Error (MAE) of the control system
📉 The goal of the optimizer is to:
Minimize the absolute error between reference and plant output
✔️ Lower objective function value indicates better controller performance.
🔄 Optimization Process Flow
The optimization proceeds as follows:
🦅 Initialize golden eagle population (random Kp, Ki, Kd values)
▶️ Run Simulink model for each candidate solution
📊 Compute objective function (absolute error)
🔁 Update positions using spiral attack and cruise equations
🔍 Evaluate new solutions
🏁 Repeat until maximum iterations are reached
Throughout the iterations, the algorithm continuously improves PID parameters to reduce error.
📈 Optimization Results
During execution:
🔄 Iteration count increases progressively
📉 Mean absolute error decreases with each iteration
📊 Error converges to a minimum value
📌 Final results show:
Optimal Kp, Ki, Kd values stored in the solution vector
Objective function value reduced from initial high value to around 2.6
Stable convergence behavior of the Golden Eagle Algorithm
⏱️ Closed-Loop System Response
After applying the optimized PID gains:
✅ System output settles in approximately 2 seconds
📉 Reduced steady-state error
⚖️ Improved dynamic performance
🔁 Smooth transient response
This confirms the effectiveness of the Golden Eagle Algorithm–based PID tuning.
⭐ Advantages of Golden Eagle–Optimized PID
🧠 Intelligent, nature-inspired optimization
⚡ Faster convergence compared to manual tuning
🎯 Better control accuracy
🔧 Suitable for complex and nonlinear systems
🔁 Easily extendable to other controllers and plants
🏁 Conclusion
This blog presented a detailed explanation of the Golden Eagle Algorithm–optimized PID controller using MATLAB/Simulink. By leveraging the hunting behavior of golden eagles, the algorithm efficiently tunes PID parameters to minimize control error and improve system performance. The results clearly demonstrate faster settling time, reduced error, and stable closed-loop operation.
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