Nonlinear System Identification and Control

Multi-architecture control of two nonlinear black-box systems using optimization, fuzzy logic, and neural networks

Python · MATLAB · Neural Networks · Fuzzy Logic · PID Control · System Identification

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📌 Project Summary

This project explores intelligent control strategies applied to two nonlinear, black-box dynamic systems. The goal is to identify system models and develop high-performance controllers using a mix of classical, fuzzy, and data-driven methods.

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🧩 System 1 – Identification and Feedforward Control

• Identification via step and ramp responses:
  → Static gain and offset derived from regression
  → System approximated as a first-order linear model

• Controller Design:
  → Feedforward control law:
  [ u_{ff} = \frac{r_{desired} - C_{est}}{K_{est}} ]
  → Simulated in Python and validated through step tracking performance

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🧠 System 2 – Identification and Intelligent Control

🔍 b.1) System Identification

• Assumed model:
  [ G(s) = \frac{K}{s(\tau s + 1)} ]
• Nonlinear least squares used to fit step response
• Asymptotic fitting included for comparison

🔬 b.2) Neural Network Modeling

• Architecture: 2 input, 1 output NARX model
• Training: MLP with ReLU layers, trained on 2,189 synthetic samples
• Validation:
  • R² score: 0.9801
  • MSE: 0.0046
  • Generalization tested on unseen input signals

🤖 b.3) Controller Comparison

Controller	Mean Squared Error	Final 50-step Avg Error
Adaptive Neuron-PID	0.2831	0.1541
NN Model-Based Control	8.3008	3.1487
Classic PID (Kp=0.8...)	0.1725	0.3452

• Neuron-PID adapts gains online based on a nonlinear activation function and gradient updates
• NN Model-Based Control uses iterative inversion to compute ( u(k) ) based on the trained forward model
• Classical PID is used for performance benchmarking

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📈 Results & Figures

Adaptive Neuron-PID Controller

Neural Network Model-Based Control

Classic PID Control

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🗂️ Project Structure

.
├── Question_1
│   ├── Part_a
│   │   ├── part_a_1_2.py
│   │   └── q1a_step_response.png ...
│   ├── Part_b
│   │   ├── part_b_1.py
│   │   ├── part_b_2_1.py
│   │   ├── part_b_2_2.py
│   │   ├── part_b_3_PID.py
│   │   ├── part_b_3_NARX.py
│   │   └── part_b_4.py
│   └── outputs (.png, .npy)
├── main.tex
└── report.pdf  # Final LaTeX report