control_state_feedback

MATLAB and Python simulation code for state feedback control design — pole placement, LQR, integral servo, observer-based feedback, and LMI-based design.

Companion code for blog.control-theory.com.

Author: Hiroshi Okajima, Associate Professor, Kumamoto University, Japan
Blog: https://blog.control-theory.com/
Hub article: State Feedback Control and State-Space Design: A Comprehensive Guide

Contents

Folder	Blog Article	Hub Section	Description
01_pole_placement/	State Feedback Control: Pole Placement	State Feedback: Pole Placement	Step response comparison before/after pole placement, pole map on the s-plane, effect of pole locations on transient response
02_lqr_design/	State Feedback Control: Optimal Regulators	State Feedback: Optimal Regulator (LQR)	LQR responses for different Q/R weights, state vs. control input trade-off, Riccati equation convergence
03_integral_servo/	(Hub section only — no separate spoke article)	Integral-Type Servo System	Step tracking with integral action, comparison of steady-state error with/without integrator
04_observer_based_feedback/	State Observer for State Space Model	Observer-Based Feedback and the Separation Principle	Separation principle demo using the same plant as 01–03 (lightweight version — see Related Repositories)
05_lmi_state_feedback/	LMI and Controller Design / Advanced LMI Techniques	LMI-Based State Feedback Design	H∞ state feedback via LMI, comparison with pole placement and LQR

Repository Structure

Each folder contains both MATLAB and Python implementations with a shared fig/ directory:

control_state_feedback/
├── README.md
├── 01_pole_placement/
│   ├── matlab/
│   │   └── pole_placement.m
│   ├── python/
│   │   └── pole_placement.py
│   └── fig/
├── 02_lqr_design/
│   ├── matlab/
│   │   └── lqr_design.m
│   ├── python/
│   │   └── lqr_design.py
│   └── fig/
├── 03_integral_servo/
│   ├── matlab/
│   │   └── integral_servo.m
│   ├── python/
│   │   └── integral_servo.py
│   └── fig/
├── 04_observer_based_feedback/
│   ├── matlab/
│   │   └── observer_based_feedback.m
│   ├── python/
│   │   └── observer_based_feedback.py
│   └── fig/
└── 05_lmi_state_feedback/
    ├── matlab/
    │   └── lmi_state_feedback.m
    ├── python/
    │   └── lmi_state_feedback.py
    └── fig/

Requirements

MATLAB

• MATLAB R2023a or later (recommended)
• Control System Toolbox
• Robust Control Toolbox (for 05_lmi_state_feedback/ only)

Python

pip install numpy scipy matplotlib control

For 05_lmi_state_feedback/ only:

pip install cvxpy

Running the Simulations

Each script is self-contained and can be executed independently. The fig/ directory is created automatically.

MATLAB:

cd 01_pole_placement/matlab
pole_placement

Python:

cd 01_pole_placement/python
python pole_placement.py

Plot Style

All figures follow a unified plot style for consistency across the blog. Style definitions (colors, figure sizes, fonts, and save functions) are embedded directly in each script — no external dependencies or shared modules are required. Key conventions:

• Figure size: (8, 5) inches at 150 dpi for standard time-series plots
• Font: Serif, 13 pt (axes labels 14 pt)
• Colors: Black for reference/true values, blue (#1f77b4) for method 1, red (#d62728) for method 2, green (#2ca02c) for method 3, purple (#9467bd) for control input
• Background: White (facecolor='white') for blog compatibility

Related Repositories

This repository focuses on state feedback design (pole placement, LQR, integral servo) and provides a lightweight separation-principle demo in 04_observer_based_feedback/.

For comprehensive observer design — including Luenberger observer, Kalman filter, H∞ filter, multi-rate observer, and outlier-robust MCV observer — see:

• MATLAB: MATLAB_state_observer
• Python: python_state_observer
• Blog hub: State Observer and State Estimation: A Comprehensive Guide

For model-based compensation (IMC, DOB, 2-DOF, MEC) and comparison studies, see:

• control_model_based_compensation
• Blog hub: Model Error Compensator (MEC)

License

MIT License