🚗 Active Suspension Control System – State-Space, Pole Placement & LQR

This folder contains my Advanced Control Systems (Control 2) project, where we modeled, analyzed, and controlled a 2-DOF active car suspension system using state-space modeling, transfer functions, pole placement, and LQR. Simulations were performed using MATLAB & Simulink.

📌 Course

• Course: REE 409 – Control 2
• University: University of Science and Technology – Zewail City
• Supervisor: Dr. Mohamed Lotfi Eid Shaltout
• Students: Phelopater Ramsis, Youssef Tarek
• Semester: Fall 2025
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🧾 Project Overview

The goal of this project was to build a mathematical and simulation model of a quarter-car suspension system, then design controllers to minimize the vibration felt by passengers.

The work includes:

• Modeling the car body (sprung mass) and wheel assembly (unsprung mass)
• Deriving the second-order differential equations
• Converting to Laplace domain 🚀
• Building transfer functions and analyzing open-loop stability
• Constructing the full state-space model (A, B, C, D)
• Checking controllability & observability
• Designing a state-feedback controller (pole placement)
• Designing an LQR controller
• Simulating responses in Simulink for a 0.1 m road disturbance

This project represents a full pipeline from physics → math → control → simulation.
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🚘 1. System Model & Physical Parameters

We modeled two masses:

• m1 = 2500 kg → vehicle body
• m2 = 320 kg → wheel & axle assembly

Springs:

• k1 = 80,000 N/m → main suspension
• k2 = 500,000 N/m → tire stiffness

Dampers:

• B1 = 350 N·s/m → suspension damping
• B2 = 15,020 N·s/m → wheel/tire damping

These are taken from the table on page 2.
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The control objective:

Reduce the relative displacement (x1 − x2) to improve passenger comfort.

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🧮 2. Differential Equations (Newton’s Laws)

From page 3:

Equation for m1 (vehicle body):