📘 Modern Control 2

This repository contains projects from the Modern Control 2 course.

📁 Directory Structure

• Project 1/ – Codes and description for the project of 'Continuous and Discrete Kalman Filter Design '
• Project 2/ – Codes and description for the project of 'Model and Control of a Vehicle's Active Suspension System'
• README.md – You’re here!

🎯 Purposes

• Project 1: – The purpose of the project is to deepen understanding of the operation and simulation of the optimal Kalman filter estimator in continuous-time and discrete-time linear dynamic systems

• Project 2: – The purpose is to design a control system for an active suspension system of a vehicle.

🧠 Technical Notes

• All code is written in MATLAB/Simulink.

🛠️ Project 1

Description:

The system dynamic equations are given as follows:

In these equations, 𝑤(𝑡) is the disturbance input vector, and 𝑣(𝑡) is the measurement noise. Assume that the initial conditions of this system are random variables with a Gaussian distribution such that:

The input 𝑢(𝑡) is a known deterministic input function. Assume that the disturbance input vector 𝑤(𝑡) and the output noise 𝑣(𝑡) are white Gaussian stochastic processes with the following characteristics:

It is assumed that the initial condition vector, the disturbance input vector, and the output noise vector are all mutually uncorrelated.

Continuous-time system:

• a: Write the complete Kalman filter equations (including the one-step ahead prediction equation, the estimation equation, the one-step ahead estimation error covariance matrix equation, the estimation covariance matrix, and the Kalman gain) for this continuous-time system.
• b: By simulating the results in MATLAB software, plot the time variation curves of the estimated state variables 𝑥hat_𝑖(𝑡∣𝑡) and the estimation error covariance matrix as functions of time.
• c: By varying the values of the initial condition covariance, output noise covariance, and input disturbance covariances, examine their effects on the system response.

Discrete-time system:

• a: Using MATLAB simulation, plot the time response of the estimated state variables 𝑥hat_𝑖(𝑡∣𝑡) and the estimation error covariance matrix.
• b: By varying the values of the initial condition covariance, output noise covariance, and disturbance input covariances, examine their effects on the response of the discrete-time system.

🛠️ Project 2

Description:

The Figure shows a two-degree-of-freedom model of a quarter-car active suspension system.

• a: Design a linear quadratic optimal controller for this system that minimizes the following cost function.
• b: Simulate the behavior of the optimal control system in MATLAB and plot all state variables, inputs, and outputs as functions of time.
• c: Simulate the passive suspension system and plot the system’s state variables over time. Determine the peak response values and the settling time.
• d: Simulate the active suspension system and plot the system’s state variables over time. Determine the peak response values and settling time.
• e: Design a Kalman filter estimator for the passive suspension system, then simulate the system and plot the state variables over time.