📘 Modern Control 1

This repository contains projects from the Modern Control 1 course.

📁 Directory Structure

• Project 1/ – Codes and description for the project of 'State-Space Control of a Two-Liquid-Tank System'
• Project 2/ – Codes and description for the project of 'Modeling and Control of a Quarter-Car Suspension Vibration System'
• Project 3/ – Codes and description for the project of 'Modeling and Control of a Bicycle Vehicle System'
• Project 4/ – Codes and description for the project of 'Modeling and Digital Control of a Quarter-Car Suspension Vibration System'
• README.md – You’re here!

🎯 Purposes

• Project 1: – The purpose of this project is to simulate both the nonlinear open-loop system and its linearized equivalent. Additionally, the project analyzes the controllability and observability of the linearized system. It also involves the design and implementation of a state feedback controller and an observer in continuous time.

• Project 2: – The purpose of this project is to simulate the open-loop dynamics of a Quarter-Car Suspension Vibration System. Additionally, various controllers will be designed for the system. In the advanced control approach, a state observer (SVFC) along with classical full-state feedback controllers—such as PID, PI, or P action—will be used to estimate the state variables.

• Project 3: – The purpose of this system is to simulate the open-loop behavior and control the vehicle’s lateral dynamics using the steering angle as the input.

• Project 4: – The purpose of this project is to simulate both the nonlinear open-loop system and its linearized equivalent. Additionally, the project analyzes the controllability and observability of the linearized system. It also involves the design and implementation of a state feedback controller and an observer in discrete time.

🧠 Technical Notes

• All code is written in MATLAB/Simulink.

🛠️ Project 1

Description:

Consider a fluid system consisting of two tanks with two input flow rates ( u_1 = q_{1f}(t) ) and ( u_2 = q_{2f}(t) ), and outputs ( y_1 = q_1(t) ) and ( y_2 = q_2(t) ), as illustrated in the figure below.

• a: Linearize the nonlinear system equations around the equilibrium point and derive the linearized state-space equations.
• b: Obtain the transfer function matrices of the linearized system.
• c: Apply step, sinusoidal, and impulse inputs to the nonlinear system, compute and plot the system’s response. Then repeat the same for the linearized system and compare the results.
• d: For the linearized system, analyze the controllability and observability.
• e: If it is possible to design a state feedback controller and observer for the linearized system, design and implement the closed-loop control system along with the state estimator.
• f: Investigate the effect of parameter variations on the designed control system.
• g: Investigate the effect of measurement noise on the output of the designed control system.

🛠️ Project 2

Description:

This system models the quarter-car vibration as shown in the figure. The input to the system is the force U(t), and the output is the displacement 𝑥1(𝑡).

• a: Find the transfer function between the input u and the output y = x1
• b: To simulate the open-loop behavior of the system, obtain and plot the state variables’ responses considering non-zero initial conditions.
• c: Investigate which classical controllers (P-action, PI-action, or PID-action) can be applied to the system to satisfy the controller design requirements. Implement each controller that is feasible for the system.
• d: Investigate whether an advanced state vector feedback controller (SVFC) can be designed for the system. If yes, design and implement such a controller that meets the specified requirements.
• e: Design a continuous-time full-state observer to estimate the system’s state variables and demonstrate that the estimation performs correctly.

🛠️ Project 3

Description:

This project aims to investigate the lateral dynamics of a vehicle based on the bicycle model and design its control. The system model is illustrated in the figure below.

• a: Considering the steering angle input 𝛿(𝑡) as:a) unit impulse,b) step input,c) A sinusoidal input (with one period), simulate the open-loop lateral dynamics equations of the vehicle.
• b: Implement the state vector feedback control strategy for this system.
• c: For the state vector feedback control system designed in the previous part, design a continuous-time full-order state observer that, during the implementation of the closed-loop state vector feedback control system, can simultaneously estimate the state variables and provide them to the controller. Then, perform a complete simulation of the resulting closed-loop system.
• d: Assume that in the above vehicle system model, there is a disturbance input and also measurement noise in the output signals. Investigate whether the designed control system still performs correctly under these conditions.

🛠️ Project 4

Description:

Consider again the dynamic system from Project 1. In this section, we aim to discretize the continuous-time system with a sampling time 𝑇, and then design a finite-time settling digital controller (Finite Time Settling Control: FTSC) along with a two-stage finite-time settling observer that achieves zero steady-state estimation error.

• a: Discretize the state-space equations of the system.
• b: Design and implement a finite-time digital feedback controller with zero steady-state error, without considering the observer. Demonstrate that the steady-state error is eliminated.
• c: Considering the observer, design and implement a fully digital closed-loop control system with state estimation that ensures zero steady-state error
• d: Investigate the effect of system parameter variations.
• `e:v Assuming the presence of noise in the output, does the designed system still function correctly?