Advanced Digital Control Systems

This repository contains a collection of MATLAB and Simulink implementations covering advanced control strategies for linear systems, progressing from classical state-space methods to modern constrained optimization techniques.

Repository Overview

The repository is structured as a progressive path in digital control:

1. Algebraic Design: Closed-loop analysis and algebraic controller design via the Diophantine equation, covering pole placement, plant pole cancellations, steady-state constraints, and unstable plants.
2. LQR Fundamentals & Tracking: Infinite-horizon Linear Quadratic Regulation, including augmented state-space models for integral action and steady-state tracking.
3. LQR Receding Horizon: Finite-horizon optimal control and the transition towards Predictive Control, featuring Quadratic Programming (QP) to handle physical constraints.
4. Model Predictive Control (MPC): Closed-loop MPC controllers with hard constraint enforcement on inputs and outputs, applied to open-loop unstable plants.

Repository Structure

• /01_Algebraic_Design: Closed-loop 1-DOF analysis and algebraic controller design (Diophantine equation, Sylvester matrix).
• /02_LQR_Fundamentals_and_Tracking: Zero regulation and integral tracking with Simulink schemes.
• /03_LQR_Receding_Horizon: Finite-horizon optimization and input/state saturation handling.
• /04_Model_Predictive_Control: Constrained output tracking and full state regulation via MPCtools.

Requirements

• MATLAB (including Control System Toolbox and Optimization Toolbox).
• Simulink.
• MPCtools toolbox (required for the MPC module).