Applied Control Systems 1: autonomous cars: Math + PID + MPC Course Syllabus

An in-depth, simulation-driven control engineering course that equips you with the modelling, PID, and MPC skills needed to design robust, high-performance systems. This course spans approximately 6 hours of content, structured into eight focused modules that progress from dynamic system modelling to real-world deployment. Each module combines theoretical foundations with hands-on MATLAB/Simulink implementations, enabling you to simulate and analyze control strategies used in autonomous vehicles and industrial systems.

Module 1: Dynamic System Modelling

Estimated time: 0.75 hours

• Deriving transfer functions from first-order physical systems
• Deriving transfer functions from second-order physical systems
• Building state-space representations
• Converting between transfer function and state-space forms

Module 2: Time- and Frequency-Domain Analysis

Estimated time: 1 hour

• Step response analysis for system characterization
• Impulse response analysis
• Bode plot analysis and frequency-domain behavior
• Poles, zeros, and stability criteria using Routh, Nyquist, and root locus

Module 3: PID Control Fundamentals

Estimated time: 1 hour

• Proportional control action and its effect on rise time
• Integral action and steady-state error reduction
• Derivative action and overshoot damping
• Closed-loop tuning using Ziegler–Nichols, Cohen–Coon, and manual methods

Module 4: Advanced PID Implementation

Estimated time: 0.75 hours

• Anti-windup strategies for integral control
• Filter design in PID controllers
• Discrete-time implementation of PID controllers
• Handling noise, saturation, and non-ideal actuator dynamics

Module 5: Introduction to Model Predictive Control (MPC)

Estimated time: 1 hour

• MPC theory: prediction and control horizons
• Cost function formulation
• Constraint handling on inputs, states, and outputs

Module 6: MPC Design & Simulation

Estimated time: 1 hour

• Setting up MPC controllers in MATLAB/Simulink
• Using built-in MPC toolboxes
• Case study: multivariable process control
• Case study: temperature control and constrained tracking

Module 7: Robustness & Performance Evaluation

Estimated time: 0.75 hours

• Sensitivity functions and robustness analysis
• Gain and phase margins
• Worst-case disturbance rejection
• Comparative analysis of PID vs. MPC in practical scenarios

Module 8: Real-World Applications & Code Deployment

Estimated time: 0.75 hours

• Generating C/C++ code from Simulink for embedded systems
• Hardware-in-the-loop testing
• Integration tips for real-time control applications

Prerequisites

• Familiarity with basic MATLAB programming
• Understanding of fundamental control theory concepts
• Basic knowledge of linear systems and differential equations

What You'll Be Able to Do After

• Formulate mathematical models of dynamic systems using transfer functions and state-space representations
• Design and tune PID controllers for stable and responsive system performance
• Implement Model Predictive Control (MPC) for multi-variable systems with constraints
• Simulate and analyze control strategies in MATLAB/Simulink
• Deploy control algorithms to embedded platforms using automatic code generation