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1. Course Overview

Welcome to the world of Automatic Control of Continuous Linear Systems! This course is a foundational pillar in engineering, equipping students with the principles and techniques to analyze, design, and simulate automatic control systems for continuous-time linear systems. The curriculum bridges classical control theory and modern state‑space methods, emphasizing both theoretical understanding and practical implementation using tools such as MATLAB & Simulink. The course is typically offered in a blended format, combining lectures, tutorials, and hands‑on laboratory sessions and is supported by a dedicated Moodle site for resources, quizzes, and assignments.

2. Learning Objectives

Upon successful completion of this course, students will be able to:

· Model physical systems (mechanical, electrical, thermal, fluid) using differential equations, transfer functions, and state‑space representations.

· Analyze system behaviour in both time and frequency domains, including transient response, steady‑state error, and stability.

· Design classical controllers (P, PI, PID, lead‑lag) and tune them using methods such as Ziegler‑Nichols.

· Apply frequency‑domain analysis techniques (Bode, Nyquist, Nichols) to assess relative stability and robustness.

· Use root‑locus methods to visualize and design closed‑loop pole placement.

· Implement state‑space design (controllability, observability, state feedback, observers) for more complex systems.

· Simulate and validate control systems using MATLAB & Simulink.

3. Prerequisites

· Mathematics: Ordinary differential equations, Laplace transforms, complex numbers, linear algebra.

· Signals and Systems: Basic concepts of continuous‑time signals, convolution, Fourier analysis.

· Physics: Fundamentals of mechanics and electrical circuits.

· Programming: Elementary experience with MATLAB/Simulink is recommended.

4. Syllabus – Weekly Breakdown

Week	Topic	Key Activities
1	Introduction to Automatic Control – Historical overview, motivation, classification of control systems (open‑loop vs. closed‑loop, linear vs. nonlinear, continuous vs. discrete).	Quiz 1, Reading assignment
2	Mathematical Modelling – Differential equations, linearisation, block diagram algebra, reduction rules.	Homework 1
3	Transfer Functions & Laplace Domain – Poles, zeros, impulse/step responses, convolution. Mason’s gain rule.	Lab 1
4	Time‑Domain Specifications – Rise time, settling time, overshoot, steady‑state error constants (position, velocity, acceleration error coefficients).	Quiz 2, Homework 2
5	Stability Analysis – Routh‑Hurwitz criterion, relation between closed‑loop pole locations and stability.	Lab 2
6	Root Locus Method – Drawing rules, gain selection, analysis of system performance from root locus plots.	Homework 3, Quiz 3
7	Frequency Response – Bode plots (magnitude/phase), Nyquist plots, Nichols charts, gain and phase margins.	Mid‑term written exam
8	Nyquist Stability Criterion – Mapping the Nyquist contour, determination of closed‑loop stability from open‑loop frequency response.	Lab 3
9	PID Controllers – P, I, D actions, transfer function, effects on system dynamics, tuning rules (Ziegler‑Nichols, Cohen‑Coon, etc.).	Homework 4
10	Lead/Lag Compensation – Phase lead, phase lag, lead‑lag networks; design via Bode plots and root locus.	Quiz 4, Lab 4
11	Introduction to State‑Space – State variables, state equations, solution of the state equation (state transition matrix), relationship to transfer functions.	Homework 5
12	Controllability & Observability – Kalman rank conditions, canonical forms (controllable, observable, diagonal, Jordan).	Lab 5
13	State Feedback & Observers – Pole placement via state feedback, full‑order and reduced‑order observers, separation principle.	Homework 6
14	Advanced Topics – Introduction to optimal control (LQR), robust control concepts, anti‑windup techniques for PID.	Final exam review, Course evaluation
15	Final Written Exam – Comprehensive assessment of all topics.

5. Laboratory Exercises

Practical skills are developed through six mandatory laboratory sessions (each worth 3 points). A typical lab session follows this structure:

· Pre‑lab homework (submitted electronically) – 1 point.

· In‑lab work – 1 point.

· Post‑lab quiz – 1 point.

Lab #	Title	Main Activities
1	Modelling & Simulation in Simulink	Build block diagrams, simulate step responses of first‑ and second‑order systems.
2	PID Tuning on a DC Motor	Use Ziegler‑Nichols ultimate‑gain method to tune a PID controller for a DC motor speed loop.
3	Frequency Response Analysis	Obtain Bode and Nyquist plots using MATLAB, compute gain/phase margins.
4	Root Locus Design	Design a lead compensator to meet transient response specifications.
5	State‑Space Control	Implement state feedback pole placement on a simulated inverted pendulum.
6	Observer Design	Build a full‑order observer and compare state estimates with true states.

6. Assessment and Grading

The overall grade is composed of continuous assessment and a final exam (typical scheme):

Component	Weight	Description
Laboratory exercises	6%	Completion of 6 labs (each 3 points, total 18 points, scaled to 6%).
Homework assignments	6%	6 graded problem sets (submitted online via Moodle).
Quizzes	6%	Short online quizzes on Moodle (after each lecture).
Mid‑term written exam	35%	Covers weeks 1–7; required minimum 40% to qualify for final exam.
Final written exam	47%	Comprehensive, 2‑hour closed‑book exam.
Oral exam	(0–41%)	Optional or mandatory depending on performance; threshold 50% to pass overall.

Note: Students must complete all laboratory exercises to receive a passing grade.

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