Digital Textbook

Control Systems

Name: Control Systems
Author: Prof. Mithun Mondal

From a single feedback loop to state-space and digital control — a complete, chapter-by-chapter course in the analysis and design of control systems

Prof. Mithun Mondal EEE / ECE / EIE Undergraduate Course Free & Open Access

7Parts

30Chapters

3Analysis Domains

Welcome

One feedback principle, built one chapter at a time

This is a living, web-native edition of a classic course in Control Systems. Each of the 30 chapters lives on its own page — readable on any device, searchable, and free to share. The journey starts with how we capture a physical system as a mathematical model and ends with the design of controllers that make real machines behave — fast, accurate, and stable.

The sequence follows the standard electrical, electronics, and instrumentation engineering undergraduate syllabus, building from system modeling and transfer functions through time-domain response, stability and the root locus, frequency-domain methods, controller and compensator design, the state-space framework, and finally digital and advanced control. Pick any chapter below to begin, or follow the seven parts in order for a complete first course.

How to use this book. Each part groups chapters by theme — first how a system is modeled and represented, then how it responds in time, how we judge and shape its stability in both the time and frequency domains, and finally how we design controllers for it using classical, state-space, and digital techniques. Click a chapter card to open its dedicated page with concepts, equations, worked reasoning, and figures.

Part 1

Modeling & System Representation

Open vs Closed Loop · Modeling · Laplace · Transfer Functions · Block Diagrams · SFG

01Introduction to Control Systems 02Mathematical Modeling of Physical Systems 03The Laplace Transform and Transfer Functions 04Block Diagram Algebra and Reduction 05Signal Flow Graphs and Mason's Gain Formula

Part 2

Time-Domain Analysis

Test Signals · First Order · Second Order · Transient Specs · Steady-State Error

06Standard Test Signals and System Time Response 07First-Order System Response 08Second-Order Systems and Transient Specifications 09Steady-State Error and Static Error Constants

Part 3

Stability and the Root Locus

BIBO Stability · Routh–Hurwitz · Root Locus · Locus Design

10The Concept of Stability 11The Routh–Hurwitz Stability Criterion 12The Root Locus Technique 13Root Locus Analysis and Design

Part 4

Frequency-Domain Analysis

Bode · Polar · Nyquist Criterion · Gain & Phase Margins · Nichols

14Frequency Response and Bode Plots 15Polar Plots and Nyquist Diagrams 16The Nyquist Stability Criterion 17Relative Stability: Gain and Phase Margins 18Closed-Loop Frequency Response and the Nichols Chart

Part 5

Controllers & Compensator Design

P · PI · PD · PID · Tuning · Lead–Lag Compensation

19Control Actions: P, PI, PD, and PID Controllers 20PID Controller Tuning Methods 21Lead, Lag, and Lead–Lag Compensator Design 22Compensation in the Time and Frequency Domains

Part 6

State-Space Analysis

State Variables · State Transition Matrix · Controllability · Observability · Pole Placement

23State-Space Representation of Systems 24Solution of State Equations and the State Transition Matrix 25Controllability and Observability 26Pole Placement, State Feedback, and Observer Design

Part 7

Digital & Advanced Control

Z-Transform · Sampled-Data · Digital Design · Nonlinear · Optimal & Adaptive

27Sampled-Data Systems and the Z-Transform 28Analysis and Design of Digital Control Systems 29Nonlinear Control Systems 30Modern Control: Optimal, Robust, and Adaptive

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Start Here

Begin with Chapter 1 — Introduction to Control Systems

Every controller rests on one idea: measure the output, compare it to what you wanted, and feed the difference back. The first chapter builds that foundation — open- versus closed-loop control, the language of plants, sensors, and feedback, and the real-world examples the entire course is built around. Open Chapter 1 →