Introduction to Control Systems Analysis with MATLAB

Lesson 1 • System Classification and Terminology

Categorizes systems by order, type, linearity, and time-invariance. Provides the classification framework applied in later chapters.

Lesson 2 • Open-Loop vs. Closed-Loop Systems

Contrasts feedforward and feedback architectures using block diagrams. Motivates feedback as the foundation of robust control.

Lesson 3 • What Is a Control System

Defines control systems through real-world examples and core vocabulary. Establishes the language used throughout the course.

Lesson 1 • Transfer Function Representation

Derives transfer functions from differential equations and defines poles and zeros. Establishes the s-domain model used throughout the course.

Lesson 2 • Laplace Transform Review

Reviews Laplace transform properties essential for converting differential equations to algebraic form. Enables transfer function derivation.

Lesson 3 • State-Space Representation

Introduces state variables and the A, B, C, D matrix formulation. Provides an alternative model form used in modern control.

Lesson 4 • Block Diagram Algebra

Reduces complex block diagrams to single transfer functions using algebraic rules. Prepares students for closed-loop analysis.

Lesson 1 • Plotting and Visualization Fundamentals

Covers plot(), step(), impulse(), and figure formatting. Builds the visualization skills needed for response analysis.

Lesson 2 • MATLAB Environment and Syntax Basics

Covers the MATLAB workspace, command window, and script creation. Provides the programming foundation for all subsequent toolbox work.

Lesson 3 • Defining Models with the Control System Toolbox

Introduces tf(), ss(), and zpk() functions for model entry. Links mathematical representations to MATLAB objects.

Lesson 1 • First-Order System Response

Derives and interprets the step response of first-order systems. Introduces time constant as the key performance parameter.

Lesson 2 • Steady-State Error Analysis

Computes steady-state error using error constants and system type. Connects open-loop gain and type to tracking accuracy.

Lesson 3 • Standard Test Inputs

Defines step, ramp, impulse, and sinusoidal inputs and their Laplace transforms. Establishes the excitation signals used in all response analyses.

Lesson 4 • Time-Domain Analysis in MATLAB

Uses step(), impulse(), and lsim() to extract and compare performance metrics. Reinforces analytical results with computational verification.

Lesson 1 • Introduction to Lyapunov Stability

Presents Lyapunov's direct method for stability assessment without solving differential equations. Extends stability analysis beyond linear systems.

Lesson 2 • Routh-Hurwitz Stability Criterion

Constructs the Routh array to count right-half-plane poles without factoring. Provides an algebraic stability test for polynomial denominators.

Lesson 3 • Concept of Stability

Defines BIBO and asymptotic stability in terms of pole locations. Establishes stability as the prerequisite for all control design.

Lesson 4 • Root Locus Fundamentals

Introduces root locus rules for plotting closed-loop poles vs. gain. Visualizes how gain variation moves poles and affects stability.

Lesson 1 • Bode Plot Construction and Interpretation

Derives asymptotic Bode approximations for poles, zeros, and gain factors. Enables rapid hand-sketching and MATLAB verification.

Lesson 2 • Gain and Phase Margins

Defines gain margin and phase margin as quantitative stability robustness measures. Links margins to closed-loop transient behavior.

Lesson 3 • Frequency Response Fundamentals

Defines frequency response as the steady-state sinusoidal output-to-input ratio. Connects s-domain transfer functions to magnitude and phase plots.

Lesson 4 • Nyquist Criterion and Plots

Applies the Nyquist stability criterion using polar frequency response plots. Handles systems with open-loop poles on the imaginary axis.

Lesson 1 • PID Controller Structure and Tuning

Derives the PID control law and explains each term's effect on response. Introduces Ziegler-Nichols and manual tuning methods.

Lesson 2 • Controller Design and Verification in MATLAB

Implements PID and compensator designs using pidtune(), sisotool, and manual tf() entry. Validates designs against specifications with simulation.

Lesson 3 • Lag Compensator Design

Designs lag compensators to improve steady-state accuracy with minimal phase penalty. Complements lead design for combined objectives.

Lesson 4 • Lead-Lag Compensator Design

Combines lead and lag elements to meet simultaneous transient and steady-state specs. Demonstrates integrated compensator synthesis.

Lesson 1 • Controllability and Observability

Defines controllability and observability matrices and their rank conditions. Determines whether state feedback and observer design are feasible.

Lesson 2 • Integral Action and Reference Tracking

Augments state feedback with integral states to eliminate steady-state error. Extends pole placement to tracking control problems.

Lesson 3 • State Feedback and Pole Placement

Designs full-state feedback gain vectors to place closed-loop poles at desired locations. Connects desired transient specs to pole positions.

Lesson 4 • Luenberger Observer Design

Designs a full-order observer to estimate unmeasured states from outputs. Enables state feedback when full state measurement is unavailable.