Control Theory Course

Lesson 1 • Signals and Signal Representations

Introduces standard test signals and their mathematical forms used to characterise system responses. Links signal types to performance evaluation.

Lesson 2 • Mathematical Prerequisites Review

Reviews differential equations, complex numbers, and linear algebra essential for system modelling. Connects maths tools to physical system behaviour.

Lesson 3 • Introduction to Control Systems

Defines open-loop and closed-loop architectures and their real-world roles. Establishes vocabulary used throughout the course.

Lesson 4 • System Classification and Properties

Categorises systems by linearity, time-invariance, causality, and order. Provides criteria for selecting appropriate analysis methods.

Lesson 1 • State-Space Representation

Introduces state variables and the state-space formulation as an alternative to transfer functions. Supports multi-input multi-output and modern control analysis.

Lesson 2 • Differential Equation Models

Derives governing equations for physical systems using Newton's and Kirchhoff's laws. Establishes the input-output relationship in the time domain.

Lesson 3 • Transfer Function Representation

Defines the transfer function as the ratio of output to input in the s-domain. Connects poles and zeros to system dynamics and stability.

Lesson 4 • Laplace Transform Methods

Applies the Laplace transform to convert differential equations into algebraic form. Enables transfer function derivation and algebraic system manipulation.

Lesson 1 • First-Order System Response

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

Lesson 2 • Higher-Order System Analysis

Extends time-domain analysis to systems with more than two poles using approximation methods. Identifies dominant dynamics for simplified design.

Lesson 3 • Second-Order System Response

Analyses underdamped, critically damped, and overdamped second-order responses. Connects damping ratio and natural frequency to performance metrics.

Lesson 4 • Stability Concepts in Time Domain

Defines BIBO and Lyapunov stability and relates them to pole locations. Provides the conceptual basis for stability analysis methods in later chapters.

Lesson 1 • Root Locus Method

Traces closed-loop pole trajectories as gain varies using root locus rules. Enables gain selection to meet transient performance specifications.

Lesson 2 • Routh-Hurwitz Stability Criterion

Uses the Routh array to determine the number of unstable poles algebraically. Provides a fast stability check for polynomial characteristic equations.

Lesson 3 • Gain and Phase Margins

Quantifies robustness using gain margin and phase margin from Bode and Nyquist plots. Establishes design targets for robust stability.

Lesson 4 • Nyquist Stability Criterion

Applies the Nyquist plot and encirclement principle to assess closed-loop stability from open-loop frequency data. Handles systems with time delays and RHP poles.

Lesson 1 • Frequency Response Fundamentals

Defines frequency response as the steady-state sinusoidal output-to-input ratio. Connects magnitude and phase to system behaviour across frequencies.

Lesson 2 • Lead and Lag Compensator Design

Designs lead compensators to improve phase margin and lag compensators to reduce steady-state error. Applies frequency-domain specifications to compensator parameter selection.

Lesson 3 • Closed-Loop Frequency Response

Derives closed-loop frequency response from open-loop data using the Nichols chart and M-circles. Links open-loop design to closed-loop bandwidth and peaking.

Lesson 4 • Bode Plot Construction and Interpretation

Constructs asymptotic Bode plots for poles, zeros, and gain factors. Enables rapid graphical assessment of frequency-domain performance.

Lesson 1 • PID Controller Structure and Actions

Explains proportional, integral, and derivative actions and their individual effects on response. Provides the foundation for systematic PID tuning.

Lesson 2 • PID Performance Assessment and Retuning

Evaluates controller performance using variance, IAE, and oscillation indices. Identifies when and how to retune for changed process conditions.

Lesson 3 • Practical PID Implementation Issues

Addresses integrator windup, derivative filtering, and bumpless transfer in real implementations. Ensures reliable controller behaviour under operational constraints.

Lesson 4 • Classical PID Tuning Methods

Applies Ziegler-Nichols and Cohen-Coon rules to derive initial PID parameters from process data. Enables rapid controller commissioning without detailed models.

Lesson 1 • Linear Quadratic Regulator Design

Formulates the LQR problem and solves the algebraic Riccati equation for optimal gain. Balances control effort against state regulation performance.

Lesson 2 • Full-State Feedback and Pole Placement

Designs state feedback gain matrices to place closed-loop poles at desired locations. Achieves specified transient performance for controllable systems.

Lesson 3 • Controllability and Observability

Defines controllability and observability using Gramian and rank conditions. Determines whether pole placement and observer design are feasible for a given system.

Lesson 4 • State Observer Design

Designs Luenberger observers to estimate unmeasured states from outputs. Enables state feedback when full state measurement is unavailable.

Lesson 1 • H-Infinity Control Design

Formulates the H-infinity synthesis problem and solves it via Riccati equations or LMIs. Produces controllers that minimise worst-case disturbance amplification.

Lesson 2 • Nonlinear Control Techniques

Introduces feedback linearisation, sliding mode, and Lyapunov-based design for nonlinear systems. Extends control capability beyond linear approximations.

Lesson 3 • Adaptive Control Concepts

Presents model reference adaptive control and self-tuning regulators for systems with varying parameters. Addresses stability and convergence of adaptive schemes.

Lesson 4 • Introduction to Robust Control

Frames robust control as designing controllers that maintain performance under bounded uncertainty. Introduces H-infinity and structured singular value concepts.