Analysis and Design of Feedback Control Systems Course

Lesson 1 • Mathematical Modelling of Physical Systems

Derives differential equations for mechanical, electrical, and thermal systems. Models serve as the basis for all subsequent analysis techniques.

Lesson 2 • Transfer Functions and Block Diagrams

Converts differential equations to transfer functions using the Laplace transform. Block diagram algebra enables system simplification.

Lesson 3 • Introduction to Control Systems

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

Lesson 4 • System Variables and Signal Flow

Identifies inputs, outputs, disturbances, and error signals in a feedback loop. Connects signal roles to block diagram notation.

Lesson 1 • Steady-State Error Analysis

Computes steady-state errors using error constants for type-zero, type-one, and type-two systems. Reveals the trade-off between system type and disturbance rejection.

Lesson 2 • Second-Order System Dynamics

Analyses underdamped, critically damped, and overdamped responses. Links damping ratio and natural frequency to transient specifications.

Lesson 3 • First-Order System Dynamics

Derives step and ramp responses for first-order transfer functions. Identifies time constant and DC gain as primary descriptors.

Lesson 4 • Standard Test Inputs and System Response

Introduces step, ramp, parabolic, and impulse inputs used to characterise systems. Connects input type to the performance metric it reveals.

Lesson 1 • Relative Stability and Gain Margin

Quantifies how far a system is from instability using gain and phase margins. Connects s-plane geometry to frequency-domain margin concepts.

Lesson 2 • Routh-Hurwitz Stability Criterion

Constructs the Routh array to count right-half-plane poles without factoring. Handles special cases including zero rows and zero first-column entries.

Lesson 3 • Root Locus Method Fundamentals

Traces closed-loop pole paths as gain varies using angle and magnitude conditions. Provides a graphical link between gain and transient performance.

Lesson 4 • Advanced Root Locus Applications

Extends root locus to parameter variations other than gain and to systems with zeros. Supports controller zero placement decisions.

Lesson 1 • Bode Plot Construction and Interpretation

Constructs asymptotic Bode plots for poles, zeros, and gain factors. Reads bandwidth, resonant peak, and crossover frequencies directly from plots.

Lesson 2 • Nyquist Stability Criterion

Applies the Nyquist criterion to determine closed-loop stability from the open-loop frequency response. Handles systems with open-loop poles on the imaginary axis.

Lesson 3 • Frequency Response Fundamentals

Derives the sinusoidal steady-state response from the transfer function evaluated on the imaginary axis. Introduces magnitude and phase as functions of frequency.

Lesson 4 • Bandwidth, Sensitivity, and Robustness

Relates closed-loop bandwidth to speed of response and noise sensitivity. Introduces sensitivity and complementary sensitivity functions as robustness measures.

Lesson 1 • Lead-Lag and PID Equivalence

Combines lead and lag elements into a unified compensator and maps it to PID structure. Enables systematic tuning from frequency-domain specifications.

Lesson 2 • Lag Compensator Design

Designs lag compensators to improve steady-state accuracy without destabilising the system. Contrasts lag with integral action.

Lesson 3 • PID Controller Design

Derives PID transfer functions and tunes parameters using Ziegler-Nichols and analytical methods. Addresses derivative filtering and integral windup.

Lesson 4 • Proportional Control and Its Limitations

Analyses the effect of proportional gain on steady-state error and stability margins. Motivates the need for integral and derivative actions.

Lesson 1 • Lyapunov Stability Analysis

Assesses stability of equilibria using Lyapunov's direct method without solving equations. Provides a framework for nonlinear and robust stability assessment.

Lesson 2 • Similarity Transformations and Canonical Forms

Applies state transformations to obtain controllable, observable, and Jordan canonical forms. Simplifies analysis and reveals system structure.

Lesson 3 • Solution of State Equations

Derives the state transition matrix and computes time responses analytically. Connects eigenvalues of A to system poles and stability.

Lesson 4 • Controllability and Observability

Tests whether states can be driven to any target and whether they can be inferred from outputs. These properties determine feasibility of state feedback and observer design.

Lesson 1 • Luenberger Observer Design

Constructs a full-order observer to estimate unmeasured states from inputs and outputs. Observer pole placement governs estimation speed and noise sensitivity.

Lesson 2 • Full-State Feedback and Pole Placement

Computes state feedback gain vectors to assign closed-loop eigenvalues to desired locations. Ackermann's formula provides a direct algebraic solution.

Lesson 3 • Separation Principle and Output Feedback

Proves that controller and observer poles can be designed independently and combined. Implements output feedback using the observer-based controller structure.

Lesson 4 • Reference Tracking with State Feedback

Adds a precompensator gain to eliminate steady-state error in state feedback systems. Addresses integral action for robust tracking.

Lesson 1 • Digital Control System Design

Discretises continuous controllers and designs directly in the z-domain. Addresses sampling rate selection, quantisation, and computational delay.

Lesson 2 • System Integration and Design Verification

Assembles complete control architectures and verifies all specifications through simulation and analysis. Covers documentation and design review practices.

Lesson 3 • Multivariable System Interaction Analysis

Quantifies coupling between loops using the relative gain array and condition number. Guides loop pairing and decoupling compensator design.

Lesson 4 • Robust Control Concepts

Quantifies stability and performance robustness under structured and unstructured uncertainty. Introduces H-infinity norm as a robustness measure.