Principles of Automatic Control Course

Lesson 1 • Control System Performance Criteria

Introduces stability, accuracy, and speed as the three primary performance goals. Frames these criteria as design targets used throughout the course.

Lesson 2 • System Components and Variables

Identifies plants, actuators, sensors, and controllers as functional blocks. Connects component roles to overall system behaviour.

Lesson 3 • Introduction to Control Engineering

Defines control systems and their role in automation and engineering. Establishes vocabulary and context for all subsequent sections.

Lesson 1 • Block Diagram Algebra

Reduces complex interconnected systems to single equivalent transfer functions. Prepares students for closed-loop analysis in later sections.

Lesson 2 • State-Space Representation

Introduces state variables as an alternative to transfer functions for multi-input, multi-output systems. Connects state-space to transfer function forms.

Lesson 3 • Transfer Function Representation

Defines the transfer function as the ratio of output to input in the s-domain. Links mathematical models to block diagram representations.

Lesson 4 • Differential Equations of Physical Systems

Applies Newton's and Kirchhoff's laws to derive governing equations. Provides the mathematical foundation for all subsequent modelling techniques.

Lesson 1 • Higher-Order System Approximations

Extends second-order analysis to higher-order systems using dominant pole concepts. Validates approximations through comparison with exact responses.

Lesson 2 • Standard Test Input Signals

Defines step, ramp, parabolic, and impulse inputs used for system evaluation. Establishes a common testing framework applied throughout the section.

Lesson 3 • Steady-State Error Analysis

Quantifies steady-state error for different input types using error constants. Links system type number to achievable accuracy.

Lesson 4 • Second-Order System Response

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

Lesson 1 • Root Locus Method

Traces closed-loop pole movement as gain varies using root locus rules. Enables graphical prediction of stability and transient behaviour.

Lesson 2 • Concept of Stability in Control

Defines BIBO and asymptotic stability in terms of pole locations. Establishes stability as a prerequisite for all controller design work.

Lesson 3 • Relative Stability Measures

Quantifies how far a system is from instability using gain and phase margins. Connects relative stability to practical robustness requirements.

Lesson 1 • Frequency Response Fundamentals

Defines frequency response as the steady-state output to sinusoidal inputs. Connects magnitude and phase to system transfer function evaluation.

Lesson 2 • Nyquist Stability Criterion

Applies the Nyquist criterion to assess closed-loop stability from open-loop plots. Handles systems with open-loop poles in the right half-plane.

Lesson 3 • Nichols Chart and Closed-Loop Frequency Response

Uses the Nichols chart to read closed-loop frequency response from open-loop data. Extracts bandwidth, peak magnitude, and resonant frequency.

Lesson 4 • Correlation Between Time and Frequency Domains

Establishes quantitative links between frequency-domain metrics and time-domain specifications. Enables designers to translate between the two domains.

Lesson 1 • Proportional, Integral, and Derivative Control

Explains the effect of P, I, and D actions on system response individually. Builds intuition for combined PID behaviour before formal tuning.

Lesson 2 • Lead and Lag Compensator Design

Designs phase-lead and phase-lag compensators to improve transient and steady-state performance. Uses Bode and root locus methods for compensator placement.

Lesson 3 • Controller Implementation Considerations

Addresses practical issues including actuator saturation, integrator windup, and derivative filtering. Bridges the gap between theoretical design and real implementation.

Lesson 4 • Lead-Lag Compensator Design

Combines lead and lag elements to simultaneously improve speed and accuracy. Addresses design trade-offs when single compensators are insufficient.

Lesson 1 • State Observer Design

Constructs full-order and reduced-order observers to estimate unmeasured states. Applies separation principle to combine observer with state feedback.

Lesson 2 • Introduction to Optimal Control

Introduces the linear quadratic regulator as a systematic optimal state feedback design. Explains the role of Q and R weighting matrices in performance trade-offs.

Lesson 3 • Controllability and Observability

Defines controllability and observability as prerequisites for state-space design. Provides matrix tests to verify these properties before proceeding.

Lesson 4 • Full-State Feedback and Pole Placement

Designs state feedback gain matrices to place closed-loop poles at desired locations. Connects desired transient specifications to target pole positions.

Lesson 1 • Stability of Discrete-Time Systems

Maps stability conditions from the s-plane to the z-plane unit disk. Applies the Jury stability test as the discrete analog of Routh-Hurwitz.

Lesson 2 • Z-Transform and Discrete Transfer Functions

Applies the z-transform to convert discrete-time equations into algebraic form. Derives discrete transfer functions from continuous models.

Lesson 3 • Discrete Controller Design

Designs digital PID and pole-placement controllers directly in the z-domain. Compares emulation-based and direct discrete design approaches.

Lesson 4 • Practical Digital Implementation

Addresses quantisation, computational delay, and finite word-length effects in real processors. Provides guidelines for robust digital controller implementation.