Servomechanism Course

Lesson 1 • Physical Units and System Variables

Establishes the physical quantities—position, velocity, torque, and current—used in servo analysis. Provides unit consistency for later mathematical modelling.

Lesson 2 • Core Components of a Servomechanism

Identifies actuators, sensors, controllers, and plant elements within a servo loop. Connects each component to its functional role.

Lesson 3 • Introduction to Control Systems

Defines open-loop vs. closed-loop control and establishes why feedback is essential. Sets the vocabulary used throughout the course.

Lesson 1 • Laplace Transform and Transfer Functions

Converts time-domain differential equations into s-domain transfer functions. Enables algebraic manipulation of system dynamics.

Lesson 2 • Differential Equations for Mechanical Systems

Applies Newton's laws to derive equations of motion for rotational and translational loads. Establishes the mathematical foundation for transfer function derivation.

Lesson 3 • Electrical Circuit Modelling

Models DC motor armature circuits and amplifier stages using Kirchhoff's laws. Links electrical dynamics to mechanical load equations.

Lesson 4 • Model Validation and Simplification

Compares model predictions against measured data and applies order-reduction techniques. Ensures models are accurate yet computationally tractable.

Lesson 1 • Standard Test Inputs and System Response

Defines step, ramp, and parabolic inputs and derives the corresponding output responses. Provides a consistent basis for comparing system performance.

Lesson 2 • Steady-State Error Analysis

Calculates position, velocity, and acceleration error constants for different system types. Determines how system type affects tracking accuracy.

Lesson 3 • Transient Response Specifications

Quantifies rise time, peak time, overshoot, and settling time from step responses. Connects these metrics to damping ratio and natural frequency.

Lesson 1 • Gain and Phase Margin Evaluation

Defines gain margin and phase margin as quantitative stability indicators. Establishes minimum margin guidelines for robust servo operation.

Lesson 2 • Nyquist Stability Criterion

Applies the Nyquist criterion to determine closed-loop stability from open-loop frequency response. Handles systems with right-half-plane poles and time delays.

Lesson 3 • Sensitivity and Complementary Sensitivity

Introduces sensitivity functions to quantify disturbance rejection and robustness. Connects loop shaping objectives to sensitivity function bounds.

Lesson 4 • Bode Plot Construction and Interpretation

Constructs magnitude and phase Bode plots from transfer functions using asymptotic approximations. Identifies gain crossover and phase crossover frequencies.

Lesson 1 • Gain Selection Using Root Locus

Selects controller gain to achieve desired damping ratio and natural frequency on the root locus. Verifies performance specs through closed-loop pole placement.

Lesson 2 • Root Locus for System Design

Extends root locus to evaluate the effect of adding poles and zeros via compensators. Prepares students for controller design in the following chapter.

Lesson 3 • Root Locus Construction Rules

Derives the rules governing root locus branches as gain varies from zero to infinity. Enables graphical prediction of closed-loop pole trajectories.

Lesson 1 • Lead-Lag and Notch Compensation

Combines lead and lag elements to simultaneously improve transient response and steady-state accuracy. Introduces notch filters for resonance suppression.

Lesson 2 • State Feedback and Pole Placement

Designs full-state feedback controllers by placing all closed-loop poles at specified locations. Introduces integral augmentation for zero steady-state error.

Lesson 3 • PID Controller Structure and Tuning

Explains proportional, integral, and derivative actions and their individual effects on servo response. Covers Ziegler-Nichols and analytical tuning methods.

Lesson 4 • Lag Compensator Design

Designs phase-lag networks to improve steady-state accuracy without significantly reducing stability margins. Addresses low-frequency gain enhancement.

Lesson 1 • AC Servo Motors and Drives

Describes permanent-magnet synchronous and induction motor servo drives and their vector control principles. Links drive output to closed-loop position and velocity control.

Lesson 2 • Drive Amplifier Selection and Interfacing

Covers PWM amplifier topologies, current limiting, and analogue/digital command interfaces. Guides students through drive commissioning and protection setup.

Lesson 3 • DC and Brushless DC Servo Motors

Compares brush-type and brushless DC motors in terms of torque-speed characteristics and control complexity. Covers winding configurations and thermal ratings.

Lesson 4 • Position and Velocity Feedback Sensors

Evaluates encoders, resolvers, tachometers, and linear scales for position and velocity feedback. Addresses resolution, accuracy, and signal conditioning.

Lesson 1 • Adaptive and Gain-Scheduling Control

Introduces parameter adaptation and gain scheduling to handle varying load inertia and friction. Covers model reference adaptive control structure for servo applications.

Lesson 2 • Disturbance Observers and Friction Compensation

Designs disturbance observers to estimate and reject torque disturbances in real time. Applies friction models to compensate for Coulomb and Stribeck effects.

Lesson 3 • Digital Control and Discretization

Converts continuous controllers to discrete-time implementations using z-transform methods. Addresses sampling rate selection, quantisation, and computational delay.

Lesson 4 • Cascade and Multi-Loop Control

Structures position, velocity, and current loops in a cascade hierarchy to improve disturbance rejection and bandwidth. Establishes bandwidth separation rules between loops.