Applied Control Systems - Worked Examples

This page contains worked examples organized by concept. Each PDF includes detailed solutions and explanations for a specific concept covered in the course.

Work in progress: this material is being co-developed using GenAI and needs thorough review and correction before being production ready.

Module 1: Dynamical Systems

Topic 1.1: Introduction and System Modelling

• Concept 1.1.1: Introduction
• Concept 1.1.2: Modeling Concepts
• Concept 1.1.3: State Space Models
• Concept 1.1.4: Modelling Methodology

Topic 1.2: Dynamic Behaviour

• Concept 1.2.1: Solving Differential Equations
• Concept 1.2.2: Qualitative Analysis
• Concept 1.2.3: Stability
• Concept 1.2.4: Examples

Topic 1.3: Linear Systems

• Concept 1.3.1: Basic Definitions
• Concept 1.3.2: The Matrix Exponential
• Concept 1.3.3: Input/Output Response
• Concept 1.3.4: Linearisation

Module 2: Control System Concepts

Topic 2.4: State Feedback

• Concept 2.4.1: Reachability
• Concept 2.4.2: Stabilisation by State Feedback
• Concept 2.4.3: Design Considerations
• Concept 2.4.4: Integral Action
• Concept 2.4.5: Output Feedback Basics

Topic 2.5: Transfer Functions

• Concept 2.5.1: Frequency Domain Modeling
• Concept 2.5.2: Determining the Transfer Function
• Concept 2.5.3: Laplace Transforms
• Concept 2.5.4: Block Diagrams and Transfer Functions
• Concept 2.5.5: Zero Frequency Gain, Poles, and Zeros
• Concept 2.5.6: The Bode Plot

Topic 2.6: Frequency Domain Analysis

• Concept 2.6.1: The Loop Transfer Function
• Concept 2.6.2: The Nyquist Criterion
• Concept 2.6.3: Stability Margins
• Concept 2.6.4: Bode’s Relations and Minimum Phase Systems

Module 3: Control System Design

Topic 3.7: PID Control

• Concept 3.7.1: Basic Control Functions
• Concept 3.7.2: Simple Controllers for Complex Systems
• Concept 3.7.3: PID Tuning
• Concept 3.7.4: Integrator Windup
• Concept 3.7.5: Implementation

Topic 3.8: Frequency Domain Design

• Concept 3.8.1: Sensitivity Functions
• Concept 3.8.2: Performance Specifications
• Concept 3.8.3: Feedback Design via Loop Shaping
• Concept 3.8.4: The Root-Locus Method

Topic 3.9: Robust Performance & Fundamental Limits

• Concept 3.9.1: Modeling Uncertainty
• Concept 3.9.2: Stability and Performance in the Presence of Uncertainty
• Concept 3.9.3: System Design Considerations
• Concept 3.9.4: Robust Pole Placement
• Concept 3.9.5: Nonlinear Effects

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Applied Control Systems © Assoc. Prof. William Robertson & Dr Sean McGowan
University of Adelaide