Modeling and Simulation of Dynamic Systems Course

Lesson 1 • System Classification and Properties

Categorises systems as linear/nonlinear, time-invariant/time-varying, and continuous/discrete. Classification guides model selection in later chapters.

Lesson 2 • What Is a Dynamic System

Defines dynamic systems through time-dependent behaviour and cause-effect relationships. Establishes vocabulary used throughout the course.

Lesson 3 • Physical Domains and Analogies

Maps mechanical, electrical, thermal, and fluid domains onto unified modelling concepts. Cross-domain analogies accelerate model construction in later chapters.

Lesson 4 • State Variables and State Space

Introduces state variables as the minimal information set describing system evolution. Connects state-space representation to differential equation formulations.

Lesson 1 • Deriving Equations from Physical Laws

Applies Newton's laws, Kirchhoff's laws, and energy balances to derive system equations. Systematic derivation prevents modelling errors in simulation.

Lesson 2 • Linearization of Nonlinear Models

Linearises nonlinear equations around equilibrium points using Taylor series expansion. Enables linear analysis tools on inherently nonlinear systems.

Lesson 3 • Bond Graph Modelling Method

Uses bond graphs to model multi-domain systems through power flow representation. Provides a unified graphical derivation method across physical domains.

Lesson 4 • Difference Equations for Discrete Systems

Formulates discrete-time models using difference equations for sampled-data and digital systems. Prepares students for discrete simulation methods.

Lesson 1 • Laplace Transform Fundamentals

Converts time-domain ODEs to algebraic equations using the Laplace transform. Establishes the mathematical bridge to transfer function analysis.

Lesson 2 • Transfer Function Derivation

Derives transfer functions from system equations and block diagrams. Connects algebraic representation to physical input-output behaviour.

Lesson 3 • Stability Analysis in the Frequency Domain

Applies Routh-Hurwitz, Nyquist, and gain/phase margin criteria to assess stability. Stability analysis is prerequisite to simulation result interpretation.

Lesson 4 • Time-Domain Response from Transfer Functions

Computes step, impulse, and ramp responses from pole-zero locations. Links pole placement to transient performance metrics.

Lesson 1 • Eigenvalues, Eigenvectors, and System Modes

Computes eigenvalues of the system matrix to characterise natural modes and stability. Modal analysis explains transient behaviour observed in simulation.

Lesson 2 • Numerical Integration Methods

Implements Euler, Runge-Kutta, and adaptive step methods to solve state equations numerically. Method selection affects simulation accuracy and computational cost.

Lesson 3 • State-Space Representation

Expresses system dynamics as first-order matrix ODEs using A, B, C, D matrices. State-space form is the foundation for numerical simulation and control design.

Lesson 4 • Simulation of Linear State-Space Models

Runs time-domain simulations of state-space models and visualises state trajectories. Simulation output is validated against analytical solutions.

Lesson 1 • Scripting Simulations Programmatically

Implements ODE solvers and state-space simulations through code for reproducibility and automation. Scripted simulations enable parameter sweeps and batch runs.

Lesson 2 • Simulation Configuration and Performance

Configures solver settings, time steps, and output intervals for accuracy and speed. Proper configuration prevents silent errors in long-duration simulations.

Lesson 3 • Building Block-Diagram Models

Constructs dynamic system models using interconnected functional blocks and signal routing. Block-diagram models map directly to transfer function and state-space forms.

Lesson 4 • Model Debugging and Troubleshooting

Identifies and resolves common simulation errors including algebraic loops, unit mismatches, and solver failures. Debugging skills reduce time lost to non-physical results.

Lesson 1 • Phase Plane Analysis

Visualises nonlinear system trajectories in the phase plane to identify equilibria and limit cycles. Phase plane analysis replaces transfer function tools for nonlinear systems.

Lesson 2 • Simulating Nonlinear Models Accurately

Selects solvers and step sizes appropriate for stiff and highly nonlinear systems. Accuracy verification prevents misinterpretation of nonlinear simulation artefacts.

Lesson 3 • Bifurcation and Chaos in Simulations

Simulates parameter-driven bifurcations and identifies chaotic attractors through numerical experiments. Bifurcation diagrams reveal qualitative changes in system behaviour.

Lesson 4 • Sources of Nonlinearity in Physical Systems

Catalogues common nonlinearities such as saturation, dead zone, hysteresis, and Coulomb friction. Recognising nonlinearity sources guides accurate model construction.

Lesson 1 • Parameter Estimation from Data

Fits model parameters to measured data using least-squares and optimisation-based methods. Estimated parameters improve model fidelity before validation testing.

Lesson 2 • Sensitivity Analysis Techniques

Quantifies how output uncertainty propagates from parameter variation using local and global methods. Sensitivity analysis prioritises which parameters require precise measurement.

Lesson 3 • Model Credibility and Reporting

Structures credibility evidence using maturity matrices and simulation reports for stakeholder review. Credibility documentation supports decision-making based on simulation.

Lesson 4 • Verification vs. Validation Defined

Distinguishes model verification (solving equations correctly) from validation (correct equations for reality). Clear V&V definitions prevent misuse of simulation results.

Lesson 1 • Model-Based Design Workflow

Integrates modelling, simulation, code generation, and testing into a unified model-based design process. MBD reduces development time and defect rates in complex systems.

Lesson 2 • Hardware-in-the-Loop Simulation

Integrates physical hardware with real-time simulation models to test embedded controllers. HIL testing bridges simulation and physical deployment safely.

Lesson 3 • Control System Design via Simulation

Designs PID and state-feedback controllers within simulation environments and evaluates closed-loop performance. Simulation-based design reduces physical prototype iterations.

Lesson 4 • Capstone Case Study Integration

Applies all course techniques to a comprehensive multi-domain dynamic system case study. Students demonstrate end-to-end modelling, simulation, validation, and reporting skills.