MATLAB Simulink modelling

Problem Statement

Students often struggle to translate theoretical differential equations into working simulation models, limiting their understanding of dynamic systems. With increasing amount of students taking this subject, personal assistance in class was needed for both the teacher and students.

What I did

I run hands-on exercise sessions where students learn to turn differential equations into working Simulink models, debug them, and interpret results. Below you will find an overview of tasks offered by me and sample solution examples for some of the most interesting.

As a result:

By taking the position, I saved 8 hours per week previously taken by the university research staff.
Exam passing rate was increased by 11%
One class slot per week was hold by me independently, therefore saving Professor's time.
I receive personal appreciation from up to 10 students every semester.

How I help students succeed

My role as a tutor:

Hosted my own exercise sessions as a course tutor (guided practice, Q&A, individual support).
Explained concepts in a structured “recipe” format: model → implement → verify → interpret.
Helped students build confidence with Simulink essentials: integrators, gains, sums, feedback loops, initial conditions, switches, and different packages.

What students get from my sessions:

Clear step-by-step methods (what block goes where and why).
Practical skills of creating Simulink scripts and models.
Skills how to spot and fix typical mistakes (sign errors, wrong IC placement, wrong units, unstable solver settings).
Quick and understandable roadmap to understand, implement and expand solutions.

I teach - they solve

Undamped Oscillator

Students model a basic oscillatory system and learn how to implement second-order dynamic behavior in Simulink. The focus is on building feedback structures with integrators, setting initial conditions correctly, and interpreting oscillatory motion in simulation results.

Nonlinear Forced Oscillator

This exercise introduces nonlinear system dynamics with external excitation. Students simulate how nonlinear damping and periodic forcing affect system response and explore solver settings, numerical stability, and response interpretation.

Mathematical Pendulum

Students model pendulum motion and compare nonlinear behavior with its linear approximation. The task highlights how modelling assumptions influence results and how parameter changes affect oscillation characteristics.

Parachutist Model

This exercise models the vertical motion of a falling parachutist, including aerodynamic drag and a sudden change in system behavior when the parachute deploys. Students work with switching dynamics, parameter scripts, and interpretation of transient responses.

Bouncing Ball Model

Students simulate a ball undergoing free fall and elastic contact with the ground. The task focuses on modelling piecewise dynamics, handling contact events, and analyzing energy dissipation over repeated impacts.

Stick–Slip Conveyor Belt System

This exercise addresses friction-driven motion where sticking and slipping phases alternate. Students learn to model discontinuous behavior, friction effects, and oscillatory responses typical for mechanical transport systems.

Predator–Prey (Lotka–Volterra) Model

Students simulate interacting populations using coupled nonlinear dynamics. The exercise includes equilibrium analysis, system linearization via Jacobian matrices, and interpretation of dynamic behavior using state-space representations.

Lotka-Volterra Prey-Predator Model

In this exercise, students model biological population dynamics using the classical Lotka–Volterra model. The task focuses on implementing coupled nonlinear differential equations in Simulink, analyzing system behavior under different initial conditions, and interpreting oscillatory population dynamics.

Special attention is given to equilibrium points, stability behavior, and the physical interpretation of model parameters such as reproduction rate, predation rate, and mortality effects. Students also explore how parameter variations influence long-term system evolution and phase-plane trajectories.

A key part of the task is the linearization of the nonlinear system around equilibrium points using the Jacobian matrix. From this linearization, students derive a state-space representation of the system, enabling stability analysis, local dynamic behavior assessment, and comparison between nonlinear simulation results and their linear approximations.

Falling Body with Parachute Deployment

This exercise focuses on modelling the vertical motion of a falling parachutist under gravity and aerodynamic drag using MATLAB/Simulink. Students implement the nonlinear equation of motion including gravitational force and quadratic air resistance, and simulate how velocity and altitude evolve over time.

A key aspect of the task is modelling the parachute opening as a switching event where the effective drag area changes abruptly, leading to a significant alteration of the system dynamics, as well as Look-up Table to implement height-dependent air density.

The exercise highlights nonlinear dynamics, event-driven modelling, and interpretation of transient and steady-state behavior in physical simulation systems.

References and Links

Lecture and exercises were created by Prof. Dr.-Ing. Thorsten Brandt at Rhine-Waal University of Applied Sciences.
Sample solutions were created by Grigorii Fediakov, a student of Rhine-Waal University of Applied Sciences.

LinkedIn | +1 (917) 916 4549 | Brooklyn, NY 11226 | feduakov17@gmail.com

Page updated

Google Sites

Report abuse