Course detail

Simulation of Dynamic Systems

FSI-FSI Acad. year: 2027/2028 Winter semester

Before a prototype of a machine, structure or vehicle is built, simulation answers the key questions. How will the system behave in operation? Will it withstand even the most adverse operating conditions? Which parameters govern its behaviour, and how should they be set? This course teaches you to ask such questions correctly and to answer them with a model you can trust.

We start with the fundamentals: what a model is, where its validity ends, and how a numerical solver turns differential equations into a time response. We then progress from first-order systems through coupled systems of equations with multiple degrees of freedom to designing modifications of real systems for specific operating conditions. You will learn to solve the same problem in several ways: as a MATLAB script, as a Simulink block diagram and as a Simscape physical network. Comparing these approaches is the best check that the model is free of errors.

In the second half of the semester, simulation stops being a one-off calculation. You will run hundreds of simulations at once, find out which parameters matter, identify a robust design and learn to calibrate a model against measured data. The methods are demonstrated on mechanical systems, including spatial mechanisms with 3D animation of motion, and you will then apply them to electrical, thermal and multiphysics models. When a full model is too slow for such work, you will replace it with a reduced-order or surrogate model that computes the same result in a fraction of the time. You will also try out how AI agents can help build and verify models, and why you must be able to check their outputs.

Teaching takes place in a computer lab. Lectures explain the principles using concrete engineering examples, and exercises immediately turn them into your own models. The semester culminates in an individual simulation study of a real system of your choice, which you present in week 13.

Language of instruction

Czech

Number of ECTS credits

5

Supervisor

Ing. Filip Kšica, Ph.D.

Department

Institute of Automation and Computer Science

Entry knowledge

Knowledge from previous studies is assumed, namely the ability to:

  • formulate and solve simple linear differential equations, use the Laplace transform and derive a transfer function,
  • work with matrices, including computing eigenvalues and eigenvectors,
  • apply the fundamentals of kinematics and dynamics of a particle and a rigid body,
  • formulate the equations of simple physical systems: mechanical (mass, spring, damper), electrical (resistor, capacitor, inductor) and thermal (heat capacity, thermal resistance),
  • describe the fundamentals of control theory of dynamic systems (feedback, stability, step and frequency response),
  • write a script and a function in MATLAB, use a loop, work with variables and plot a graph.

Rules for evaluation and completion of the course

The course is completed by course-unit credit and an examination; credit is a prerequisite for registering for the examination.

Requirements for course-unit credit

  1. Active participation in exercises. Attendance is compulsory and recorded; one absence notified in advance is tolerated, and any further absence must be compensated by completing the tasks of the missed session. Lectures are optional; however, their content is assumed in the exercises and is not explained again.
  2. Continuous notes from all exercises submitted to the e-learning system.
  3. Semester project: an individual simulation study of a chosen real dynamic system (description of the system, practical question, inputs, outputs, parameters, initial conditions, simulation plan and documented solution), presented in week 13.

Assessment

  • Semester project and its presentation: 0–20 points.
  • Written part of the examination (test and simple problems): 0–50 points.
  • Oral part of the examination (course content and the semester project): 0–30 points.

At least 50 % of the points must be obtained separately in the written and in the oral part. The final grade corresponds to the total number of points (maximum 100) according to the ECTS scale under Art. 14 of the BUT Study and Examination Rules. The lecture content is examined in full.

Artificial intelligence tools may be used in the semester project; the student states what they were used for and is responsible for the correctness of the results. They are not permitted in the written part of the examination.

Aims

A graduate of the course is able to:

  1. define, for a given engineering question, the system boundaries, its inputs, states, parameters and outputs, and justify the simplifications adopted in the model,
  2. formulate the equations of motion of a mechanical system with one or more degrees of freedom, convert them into a state-space description and transfer functions, and compute natural frequencies and mode shapes,
  3. implement a model as a MATLAB script, a Simulink block diagram and a Simscape physical network for mechanical systems, including spatial mechanisms, as well as for electrical, thermal and multiphysics systems, and verify the correctness of the computation by comparing different solution approaches and the sensitivity of the result to solver settings,
  4. design and run a batch of repeated simulations (design of experiments, sensitivity analysis, Monte Carlo) and use it to select robust design parameters,
  5. identify a model and calibrate its parameters from real measured data, and assess the agreement of the model with measurements on an independent data set,
  6. produce a simulation study from the formulation of the question to a conclusion assessing the validity of the results, critically evaluate the outputs of the tools used, including AI, and present the results clearly.

Study aids

The course e-learning provides lecture slides, exercise assignments, sample scripts and models in MATLAB, Simulink and Simscape, and the assignment and structure of the semester project.

The study programmes with the given course

Programme B-STR-P: Engineering, Bachelor's
specialization AIŘ: Applied Computer Science and Control, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Syllabus


  1. Model, modelling and simulation: from an engineering question to a model, purpose and limits of validity of a model, types of models, verification and validation; first steps in MATLAB and Simulink.

  2. Numerical solution of differential equations: how a solver turns equations into a time response, accuracy and stability of the computation, choosing and configuring a solver, and why a smooth graph does not guarantee a correct result.

  3. Models of basic physical problems: from physical laws to equations of motion, initial conditions, a single-degree-of-freedom system and the effect of damping on its behaviour.

  4. Linear models: transfer function and state-space description as two views of the same system, poles and stability, response in the time and frequency domains.

  5. Physical modelling in Simscape: models assembled from physical components instead of manually derived equations, the acausal approach and its comparison with a signal-based Simulink model.

  6. Coupled systems of equations: multi-degree-of-freedom systems in mechanics, electrical engineering and other fields, matrix formulation and coupling of states, natural frequencies and mode shapes, modal decomposition, resonance.

  7. Case study of a real multi-degree-of-freedom system: building a model from operating conditions and loads, simulating the behaviour of the system in operation, detecting critical states (such as resonance), and designing and optimising modifications that eliminate them.

  8. Simulation experiments: from one simulation to hundreds, design of experiments, sensitivity analysis, the effect of uncertainties and the search for a robust optimum.

  9. Model identification and calibration: estimating parameters or an entire model from measured data and verifying that the model matches reality.

  10. Multibody modelling: spatial mechanisms, joints and constraints in Simscape Multibody, importing geometry from CAD and 3D visualisation of motion.

  11. Multiphysics modelling: coupling mechanical, electrical and thermal domains in a single model, electromechanical energy conversion and energy flow between domains.

  12. Advanced approaches: reduced-order and surrogate models for cases where the full model is too slow, and AI agents as assistants in building models and simulation experiments, including critical verification of their outputs.

  13. Presentations of semester projects.

Computer-assisted exercise

26 hours, compulsory

Syllabus


  1. First steps in MATLAB and Simulink: scripts, vectors, plots and simulation models of simple physical problems.

  2. Numerical solvers in practice: implementing a simple method, comparison with MATLAB and Simulink solvers, effect of step size and tolerances on the result.

  3. Formulating and solving equations of motion of basic physical problems in MATLAB and Simulink and comparison with the analytical solution.

  4. Transfer function and state-space model in MATLAB, analysis of the response in the time and frequency domains.

  5. First model in Simscape and its verification against a Simulink model.

  6. A multi-degree-of-freedom system solved in several ways (Simulink, state-space model, Simscape), computation of natural frequencies and mode shapes, and comparison of the results.

  7. Case study: model of a real system for given operating conditions, simulation of its behaviour, design of modifications and search for optimal parameters.

  8. Hundreds of simulations with one script: automation of experiments, sensitivity analysis and parameter optimisation.

  9. Identification of a model from real measured data and its validation.

  10. Model of a spatial mechanism in Simscape Multibody with 3D visualisation of motion.

  11. Building a multiphysics model coupling electrical, mechanical and thermal parts and tracking the energy flow between them.

  12. Surrogate model and working with an AI agent; semester project consultations.

  13. Presentations of semester projects, awarding of course-unit credits.