# BCT-20306 Modelling Dynamic Systems

## Course

Credits 6.00

 Teaching method Contact hours Lecture 48 Tutorial 20 Practical 28
 Course coordinator(s) dr. ir. LG van Willigenburg dr. RJC van Ooteghem Lecturer(s) dr. ir. LG van Willigenburg dr. RJC van Ooteghem Examiner(s) dr. RJC van Ooteghem dr. ir. LG van Willigenburg

English

### Assumed knowledge on:

BPE-10305 Process Engineering Basics; MAT-24803 Mathematics for Time-Dependent Systems.

### Continuation courses:

BCT-21306 Control Engineering; BCT-31306 Systems and Control Theory; BCT-31806 Parameter Estimation and Model Structure Identification.

### Contents:

What are the most important means of engineers for system design, such as the design of a bioreactor or a climate control system? What are the most important means of scientists to answer research questions such as how bacteria influence the growth rate in a bioreactor or how animal grazing and vegetation are related? Answer: mathematical models and measurements to identify and verify the properties of these models.
From a rough non-mathematical system description, such as a sketch, diagram or drawing, this course teaches you how to construct a mathematical model using scientific knowledge and measurement data.
Furthermore you will learn how to analyse the dynamic behaviour of the modelled system by mathematical analysis. Reality is hardly ever completely described by a mathematical model. The resistance a weed control device experiences when moving through the ground is not known precisely. Not all chemicals or their concentrations, present in a stirred tank or a bioreactor, are known perfectly. In the case of climate control several coefficients which determine heat transport phenomena such as the heat transport through the walls are not known perfectly. Therefore measurement data are useful since they provide additional information regarding these uncertainties. They can therefore be used to improve or verify the mathematical model. One third of the course is devoted to estimation of model parameters from observational data.

### Learning outcomes:

After successful completion of this course students are expected to:
- be able to create a mathematical systems model from a rough non-mathematical description of a simple system through application of scientific knowledge and measurement data;
- be able to translate mathematical systems models into the state-space form which is highly suitable for system analysis and computations;
- know and recognise the different types of variables of a systems model written in state-space form;
- know and be able to determine and compute system behavior, equilibriums, and system properties such as stability from the mathematical systems model in state-space form;
- know and be able to analyse the basic properties of elementary linear systems;
- be able to represent elementary linear systems by means of a state-space model as well as a transfer function and convert one into the other;
- be able to translate transfer functions of elementary linear systems into standard forms that facilitate their analysis;
- know and be able to apply the least squares method to estimate unknown parameters of a mathematical systems model in state-space form.

### Activities:

- lectures;
- tutorials;
- computer exercises;
- experiments;
- self-education.

### Examination:

Observations during practicals. All six practical exercises have to be passed, one may be redone. Otherwise all practical exercises have to be redone next year.
Exam consists of four open questions and has to be passed (i.e. score at least 5.5).

Programme Phase Specialization Period Compulsory for: BAT Biosystems Engineering BSc 2MO BBT Biotechnology BSc 2MO MBT Biotechnology MSc D: Process Technology 2MO MBT Biotechnology MSc E: Environmental and Biobased Biotechnology 2MO MFT Food Technology MSc H: Sustainable Food Process Engineering 2MO