# TTK4130 - Modelling and Simulation

# About

### Examination arrangement

Examination arrangement: Written examination

Grade: Letters

Evaluation form | Weighting | Duration | Examination aids | Grade deviation |
---|---|---|---|---|

Written examination | 100/100 | 4 hours | A |

### Course content

The course gives an introduction to methods for modeling and simulation of physical processes, for use in control applications.

1. Models, model properties and modeling tools:

The student will know the most common model classes, and have knowledge of some central model properties that are useful for control systems, and know principles for, and have some practical exposure of, high level modeling tools (both block-oriented (Simulink) and equation/object-oriented (Modelica/Dymola)).

2. Numerical simulation:

The student should be able to simulate a state-space model in a computer. This entails implementation of simple explicit ODE methods, and to know principles of state-of-the-art ODE solvers (e.g. as implemented in Matlab).

3. Rigid body dynamics:

The student should be able to write down equations of motion for simple systems of rigid bodies, which gives a basis for modeling of mechanical systems such as robots, marine vessels, cars, and airplanes.

4. Balanse laws/fluid systems:

The student should learn the principles of balance laws, and use them to formulate simple models of process systems (e.g. new energy, oil- and gas production, chemical process industry).

### Learning outcome

Knowledge:

At the end of the course, the student should:

1 Models, model properties and modeling tools:

- Know the most important model classes.

- Define passivity, and know how to show passivity with the use of energy functions or positive real transfer functions.

- Describe principles behind use of appropriate model inputs and outputs for aggregation and reuse of models.

- Know the difference between causal (block-oriented) and non-causal (equation-oriented) modeling tools, and the practical consequences of this.

- Recognise or transform a system as/to an ordinary differential equation.

2 Numerical simulation:

- Derive and be able to use explicit and implicit one-step methods (Runge-Kutta).

- Analyze stability of one-step methods, and know the difference in definition and interpretation of A-, L-, AN-, B- and algebraic stability, and the consequences this has for choice of method.

- Describe how one-step methods can be extended with variable step lengths.

- Formulate the principles of multi-step methods.

3 Rigid body dynamics:

- Know coordinate-based and coordinate free (dyadics) descriptions of rigid body kinematics.

- Know the most important parameterizations of rotations.

- Be able to differentiate vectors, and understand the concept of angular velocity.

- Know the principles for use of Newton-Eulers equations of motion.

- Use Lagranges equations of motion for simple rigid bodies.

4 Balance laws/fluid systems:

- Know Reynolds transport theorem, and the balance laws.

- Formulate mass balance on differential form (continuity equation) and on integral form for a control volume.

- Formulate the energy balance for a control volume.

- Formulate the impulse balance for a control volume.

- Use mass- and energy balances i multi-component systems.

- Closure of balance equations using thermodynamics.

Skills:

At the end of the course, the student should be able to:

1 Implement realistic models in appropriate high-level modeling tool.

2 Implement explicit one-step methods, and prototype implicit one-step methods.

3 Use kinematics and kinetics to write down equations of motion for simple systems of rigid bodies.

4 Use balance laws and thermodynamics to formulate simple models for process systems.

General competence:

The student should be able to communicate technological issues to both experts and others.

### Learning methods and activities

Lectures and compulsory assignments including computer exercises. 8 of 11 approved assignments are required. If there is a re-sit examination, the examination form may be changed from written to oral. The lectures may be in English if a sufficient number of students requires it.

### Compulsory assignments

- Exercises

### Specific conditions

Exam registration requires that class registration is approved in the same semester. Compulsory activities from previous semester may be approved by the department.

### Recommended previous knowledge

TTK4105 Control Systems.

### Course materials

To be announced in class.

### Credit reductions

Course code | Reduction | From | To |
---|---|---|---|

SIE3025 | 7.5 |

# Timetable

# Examination

Examination arrangement: Written examination

Term | Evaluation form | Weighting | Examination aids | Date | Time | Room * |
---|---|---|---|---|---|---|

Spring | Written examination | 100/100 | A |

If more than one room is listed, you will find your room at Studentweb.