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 (Simulink).

2. Numerical simulation:

The student should be able to simulate a state-space model in a computer. This entails implementation of explicit and implicit ODE/DAE methods, and to know principles of state-of-the-art ODE solvers (e.g. as implemented in Matlab). The students will be exposed to the challenges and pitfalls that can be encountered in numerical simulations.

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. The students will know the Lagrange method, which allows to model complex multi-body systems easily.

4. Balance laws/fluid systems:

The student should learn the basic principles of balance laws, and use some of them to formulate simple models of process systems.

Learning outcome

Knowledge:

At the end of the course, the student should know:

1 Models, model properties and some modeling tools:

- Know the most important model classes.

- Understand how to manipulate models / model approximations to change their class.

2 Numerical simulation:

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

- Analyze the stability of one-step methods, and know the difference between different classes, and the consequences this has for choice of method.

- Understand the basics of the Newton method for implicit 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 Lagrange equations of motion.

- Use constrained Lagrange for multi-body dynamics.

4 Balance laws/fluid systems:

- Know and be able to formulate the basic balance laws.

Skills:

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

1 Recognize models of different forms and their properties

2 Implement explicit and implicit Runge-Kutta methods.

3 Write down equations of motion for simple and multi-body systems of rigid bodies.

4 Understand basic balance laws.

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. Approved assignments are required. The lectures will be in English.

Compulsory assignments

• Exercises

Recommended previous knowledge

TTK4105 Control Systems.

Course materials

To be announced in class.

Credit reductions