Systems Theory and Modeling

What it is about

You will learn how to model, analyze and prepare finite-dimensional dynamic systems for numerical treatment. The focus is on linear time-invariant state-space models, their properties (stability, controllability, observability), discretization for sampling control loops, and projection methods for model order reduction.

What you will be able to do

• Know important principles of network- and variational-modeling
• Form state-space models for mechanical and electrical systems
• Understand the role of power and energy in the modeling of multiphysical systems
• Determine equilibrium positions and linearize systems
• Compute solutions of linear state-space models
• Analyze stability, controllability and observability
• Understand discretization in sampling control loops
• Apply important integration methods and their properties
• Understand principles of projection-based model order reduction
• Know the main model reduction approaches (modal reduction, balanced truncation, moment matching)

What the module consists of

• Lecture (90 min)Conveying the exam-relevant material, derived and illustrated with examples
• Exercise (45 min)Solving and partially working through exercise sheets; active participation is welcome
• voluntary RepetitoriumDeepening and exam preparation in a small group (optional)

Teaching method

• Board and projector lectureSystematic derivation of methods and illustration with examples
• Lecture notes and accompanying materialMaterial for self-study, pre- and post-lesson preparation
• Exercise sheets with model solutionsApplication and deepening of the lecture material; unsolved problems as additional practice
• Matlab or Python examplesPractical demonstration of numerical methods