The module "Systems Theory and Modeling" introduces to basic modeling principles of dynamical systems in finite and infinite dimension, which lead to state space models in terms of ordinary or partial differential equations.
The content is divided into four parts on modeling and system theoretic analysis of dynamical systems. A "classical" focus is on linear finite-dimensional state space models in continuous time. In addition, we consider time discretization in state space, and the basic principles of projective model order reduction, which are important ingredients of a "modern" computational and control-oriented treatment of multi-domain physical systems.
In the first part, the module recalls and introduces basic modeling principles of dynamical systems in finite dimension, which lead to state space models in terms of ordinary differential equations. Linearization at an equilibrium generates linear time-invariant (LTI) state space models.
We sum up the necessary concepts from linear algebra and discuss the time-domain solutions of LTI state space models. We analyze fundamental system properties like stability, controllability, and observability, which are relevant for design and control, based on the eigenvalues and invariant zeros of the state space model and suitable state transformations. We clarify relations with the frequency-domain representation employing the Laplace transform.
The third part of the lecture is devoted to discrete-time state space models, which are required in sampled control systems. We present the discretization of state space models using numerical integration, and we show how discrete-time models for mechanical systems can be derived from discrete variational principles. In the latter case, important physical properties (like conservation of energy or other quantities) are naturally preserved in the discrete-time model.
Finally, we give a brief introduction to projection-based methods of model order reduction (MOR) for LTI systems. With modal reduction, Balanced Truncation and Moment Matching, the most popular approaches are presented to reduce a high-dimensional system model to a computationally treatable one, e.g., for real-time control, preserving its dominant properties.
Lecture (90 min) and exercise (45 min) cover all topics relevant for the exam. Additionally, a revision exercise (60 min) is offered on a voluntary basis. It is meant to be attended based on the individual needs and interests of the course participants. As a discussion group with only a small number of participants, this additional exercise serves a) to discuss and deepen the lecture topics and exercise problems, and b) to support the preparation of the exam.
The modules "Systems Theory and Modeling" (English) and "Systemtheorie in der Mechatronik" (German) have large content overlaps and are therefore locked against each other, i.e. you can only register for the exam in one of the two modules.