de | en

Advanced Control

Modul MW1420

Dieses Modul wird durch Lehrstuhl für Regelungstechnik (Prof. Lohmann) bereitgestellt.

Diese Modulbeschreibung enthält neben den eigentlichen Beschreibungen der Inhalte, Lernergebnisse, Lehr- und Lernmethoden und Prüfungsformen auch Verweise auf die aktuellen Lehrveranstaltungen und Termine für die Modulprüfung in den jeweiligen Abschnitten.

Modulversion vom WS 2017/8 (aktuell)

Von dieser Modulbeschreibung gibt es historische Versionen. Eine Modulbeschreibung ist immer so lange gültig, bis sie von einer neuen abgelöst wird.

verfügbare Modulversionen
WS 2017/8WS 2012/3


MW1420 ist ein Semestermodul in Englisch auf Master-Niveau das im Wintersemester angeboten wird.

Das Modul ist Bestandteil der folgenden Kataloge in den Studienangeboten der Physik.

  • Allgemeiner Katalog der nichtphysikalischen Wahlfächer
GesamtaufwandPräsenzveranstaltungenUmfang (ECTS)
150 h 45 h 5 CP

Inhalte, Lernergebnisse und Voraussetzungen


1. State space models of linear time-invariant (LTI) dynamical systems
- Mathematical modeling of lumped dynamical systems from physical laws
- Equilibria and stability
- Linearization
- Control tasks and controller structures
2. Mathematical analysis of LTI systems
- Solution of the linear state differential equations
- Eigenvalues, eigenvectors, poles and zeros
- Canonical forms of the state space representation
- System properties: stability, controllability, observability
- Effects of pole-zero cancellations
- Relations between system representations in time and frequency domain
3. Design of linear state feedback controllers in a two-degrees-of-freedom structure
- Eigenvalue placement
- LQR optimal control
4. Design of linear state observers
- Duality between controller and observer design
- Separation principle
- Decoupling control
5. Methods for disturbance attenuation
6. Exact trajectory tracking for linear systems


Upon successful completion of the module the students are able to

- represent real-world dynamical systems in state space form, determine their equilibria and to obtain linear state space models by linearization.
- compute the solutions of linear state differential equations and analyze the dynamical system for stability, observability and controllability.- understand the purpose and advantage of a two-degrees-of-freedom controller structure
- design feedforward controllers that guarantee zero output error in nominal steady state
- design state-feedback controllers using the pole placement method and as a Linear Quadratic Regulator (LQR).
- design a Luenberger state-observer to reconstruct non-measurable states of the system
- further modify the closed loop system by adding measures to cope with different disturbances. - have a basic knowledge about flatness-based feedforward control


We require the students to have basic background in the field of automatic control and the necessary mathematical tools. The prerequisites are in general taught in

- undergraduate courses in higher mathematics dealing with basic linear algebra (matrix computations, eigenvalues, determinants,...) and complex numbers' theory.

- an undergraduate course in automatic control comprising the analysis of dynamical systems in time and frequency domain (Laplace transform, transfer functions, impulse responses, poles and zeros, stability, ), and the design of basic controllers (PID) in single-loop control systems.

Lehrveranstaltungen, Lern- und Lehrmethoden und Literaturhinweise

Lehrveranstaltungen und Termine

VO 2 Advanced Control - Lecture - (MW1420) Mi, 13:30–15:00, MW 1250
UE 1 Advanced Control - Exercise Course - (MW1420) Mi, 15:00–16:00, MW 1250
UE 2 Advanced Control - Tutorial - (MW1420) Fr, 09:00–10:30, MW 1250
KO 1.33 Advanced Control - Revision Course - (MW1420) Termine in Gruppen

Lern- und Lehrmethoden

The teaching follows a classical scheme of weekly lecture (90 min.) + exercise (45 min.), complemented by additional offers, which help the student to catch up quickly with the syllabus in the case of difficulties.

To achieve the study goals, the students are expected to prepare the lectures by a first reading of the announced sections in the lecture notes. They are supposed to try themselves to solve the problems posed in the exercises, before the solutions are presented in class and are made available online.

A set of additional problems is offered for homework. The solutions are also made available online and are presented in the weekly tutorial. This optional offer gives the opportunity to discuss problems and open questions related to the exercises.

The optional revision courses are additional opportunities to clarify open questions concerning the content of the lecture. Moreover, they allow to discuss topics and advanced questions that go beyond the scope of the course.


The lectures and exercises will be written on the blackboard and supplemented with slides and handouts.

Typeset lecture notes, exercises, homework and solutions, as well as additional material, are available for download (moodle).


The lecture is self-contained. However, the following textbooks are recommended for the interested reader:

[1] Dorf, R. C., Bishop, R. H.: Modern Control Systems. Pearson, 2011.
[2] Franklin, G. F., Powell, J. D., Emami-Naeini, A.: Feedback Control of Dynamic Systems, Prentice Hall (Pearson), 2006.
[3] Ogata, K.: Modern Control Engineering, Prentice Hall, 2009.

These three textbooks cover very broadly the topic of linear system modeling, analysis and control design, mainly in frequency domain. Chapters about state space modeling, state feedback control and observer design. Many examples, problems and Matlab exercises.

[4] Kailath, T.: Linear Systems, Prentice Hall, 1980.

Classical textbook for linear systems analysis and controller/observer design in state space.

[5] Antsaklis, P. J., Michel, A. N.: Linear Systems. Birkhäuser, 2006.

Very complete book about linear systems theory with a focus on fundamental properties and results.


Beschreibung der Prüfungs- und Studienleistungen

In a calculation part of the written exam (total exam duration 90 min), which is oriented at the exercise problems and makes up about 2/3 of the achievable points, the students demonstrate their ability to
- model and linearize dynamical systems,
- analyze the properties which are important for control design and
- compute the different components of the controller structures for the control tasks considered in the course.
In a more theoretical part (approx. 1/3 of the achievable points), the students have to show their knowledge about
- the application of the mathematical tools that are used in the context of the course,
- the system theoretic properties of linear time invariant systems,
- the general setting of the presented state space control structures (goals, prerequisites, properties, realizations),
- the applicability of control methods in terms of system properties and
- short proofs of important facts about the analysis of LTI systems and the presented control design framework.
Some of these theoretical questions are formulated as multiple choice questions, in accordance with the examination rules.
Allowed material for the exam:
- 2 handwritten (DIN A4, double-sided) sheets of paper (“cheat sheets”)
- No calculators, computers and other electronic devices


Eine Wiederholungsmöglichkeit wird im Folgesemester angeboten.

Nach oben