Advanced Control

Module MW1420

This Module is offered by Chair of Automatic Control (Prof. Lohmann).

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

MW1420 is a semester module in English language at Master’s level which is offered in winter semester.

This Module is included in the following catalogues within the study programs in physics.

  • Catalogue of non-physics elective courses
Total workloadContact hoursCredits (ECTS)
150 h 45 h 5 CP

Content, Learning Outcome and Preconditions


Contents: - Modeling of dynamical systems in state space - Linearization - Solution of the linear state differential equations - The concepts of eigenvalues, poles and zeros - Canonical forms of the state representation - System properties: stability, controllability, observability - Effects of pole-zero cancellations - Relations between system representations in time and frequency domain - Design of linear state feedback controllers in a two-degrees-of-freedom structure - Design of linear state observers - Methods for disturbance attenuation - Introduction to flatness-based feedforward control at the example of linear systems

Learning Outcome

Upon successful completion of the module the students are able to: - model real-world dynamical systems in the state-space representation and linearize them to achieve a linear state space model - 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 state-feedback controllers using the pole placement method and as a Linear Quadratic Regulator (LQR) - design a Luenberger state-observer to calculate the non measurable states of the system - further modify the closed-loop system by adding measures to cope with the different disturbances acting on the system - have a basic knowledge about flatness-based feedforward control


Prerequisites: - a basic course in automatic control dealing with the analysis of dynamical systems (transfer function, impulse response, poles and zeros, stability, Laplace Transform, and basic control loops (P, PI, PID)) - mathematical background: basic linear algebra (matrix computations, eigenvalues, determinants,...) and complex numbers' theory.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 2 Advanced Control - Lecture - Mittwoch, 13:30–15:00
Mittwoch, 13:30–15:00
UE 1 Advanced Control - Exercise Course - Mittwoch, 15:00–16:00
Mittwoch, 15:00–16:00
UE 2 Advanced Control - Tutorial - Freitag, 09:15–10:45
Freitag, 09:15–10:45

Learning and Teaching Methods

Weekly courses: - 90 min. lecture - 45 min. exercise course - 90 min. additional exercise course (optional) Exercises and their solutions, as well as additional material, will be available for download. In addition to the problems which are solved in the regular exercise course, a set of addional problems is offered for homework. The solutions of the homework are discussed in the additional exercise course (optional).


The lecture will be written on the blackboard and supplemented with slides and handouts. Exercises and their solutions as well as additional material will be available for download.


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.Prentice Hall (Pearson) 2008. [2] Franklin, G.F., Powell, J.D., Emami-Naeini, A.: Feedback Control of Dynamic Systems, 5th Edition, Prentice Hall (Pearson) 2006. [3] Kailath, T.: Linear Systems, Prentice Hall, 1980.Dorf, R.C., Bishop, R.H.: Modern Control Systems. Prentice Hall (Pearson) 2008. [4] Antsaklis, P. J., Michel, A. N.: Linear Systems.Birkhäuser, 2006. [5] Ogata, K.: Model Control Engineering, 5th Edition, Prentice Hall, 2009. [6] Ogata, K.: MATLAB for Control Engineers, 1st Edition, Prentice Hall, 2007.

Module Exam

Description of exams and course work

The written exam consists of problems involving calculations, in the style of the problems solved in the exercise sessions (approx. 2/3 of the achievable points). Theoretical questions, some of them formulated as multiple choice questions, make up approx. 1/3 of the achievable points.

Exam Repetition

There is a possibility to take the exam in the following semester.

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