Flat Systems

Flatness-based feedforward control is often used in practice as part of a two-degree-of-freedom control structure. Besides flatness-based feedforward- and feedback controller design for linear and nonlinear systems, the lecture improves system understanding and gives an overview of methods for exact linearization.

General Information



Credit Points




Start of lectures

2023-10-16, 09:45 am


Monday 09:45 - 11:15 am, ISYS Seminar room 1.02
Monday 11:30 - 13:00 am, ISYS Seminar room 1.02


The concept of differential flatness offers an approach to model based control of linear and nonlinear systems, including trajectory planning and the design of feedforward and feedback controls. It has been successfully applied in various applications such as the control of electric or pneumatic drives, cranes, inverted pendulums or process control systems.

The lecture “Flat Systems” introduces the concept of differential flatness for linear time invariant, linear time variant and nonlinear SISO and MIMO systems. It provides methods and tools for the design of two-degree-of-freedom control systems for asymptotic tracking, consisting of a feedforward control and a stabilizing feedback control. The theoretical concepts are illustrated by selected real-world examples.

The lectures “Einführung in die Regelungstechnik“ and „Konzepte der Regelungstechnik“ or equivalent knowledge of system dynamics and control theory are required as a prerequisite.


  • Single exercises can be handed in to receive a bonus in the exam. Details will be announced in the first exercise
  • There will be a written exam (120 min.).
  • All documents are available in the ILIAS-Course.


  • ISIDORI, A.: Nonlinear Control Systems (3rd Edition). Springer-Verlag 1995.
  • ROTHFUSS, R.: Anwendung der flachheitsbasierten Analyse und Regelung nichtlinearer Mehrgrößensysteme. Fortschrittberichte Nr. 8/664, VDI–Verlag 1997.
  • RUDOLPH, J.: Beiträge zur flachheitsbasierten Folgeregelung linearer und nichtlinearer Systeme endlicher und unendlicher Ordnung. Shaker Verlag 2003.
  • LÉVINE, J.: Analysis and Control of Nonlinear Systems – A Flatness–based Approach. Springer 2009.


This image shows Frank  Wolff

Frank Wolff

M. Sc.

Research Assistant

This image shows Pascal Jaufmann

Pascal Jaufmann


Research Assistant

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