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Open-Loop Control of Underactuated Mechanical Systems Using Servo-Constraints: Analysis and Some Examples

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Applications of Differential-Algebraic Equations: Examples and Benchmarks

Part of the book series: Differential-Algebraic Equations Forum ((DAEF))

Abstract

A classical trajectory tracking control approach combines feedforward control with a feedback loop. Since both parts can be designed independently, this is called a two degree of freedom control structure. Feedforward control is ideally an inverse model of the system. In case of underactuated mechanical systems the inverse model often cannot be derived analytically, or the derivation cannot follow a systematic approach. Then, the numerical approach based on servo-constraints has shown to be effective. In this approach, the equations of motion are appended by algebraic equations constraining the output to follow a specified output trajectory, representing the servo-constraints. The arising differential-algebraic equations (DAEs) are solved for the desired open-loop control input. An additional feedback loop stabilizes the system around the specified trajectories. This contribution reviews the use of servo-constraints in mechanical open-loop control problems. Since the arising set of DAEs is usually of higher index, index reduction and analysis methods are reviewed for flat as well as non-flat systems. Some typical examples are given and numerical results are presented.

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Authors and Affiliations

  1. Institute of Mechanics and Ocean Engineering, Hamburg University of Technology, Hamburg, Germany

    Svenja Otto & Robert Seifried

Authors
  1. Svenja Otto
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  2. Robert Seifried
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Correspondence to Svenja Otto .

Editor information

Editors and Affiliations

  1. Department of Mathematics, North Carolina State University, Raleigh, NC, USA

    Stephen Campbell

  2. Institut für Mathematik, Technische Universität Ilmenau, Ilmenau, Germany

    Achim Ilchmann

  3. Institut für Mathematik, Technische Universität Berlin, Berlin, Germany

    Volker Mehrmann

  4. Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany

    Timo Reis

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Otto, S., Seifried, R. (2018). Open-Loop Control of Underactuated Mechanical Systems Using Servo-Constraints: Analysis and Some Examples. In: Campbell, S., Ilchmann, A., Mehrmann, V., Reis, T. (eds) Applications of Differential-Algebraic Equations: Examples and Benchmarks. Differential-Algebraic Equations Forum. Springer, Cham. https://doi.org/10.1007/11221_2018_4

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