The optimal control structure: an approach to measuring control-law nonlinearity

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Abstract

This paper introduces the Optimal Control Structure as a design tool to examine the control-law nonlinearity of a given process design. Control-law nonlinearity is defined as the optimal degree of nonlinear compensation in the controller, a system property distinct from open-loop nonlinearity. It is determined by the nature of the open-loop process, the performance objective, and the region of operation. The Optimal Control Structure contains the structural dynamics of the optimal control law, and an assessment of the control-law nonlinearity can be found from any open-loop nonlinearity measure of this structure that takes into account a region of operation. This approach is applied to three SISO models, demonstrating how the control-law nonlinearity for a given plant can vary with the cost of control action and performance objective.

References (34)

  • J. Doyle et al.

    The Parallel Projection Operators of a Nonlinear Feedback System

    Syst. Control Lett.

    (1993)
  • M. Rouff et al.

    A New Approach to Nonlinear Optimal Feedback Law

    Syst. Control Lett.

    (1986)
  • F. Allgöwer

    Definition and Computation of a Nonlinearity Measure and Application to Approximate I/O-Linearization

  • F.A. Allgöwer et al.

    Approximate Input/Output Linearization of Nonlinear Systems

  • J.S. Bendat
  • V. Benignus

    Estimation of the Coherence Spectrum and Its Confidence Interval Using the Fast Fourier Transform

    IEEE Trans. Audio and Electroacoustics

    (1969)
  • D. Bernstein

    Nonquadratic Cost and Nonlinear Feedback Control

    Int. J. Rob. Nonl. Control

    (1993)
  • L.T. Biegler et al.

    Optimization Approaches to Nonlinear Model Predictive Control

  • G.C. Carter et al.

    Estimation of the Magnitude-Squared Coherence Function Via Overlapped Fast Fourier Transform Processing

    IEEE Trans. Audio Electroacoust.

    (1983)
  • F. Doyle et al.

    A Normal Form Approach to Approximate Input-Output Linearization for Maximum Phase Nonlinear SISO Systems

    IEEE Trans. Autom. Control

    (1996)
  • F.J. Doyle et al.

    Some Practical Considerations in the Selection of Linearizing Control over Linear Control

  • E. Eskinat et al.

    Use of Hammerstein Models in Identification of Nonlinear Systems

    AIChE J.

    (1991)
  • M. Guay

    Measurement of Nonlinearity in Chemical Process Control

  • M. Guay et al.

    Measurement of Nonlinearity in Chemical Process Control Systems: The Steady State Map

    Can. J. Chem. Eng.

    (1995)
  • R. Haber

    Nonlinearity Test for Dynamic Processes

  • H. Kwakernaak et al.
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