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Symbolically enhanced parameter estimation for reliable adaptive control

  • AI And Industrial Adaptive Controllers
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Book cover Adaptive Control Strategies for Industrial Use

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 137))

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Abstract

Adaptive controllers with linear estimators are often implemented on processes that exhibit nonlinear, nonstationary behavior. As a result, the sensitivity of these estimators must be continually adjusted to remain responsive to current process behavior. This work takes a novel approach to the practice of adjusting sensitivity. Here, the recent behavior of the process is used as the primary indicator for making decisions about when and how to make such adjustments. The diagnosis of process behavior is made at a qualitative level to place current operation into one of several categories. An inferencing system directs the diagnosis and uses the result to implement appropriate adjustment actions. The result is a preemptive action that indicates improved controller reliability. A preliminary validation is presented in the adaptive control of a nonlinear reactor simulation.

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Abbreviations

ai :

Parameters corresponding to system output, yi

bi :

Parameters corresponding to system input, ui

CA :

Concentration of species A in reactor

ci :

Parameters corresponding to the system noise, vi

d:

Unmeasured disturbance variable

F:

Flow in reactor

J:

Objective function, defined in Eqn (5) and (8)

k:

Dead time expressed as a multiple of sampling period, Δt

Kp :

Steady state process gain

ko :

Reaction rate constant

m:

Order of input in the ARMAX model in Eqn (1)

n:

Order of output in the ARMAX model in Eqn (1)

P:

Covariance matrix, defined in Eqn (7)

Q:

penalty on incremental input change, defined in Eqn (11)

t:

Integer number representing the sampling instant

td :

Process dead time

Δt:

Sampling period for estimator and controller

u:

Process input variable

V:

Reactor volume, Defined in Eqn (13)

y:

Process output variable

y′:

Estimate of output y

y fsp :

Filtered setpoint, defined in Eqn (9)

ysp :

Controller setpoint

α:

Filter rate parameter used in Eqn (9)

ε:

Error of estimation in Eqn (4)

ψ:

Vector of inputs and outputs, defined in Eqn (4)

τ i :

Process time constants in Eqn (12)

θ:

Vector of the coefficient parameters, defined in Eqn (3)

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Authors and Affiliations

  1. Department of Chemical Engineering, The University of Connecticut, 06269-3139, Storrs, CT, USA

    D. J. Cooper, A. M. Lalonde & R. Pae

Authors
  1. D. J. Cooper
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  2. A. M. Lalonde
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  3. R. Pae
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Sirish L. Shah Guy Dumont

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© 1989 Springer-Verlag

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Cooper, D.J., Lalonde, A.M., Pae, R. (1989). Symbolically enhanced parameter estimation for reliable adaptive control. In: Shah, S.L., Dumont, G. (eds) Adaptive Control Strategies for Industrial Use. Lecture Notes in Control and Information Sciences, vol 137. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0042943

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  • DOI: https://doi.org/10.1007/BFb0042943

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51869-3

  • Online ISBN: 978-3-540-46833-2

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