PARSIM

IFT

Controller Tuning by the Parameter Signature Isolation Method

Michael McKinley, Professor Kourosh Danai (Advisor)University of Massachusetts

This work is supported in part by the National Science Foundation under NSF award number 0552548, and by the Engineering Research Centers Program of the National Science Foundation under award number 0313747, James M. Smith, ’67, and the Dean’s Fund for Undergraduate Research in Engineering established in honor of Joseph I. and Barbara H. Goldstein.

Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect those of the National Science Foundation.

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Problem Definition

Tdi T,TK,θ

sT

11KθC

ir

PARSIM

IFT

Target

Publications:K. Danai, J. McCusker, 2008, Parameter Adaptation by Parameter Signature Isolation in the Time-Scale Domain. ASME J. of Dynamic Systems Measurement and Control, accepted.

K. Danai, J. McCusker, and M. McKinley, 2008, Iterative Controller Tuning by Signature Isolation in the Time-Frequency Domain. working paper.

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ikt

il

ik

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ii a,bθt,ΕW

a,bθ,θεW

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1)θ(Δθ

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Parameter Signature Isolation Method (PARSIM)

vWθt,ΕWΔθθ,θεWQ

1iii

*t

i

titi δθ

θ,tuyδθθ,tuyθ,tut,Ε

v

θθi

tQ

1ii

*t δθ

θ,tuδyΔθθ,θ,tuε

Approximation of Performance Error by First Order Taylor Series

Estimation of Parameter Effects

Wavelet Transform of Prediction Error

Parameter Error Estimation at the Signatures

PARSIM'S Parameter Adaptation

v

θ,tut,ΕΔθθ,θ,tuε i

Q

1ii

*t

Estimation of Prediction Error in terms of Parameter Effects

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Cy

v

yr

Tuning

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Gauss-Newton Tuning Approach

Cost Function

θJ min argθθ

*

Performance Error

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tt

N

tt

2tu

2ty

0 0

θuLλθy~LE2N

1θJ

Minimize Cost to Achieve Optimal Performance

Gradient-based Parameter Adaptation

θJRγ-θθ -1iii1i

Controller Tuning by the Parameter Signature Isolation Method (PARSIM)

 The Parameter Signature Isolation Method (PARSIM) relies on the added resolution attained by expanding the prediction error into the higher dimension of the time-scale plane. By taking advantage of this added resolution, PARSIM can isolate regions in the time-scale plane wherein the sensitivity of outputs to individual model parameters is dominant relative to others. At these regions, it can then estimate individual parameter errors for adaptation. Here, PARSIM is applied to tuning controllers for single-input single-output systems. The results indicate that PARSIM provides a viable solution to tuning PID controllers with results comparable to the Gauss-Newton method in noise free cases.

Target (green)

20 Iterations

Target (green)

20 Iterations