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Robust decentralized control of parallel dc/dc converters

Robuste dezentralisierte Regelung für parallele Gleichstromwandler

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Contents

Robust decentralized linear feedback controllers for parallel operating dc/dc converters, using the structured singular value approach, are investigated. Different structures of decentralized controllers were applied and tested. The controllers were designed for structured and unstructured modeluncertainty. The gain directionality compensation, due to a high condition number was considered.

Übersicht

Eine robuste und dezentralisierte Regelung für parallele Gleichstromwandler wurde untersucht. Verschiedene Strukturen des Regelungsverfahren wurden angewandt und getestet. Die Regelung wurde für den Fall der strukturierten und unstrukturierten Perturbation entworfen.

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Abbreviations

d :

disturbance signal

d i :

duty cycle of the switching transistorQ i

E/Ē/Ê :

sensitivity operator/nominal sensitivity operator/sensitivity with diagonal control

Ĥ:

complementary sensitivity with diagonal control

e=y−r :

error signal

e i :

source disturbance acting on thei-th unit

G, M :

interconnection matrix between the Δ blocks

I :

unity matrix

i inj :

input current of thej-th converter

i g :

load disturbance

\(K/\hat K,\hat K_1 ,\hat K_2 \) :

feedback controller/diagonal (decentralized) controllers

k :

matrix condition number

kv :

(worst-case) closed-loop velocity constant

k d,k d1,k d2 :

adjustable parameters of the diagonal controllers

H H ,L E :

the perturbation of the diagonal model whenP is approximated with\(\hat P\)

l u :

upper bound of modeluncertainty (modeluncertainty weighting operator)

NP :

nominal performance measure of the closed-loop system

P :

matrix transfer function of the plant (control-to-output)

P n :

matrix transfer function of the plant (disturbance-to-output)

\(\tilde P/\hat P\) :

model of the plant P/diagonal model of the plantP

RP :

robust performance measure of the closed-loop system

RS :

robust stability measure of the closed-loop system

r :

reference signal

s :

complex Laplace variable

sup x∈A {f(x)}:

the least upper bound of the functionf(x) for anyx∈A

\(U = (\bar u,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{u} )^T \) :

left singular vector matrix

\(\bar u/\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{u} \) :

left singular vectors associated with\(\bar \sigma /\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\sigma } \)

u :

control variable

\(V = (\bar v,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{v} )^T \) :

right singular vector matrix

\((\bar v,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{v} )\) :

right singular vectors associated with\(\bar \sigma /\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\sigma } \)

v ont :

output voltage of the parallel operating converters

W p :

sensitivity weighting operator

y :

controlled variable

ΔμΔ:

normalized perturbation of the plant

δ i :

load disturbance between the units

μΔ(A):

structured singular value of the matrix A computed according to the structure of the block diagonal matrix Δ.

Φ:

diagonal matrix of the singular values

σ i (A):

i-th singular value of the matrixA

\(\bar \sigma /\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\sigma } \) :

maximal/minimal singular value

τ s :

(worst-case) dominant closed-loop time constant

‖@‖2 :

matrix and vector 2-norm (Euclidean norm)

‖@‖ m :

multiplicative norm (or seminorm)

NP:

nominal performance

NS:

nominal stability

RP:

robust performance

RS:

robust stability

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Authors and Affiliations

  1. Institute for Power and Electronic Engineering, Faculty of Technical Sciences, University of Novi Sad, Fruskogorska ul. 11, P.O. Box 55, 21000, Novi Sad, Yugoslavia

    D. Garabandić

  2. Department of Control Engineering, Faculty of Electrical Engineering, University of Belgrade, Bulevar Revolucije 73, P.O. Box 816, 11001, Belgrade, Yugoslavia

    T. Petrović

Authors
  1. D. Garabandić
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  2. T. Petrović
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Garabandić, D., Petrović, T. Robust decentralized control of parallel dc/dc converters. Electrical Engineering 79, 47–53 (1996). https://doi.org/10.1007/BF01840707

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  • DOI: https://doi.org/10.1007/BF01840707

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