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By Sirish L. Shah, G. Dumont

ISBN-10: 038751869X

ISBN-13: 9780387518695

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Extra info for Adaptive control strategies for industrial use: proceedings of a workshop held in Kananaskis, Canada, 1988

Example text

2(t + d~ - 1) then by recursive substitution the following expressions can be derived, L , ( t + d , ) --- A ~ ' L ~ ( t ) + { A ~ ' - ' + - - . + I)_b~u~(t) (5) 47 where dt and d 2 a r e the prediction horizons. T ( A d l - - I ) -i-. 2 ,i 42 _ I)L2(t ) _ ~"i +... 4,b __ I) _pzrl z~ = -c- 2~ rA", 2 ~. 2 - :) B2, = C~I(A'[ "-1 + . . s of equations (8), (9) respectively, we get a system of 2 equations with 2 unknowns, ut(t}, uz(t). BuulCt) + B12u2(t) = Yri - yl(t) - pT1L_I(t ) -- pT~L2Ct ) ].

18) now becomes a function of both ~ and ~0" This function cannot be computed since it depends on the unknown unmodelled dynamics, llo~ever, bounds can be found on S(o) (Goodwin, ~layne and Salgado, 1988) which can be computed using p r i o r a v a i l a b l e information. 2 for d i f f e r e n t values of ~0 and f o r ~ normalized to 10. 40 / f ,o tr ¢D fI: ,,,g -Q, O0 20. on 40. BB 60. O0 FBEQUENCY 8Q. flQ "LaO, O~ 2G. ~ 0 Frequency domain bound for example i . 2. c. the minimum prediction e r r o r occurs approximately for that This is perfect ~=~0 in a l l cases when °O is greater than fl, the unmodelled dynamics dominates the least squares f i t t i n g and hence the model f i t t e d at useful for when ~0 ~0 is r e a l l y only ~=~0 is less than fl, tile phase s h i f t produced by the unmodetled dynamics is r c l a t i v e l y small and hence the modcl performs well at a l l low frcquencies.

Gain Case ( i ) . We f i r s t consider a simple case when the nominal model is a pure a O. Say we obtain an estimate f o r a 0 using ordinary l e a s t squares when the input is a single sinewave of frequency wO. ~e are then interested in the prediction performance of the model at some other frequency ~. 18) now becomes a function of both ~ and ~0" This function cannot be computed since it depends on the unknown unmodelled dynamics, llo~ever, bounds can be found on S(o) (Goodwin, ~layne and Salgado, 1988) which can be computed using p r i o r a v a i l a b l e information.

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Adaptive control strategies for industrial use: proceedings of a workshop held in Kananaskis, Canada, 1988 by Sirish L. Shah, G. Dumont


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