Reference
Category : GAMS NOA library
Mainfile : benz.gms
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Stability of a wire guided Daimler-Benz 0305 bus.
References:
Neculai Andrei, "Models, Test Problems and Applications for
Mathematical Programming". Technical Press, Bucharest, 2003.
Application A38, page 402.
Ackermann, J., et al. " Robust gamma-stability analysis in a plant
parameter space. Automatica, vol. 27, 1991, pp.75.
Floudas, C.A., Pardalos, P.M., et al. "Handbook of Test Problems in
Local and Global Optimization". Kluwer Academic Publishers, Dordrecht,
1999.
Section 7.3.5. Test problem 15, page 102.
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VARIABLES
q1
q2
w frequency
k stability margin
objval objective function variable;
FREE VARIABLES objval;
EQUATIONS
f Objective function
g1
g2
b1l, b1u, b2l, b2u;
f .. objval =e=k;
g1 .. (POWER(q1,2)*POWER(q2,2))*POWER(w,8) -
(1.25*1000*POWER(q1,2)*POWER(q2,2) + 16.8*POWER(q1,2)*q2 +
53.9*1000*q1*q2 + 270*1000)*POWER(w,6) +
(1.45*POWER(10,6)*POWER(q1,2)*q2 + 16.8*POWER(10,6)*q1*q2 +
POWER(10,6)*338)*POWER(w,4) -
(5.72*POWER(10,6)*POWER(q1,2)*q2 + 113*POWER(10,6)*POWER(q1,2) +
4250*POWER(10,6)*q1)*POWER(w,2) +
(453*POWER(10,6)*POWER(q1,2)) =e= 0;
g2 .. (50*POWER(q1,2)*POWER(q2,2) + 1080*q1*q2)*POWER(w,6) -
(15.6*1000*POWER(q1,2)*POWER(q2,2) + 840*POWER(q1,2)*q2 +
1.35*POWER(10,6)*q1*q2 + POWER(10,6)*13.5)*POWER(w,4) +
(6.93*POWER(10,6)*POWER(q1,2)*q2 + 911*POWER(10,6)*q1 +
POWER(10,6)*4220)*POWER(w,2) -
(528*POWER(10,6)*POWER(q1,2) + 3640*POWER(10,6)*q1) =e= 0;
b1l .. 17.5 - 14.5*k =l= q1;
b1u .. q1 =l= 17.5 + 14.5*k;
b2l .. 20.0 - 15.0*k =l= q2;
b2u .. q2 =l= 20.0 + 15.0*k;
* Bounds
q1.LO=0;
q1.UP=2;
q2.LO=0;
q2.UP=2;
w.LO =0;
w.UP =2;
k.LO =0;
k.UP =2;
* Initial values;
q1.l=0.1;
q2.l=0.1;
w.l=0.1;
k.l=0.1;
MODEL benz /ALL/;
$ifThenI x%mode%==xbook
benz.workspace=120;
$endIf
SOLVE benz USING NLP MINIMIZING objval;
* End Benz