| 1 | #*------------------------------------------------------------------- |
|---|
| 2 | * EMSO Model Library (EML) Copyright (C) 2004 - 2007 ALSOC. |
|---|
| 3 | * |
|---|
| 4 | * This LIBRARY is free software; you can distribute it and/or modify |
|---|
| 5 | * it under the therms of the ALSOC FREE LICENSE as available at |
|---|
| 6 | * http://www.enq.ufrgs.br/alsoc. |
|---|
| 7 | * |
|---|
| 8 | * EMSO Copyright (C) 2004 - 2007 ALSOC, original code |
|---|
| 9 | * from http://www.rps.eng.br Copyright (C) 2002-2004. |
|---|
| 10 | * All rights reserved. |
|---|
| 11 | * |
|---|
| 12 | * EMSO is distributed under the therms of the ALSOC LICENSE as |
|---|
| 13 | * available at http://www.enq.ufrgs.br/alsoc. |
|---|
| 14 | * |
|---|
| 15 | *-------------------------------------------------------------------- |
|---|
| 16 | * The car axis problem |
|---|
| 17 | * |
|---|
| 18 | * The problem is a stiff DAE of index 3, consisting of 8 |
|---|
| 19 | * differential and 2 algebraic equations. |
|---|
| 20 | *-------------------------------------------------------------------- |
|---|
| 21 | * Author: Rafael de Pelegrini Soares |
|---|
| 22 | * $Id: sample_car.mso 395 2007-10-21 01:22:55Z arge $ |
|---|
| 23 | *--------------------------------------------------------------------*# |
|---|
| 24 | |
|---|
| 25 | FlowSheet CarAxis |
|---|
| 26 | |
|---|
| 27 | PARAMETERS |
|---|
| 28 | l as Real(Default=1); |
|---|
| 29 | l0 as Real(Default=1/2); |
|---|
| 30 | eps as Real(Default=1e-2); |
|---|
| 31 | M as Real(Default=10); |
|---|
| 32 | h as Real(Default=1/5); |
|---|
| 33 | tau as Real(Default=3.1514/5); |
|---|
| 34 | w as Real(Default=10); |
|---|
| 35 | r as Real(Default=0.1); |
|---|
| 36 | |
|---|
| 37 | |
|---|
| 38 | VARIABLES |
|---|
| 39 | xl as Real(Default = 0, Lower=-1, Upper = 1); |
|---|
| 40 | yl as Real(Default = 0.5, Lower=-1, Upper = 1); |
|---|
| 41 | xr as Real(Default = 1, Lower=-2, Upper = 2); |
|---|
| 42 | yr as Real(Default = 0.5, Lower=-1, Upper = 1); |
|---|
| 43 | q(4) as Real(Default = -1); |
|---|
| 44 | lambda(2) as Real(Default = 0); |
|---|
| 45 | xb as Real(Default = 1); |
|---|
| 46 | yb as Real(Default = 0); |
|---|
| 47 | ll as Real(Default = 0.5, Brief="Left spring length"); |
|---|
| 48 | lr as Real(Default = 0.5, Brief="Right spring length"); |
|---|
| 49 | |
|---|
| 50 | EQUATIONS |
|---|
| 51 | diff([xl, yl, xr, yr])*'s' = q; |
|---|
| 52 | |
|---|
| 53 | eps^2*M/2 * diff(q(1))*'s' = (l0-ll)*xl/ll |
|---|
| 54 | +lambda(1)*xb +2*lambda(1)*(xl-xr); |
|---|
| 55 | |
|---|
| 56 | eps^2*M/2 * diff(q(2))*'s' = (l0-ll)*yl/ll |
|---|
| 57 | +lambda(1)*yb +2*lambda(2)*(yr-yl) - eps^2*M/2; |
|---|
| 58 | |
|---|
| 59 | |
|---|
| 60 | eps^2*M/2 * diff(q(3))*'s' = (l0-lr)*(xr-xb)/lr |
|---|
| 61 | -2*lambda(2)*(xl-xr); |
|---|
| 62 | |
|---|
| 63 | eps^2*M/2 * diff(q(4))*'s' = (l0-lr)*(yr-yb)/lr |
|---|
| 64 | -2*lambda(2)*(yl-yr) - eps^2*M/2; |
|---|
| 65 | |
|---|
| 66 | xl*xb + yl*yb = 0; |
|---|
| 67 | |
|---|
| 68 | (xl-xr)^2 + (yl-yr)^2 = l^2; |
|---|
| 69 | |
|---|
| 70 | xb = sqrt(l^2-yb^2); |
|---|
| 71 | |
|---|
| 72 | yb = r*sin(w*time*'rad/s'); |
|---|
| 73 | |
|---|
| 74 | ll = sqrt(xl^2 + yl^2); |
|---|
| 75 | |
|---|
| 76 | lr = sqrt((xr-xb)^2 + (yr-yb)^2); |
|---|
| 77 | |
|---|
| 78 | INITIAL |
|---|
| 79 | yl = 0.5; |
|---|
| 80 | xr = 1; |
|---|
| 81 | q(3) = -0.5; |
|---|
| 82 | q(4) = 0; |
|---|
| 83 | |
|---|
| 84 | OPTIONS |
|---|
| 85 | TimeStart = 0; |
|---|
| 86 | TimeStep = 0.01; |
|---|
| 87 | TimeEnd = 3; |
|---|
| 88 | Integration = "original";# "index0", "index1", "original" |
|---|
| 89 | NLASolver( |
|---|
| 90 | File = "sundials", |
|---|
| 91 | RelativeAccuracy = 1e-5, |
|---|
| 92 | AbsoluteAccuracy = 1e-5 |
|---|
| 93 | ); |
|---|
| 94 | DAESolver( |
|---|
| 95 | File = "dasslc", |
|---|
| 96 | #File = "dassl", |
|---|
| 97 | #File = "mebdf", |
|---|
| 98 | #File = "pside", |
|---|
| 99 | #File = "sundials", |
|---|
| 100 | RelativeAccuracy = 1e-5, |
|---|
| 101 | AbsoluteAccuracy = 1e-5 |
|---|
| 102 | ); |
|---|
| 103 | end |
|---|
