1 | #*------------------------------------------------------------------- |
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2 | * EMSO Model Library (EML) Copyright (C) 2004 - 2007 ALSOC. |
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3 | * |
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4 | * This LIBRARY is free software; you can distribute it and/or modify |
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5 | * it under the therms of the ALSOC FREE LICENSE as available at |
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6 | * http://www.enq.ufrgs.br/alsoc. |
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7 | * |
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8 | * EMSO Copyright (C) 2004 - 2007 ALSOC, original code |
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9 | * from http://www.rps.eng.br Copyright (C) 2002-2004. |
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10 | * All rights reserved. |
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11 | * |
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12 | * EMSO is distributed under the therms of the ALSOC LICENSE as |
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13 | * available at http://www.enq.ufrgs.br/alsoc. |
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14 | * |
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15 | *-------------------------------------------------------------------- |
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16 | * The car axis problem |
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17 | * |
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18 | * The problem is a stiff DAE of index 3, consisting of 8 |
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19 | * differential and 2 algebraic equations. |
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20 | *-------------------------------------------------------------------- |
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21 | * Author: Rafael de Pelegrini Soares |
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22 | * $Id: sample_car.mso 83 2006-12-08 20:29:34Z paula $ |
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23 | *--------------------------------------------------------------------*# |
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24 | |
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25 | FlowSheet CarAxis |
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26 | |
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27 | PARAMETERS |
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28 | l as Real(Default=1); |
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29 | l0 as Real(Default=1/2); |
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30 | eps as Real(Default=1e-2); |
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31 | M as Real(Default=10); |
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32 | h as Real(Default=1/5); |
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33 | tau as Real(Default=3.1514/5); |
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34 | w as Real(Default=10); |
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35 | r as Real(Default=0.1); |
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36 | |
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37 | |
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38 | VARIABLES |
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39 | xl as Real(Default = 0, Lower=-1, Upper = 1); |
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40 | yl as Real(Default = 0.5, Lower=-1, Upper = 1); |
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41 | xr as Real(Default = 1, Lower=-2, Upper = 2); |
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42 | yr as Real(Default = 0.5, Lower=-1, Upper = 1); |
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43 | q(4) as Real(Default = -1); |
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44 | lambda(2) as Real(Default = 0); |
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45 | xb as Real(Default = 1); |
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46 | yb as Real(Default = 0); |
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47 | ll as Real(Default = 0.5, Brief="Left spring length"); |
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48 | lr as Real(Default = 0.5, Brief="Right spring length"); |
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49 | |
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50 | EQUATIONS |
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51 | diff([xl, yl, xr, yr]) = q; |
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52 | |
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53 | eps^2*M/2 * diff(q(1)) = (l0-ll)*xl/ll |
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54 | +lambda(1)*xb +2*lambda(1)*(xl-xr); |
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55 | |
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56 | eps^2*M/2 * diff(q(2)) = (l0-ll)*yl/ll |
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57 | +lambda(1)*yb +2*lambda(2)*(yr-yl) - eps^2*M/2; |
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58 | |
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59 | |
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60 | eps^2*M/2 * diff(q(3)) = (l0-lr)*(xr-xb)/lr |
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61 | -2*lambda(2)*(xl-xr); |
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62 | |
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63 | eps^2*M/2 * diff(q(4)) = (l0-lr)*(yr-yb)/lr |
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64 | -2*lambda(2)*(yl-yr) - eps^2*M/2; |
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65 | |
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66 | xl*xb + yl*yb = 0; |
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67 | |
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68 | (xl-xr)^2 + (yl-yr)^2 = l^2; |
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69 | |
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70 | xb = sqrt(l^2-yb^2); |
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71 | |
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72 | yb = r*sin(w*time); |
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73 | |
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74 | ll = sqrt(xl^2 + yl^2); |
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75 | |
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76 | lr = sqrt((xr-xb)^2 + (yr-yb)^2); |
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77 | |
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78 | INITIAL |
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79 | yl = 0.5; |
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80 | xr = 1; |
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81 | q(3) = -0.5; |
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82 | q(4) = 0; |
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83 | |
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84 | OPTIONS |
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85 | time = [0:0.01:3]; |
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86 | integration = "index0"; # "original"; |
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87 | #DAESolver = "mebdf"; |
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88 | |
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89 | relativeAccuracy = 1e-5; |
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90 | absoluteAccuracy = 1e-5; |
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91 | indVarAccuracy = 1e-3; |
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92 | end |
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