| 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 | * FlowSheet with the Model for the index three pendulum |
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| 17 | * in Cartesian coordinates. |
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| 18 | *-------------------------------------------------------------------- |
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| 19 | * Author: Rafael de Pelegrini Soares |
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| 20 | * $Id: sample_pend.mso 542 2008-06-21 16:01:41Z arge $ |
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| 21 | *-------------------------------------------------------------------*# |
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| 22 | |
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| 23 | using "types.mso"; |
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| 24 | |
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| 25 | FlowSheet pend |
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| 26 | PARAMETERS |
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| 27 | g as acceleration (Brief = "Gravity acceleration"); |
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| 28 | L as length (Brief = "Pendulum cable length"); |
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| 29 | |
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| 30 | VARIABLES |
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| 31 | x as length_delta(Brief="Position x"); |
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| 32 | y as length_delta(Brief="Position y"); |
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| 33 | w as velocity(Brief = "Velocity for x"); |
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| 34 | z as velocity(Brief = "Velocity for y"); |
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| 35 | T as Real(Brief = "Tension on cable",Default=10,Unit='1/s^2'); |
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| 36 | |
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| 37 | EQUATIONS |
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| 38 | "Velocity on x" |
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| 39 | diff(x)=w; |
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| 40 | |
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| 41 | "Velocity on y" |
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| 42 | diff(y)=z; |
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| 43 | |
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| 44 | "Tension on x" |
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| 45 | diff(w)=T*x; |
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| 46 | |
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| 47 | "Tension on y" |
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| 48 | diff(z)=T*y-g; |
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| 49 | |
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| 50 | "Position Constraint" |
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| 51 | x^2+y^2=L^2; |
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| 52 | |
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| 53 | SET |
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| 54 | g = 9.8 * 'm/s^2'; |
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| 55 | L = 0.9 * 'm'; |
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| 56 | |
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| 57 | INITIAL |
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| 58 | "Initial Position x" |
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| 59 | x = 0.9 * 'm'; |
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| 60 | |
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| 61 | "Initial x Velocity" |
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| 62 | w = 0 * 'm/s'; |
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| 63 | |
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| 64 | OPTIONS |
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| 65 | TimeStep = 0.1; |
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| 66 | TimeEnd = 36; |
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| 67 | Integration = "original"; # original, index0, or index1 |
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| 68 | |
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| 69 | NLASolver( |
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| 70 | RelativeAccuracy = 1e-8, |
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| 71 | AbsoluteAccuracy = 1e-9 |
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| 72 | ); |
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| 73 | DAESolver( |
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| 74 | #File = "dasslc", |
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| 75 | #File = "dassl", # fail when "original" (high-index) |
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| 76 | File = "mebdf", |
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| 77 | #File = "pside", |
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| 78 | #File = "sundials", # fail when "original" (high-index) |
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| 79 | RelativeAccuracy = 1e-6, |
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| 80 | AbsoluteAccuracy = 1e-8 |
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| 81 | ); |
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| 82 | SparseAlgebra = true; |
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| 83 | end |
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| 84 | |
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| 85 | |
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| 86 | FlowSheet pend_polar |
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| 87 | PARAMETERS |
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| 88 | g as acceleration (Brief = "Gravity acceleration"); |
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| 89 | L as length (Brief = "Pendulum cable length"); |
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| 90 | |
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| 91 | VARIABLES |
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| 92 | phi as angle (Brief="Angle"); |
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| 93 | omega as frequency (Brief="Angular velocity", Lower=-100); |
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| 94 | x as length_delta(Brief="Position x"); |
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| 95 | y as length_delta(Brief="Position y"); |
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| 96 | w as velocity(Brief = "Velocity for x"); |
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| 97 | z as velocity(Brief = "Velocity for y"); |
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| 98 | T as Real(Brief = "Tension on cable",Default=10,Unit='1/s^2'); |
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| 99 | |
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| 100 | EQUATIONS |
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| 101 | "x Position" |
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| 102 | x = L*sin(phi); |
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| 103 | |
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| 104 | "y Position" |
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| 105 | y = -L*cos(phi); |
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| 106 | |
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| 107 | "Velocity on x" |
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| 108 | w = L*omega*cos(phi); |
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| 109 | |
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| 110 | "Velocity on y" |
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| 111 | z = L*omega*sin(phi); |
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| 112 | |
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| 113 | "Tension" |
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| 114 | T = -g*cos(phi)/L-omega^2; |
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| 115 | |
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| 116 | "Angular velocity" |
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| 117 | diff(phi) = omega*'rad'; |
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| 118 | |
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| 119 | "Angular acceleration" |
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| 120 | diff(omega) = -g*sin(phi)/L; |
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| 121 | |
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| 122 | SET |
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| 123 | g = 9.8 * 'm/s^2'; |
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| 124 | L = 0.9 * 'm'; |
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| 125 | |
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| 126 | INITIAL |
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| 127 | "Initial Position x" |
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| 128 | x = 0.9 * 'm'; |
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| 129 | |
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| 130 | "Initial x Velocity" |
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| 131 | w = 0 * 'm/s'; |
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| 132 | |
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| 133 | OPTIONS |
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| 134 | TimeStep = 0.1; |
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| 135 | TimeEnd = 36; |
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| 136 | Integration = "original"; # original, index0, or index1 |
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| 137 | |
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| 138 | NLASolver( |
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| 139 | RelativeAccuracy = 1e-8, |
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| 140 | AbsoluteAccuracy = 1e-9 |
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| 141 | ); |
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| 142 | DAESolver( |
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| 143 | #File = "dasslc", |
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| 144 | File = "dassl", # fail when "original" (high-index) |
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| 145 | #File = "mebdf", |
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| 146 | #File = "pside", |
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| 147 | #File = "sundials", # fail when "original" (high-index) |
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| 148 | RelativeAccuracy = 1e-6, |
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| 149 | AbsoluteAccuracy = 1e-8 |
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| 150 | ); |
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| 151 | SparseAlgebra = true; |
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| 152 | end |
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