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