source: trunk/sample/miscellaneous/sample_pend.mso @ 715

#*-------------------------------------------------------------------
* EMSO Model Library (EML) Copyright (C) 2004 - 2007 ALSOC.
*
* This LIBRARY is free software; you can distribute it and/or modify
* it under the therms of the ALSOC FREE LICENSE as available at
* http://www.enq.ufrgs.br/alsoc.
*
* EMSO Copyright (C) 2004 - 2007 ALSOC, original code
* from http://www.rps.eng.br Copyright (C) 2002-2004.
* All rights reserved.
*
* EMSO is distributed under the therms of the ALSOC LICENSE as
* available at http://www.enq.ufrgs.br/alsoc.
*
*--------------------------------------------------------------------
* FlowSheet with the Model for the index three pendulum
* in Cartesian coordinates.
*--------------------------------------------------------------------
* Author: Rafael de Pelegrini Soares
* $Id: sample_pend.mso 542 2008-06-21 16:01:41Z arge $
*-------------------------------------------------------------------*#

using "types.mso";

FlowSheet pend
        PARAMETERS
        g     as acceleration (Brief = "Gravity acceleration");
        L     as length (Brief = "Pendulum cable length");
        
        VARIABLES
        x   as length_delta(Brief="Position x");
        y   as length_delta(Brief="Position y");
        w   as velocity(Brief = "Velocity for x");
        z   as velocity(Brief = "Velocity for y");
        T   as Real(Brief = "Tension on cable",Default=10,Unit='1/s^2');
        
        EQUATIONS
        "Velocity on x"
        diff(x)=w;
        
        "Velocity on y"
        diff(y)=z;
        
        "Tension on x"
        diff(w)=T*x;
        
        "Tension on y"
        diff(z)=T*y-g;
        
        "Position Constraint"
        x^2+y^2=L^2;
        
        SET
        g     = 9.8 * 'm/s^2';
        L     = 0.9 * 'm';

        INITIAL
        "Initial Position x"
        x = 0.9 * 'm';

        "Initial x Velocity"
        w = 0 * 'm/s';
        
        OPTIONS
        TimeStep = 0.1;
        TimeEnd = 36;
        Integration = "original"; # original, index0, or index1

        NLASolver(
                RelativeAccuracy = 1e-8,
                AbsoluteAccuracy = 1e-9
        );
        DAESolver(
                #File = "dasslc",
                #File = "dassl", # fail when "original" (high-index)
                File = "mebdf",
                #File = "pside",
                #File = "sundials", # fail when "original" (high-index)
                RelativeAccuracy = 1e-6,
                AbsoluteAccuracy = 1e-8
        );
        SparseAlgebra = true;
end


FlowSheet pend_polar
        PARAMETERS
        g     as acceleration (Brief = "Gravity acceleration");
        L     as length (Brief = "Pendulum cable length");
        
        VARIABLES
        phi   as angle (Brief="Angle");
        omega as frequency (Brief="Angular velocity", Lower=-100);
        x     as length_delta(Brief="Position x");
        y     as length_delta(Brief="Position y");
        w     as velocity(Brief = "Velocity for x");
        z     as velocity(Brief = "Velocity for y");
        T     as Real(Brief = "Tension on cable",Default=10,Unit='1/s^2');
        
        EQUATIONS
        "x Position"
        x = L*sin(phi);

        "y Position"
        y = -L*cos(phi);

        "Velocity on x"
        w = L*omega*cos(phi);
        
        "Velocity on y"
        z = L*omega*sin(phi);
        
        "Tension"
        T = -g*cos(phi)/L-omega^2;

        "Angular velocity"
        diff(phi) = omega*'rad';

        "Angular acceleration"
        diff(omega) = -g*sin(phi)/L;

        SET
        g     = 9.8 * 'm/s^2';
        L     = 0.9 * 'm';

        INITIAL
        "Initial Position x"
        x = 0.9 * 'm';

        "Initial x Velocity"
        w = 0 * 'm/s';
        
        OPTIONS
        TimeStep = 0.1;
        TimeEnd = 36;
        Integration = "original"; # original, index0, or index1

        NLASolver(
                RelativeAccuracy = 1e-8,
                AbsoluteAccuracy = 1e-9
        );
        DAESolver(
                #File = "dasslc",
                File = "dassl", # fail when "original" (high-index)
                #File = "mebdf",
                #File = "pside",
                #File = "sundials", # fail when "original" (high-index)
                RelativeAccuracy = 1e-6,
                AbsoluteAccuracy = 1e-8
        );
        SparseAlgebra = true;
end