Comparison of Syntax

<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01//EN" "https://www.w3.org/TR/1999/REC-html401-19991224/strict.dtd"> <html> <head> <META http-equiv=Content-Type content="text/html; charset=UTF-8"> <title>Exported from Notepad++</title>

Deleted lines 48-49:

</head> <body>

Changed lines 62-63 from:

</div> </body> </html>

to:

</div>

Restore

June 16, 2015, at 06:09 AM by 45.56.3.184 -

Changed line 69 from:

</div></body>

to:

</div> </body>

Restore

June 16, 2015, at 06:08 AM by 45.56.3.184 -

Changed lines 18-30 from:

  Parameters
   percent_open
   c1 = 0.25    ! m^3/sec
   c2 = 0.14    ! m^1.5/sec
  Variables
   inlet_flow   ! m^3/sec
   outlet_flow  ! m^3/sec
   volume       ! m^3
  Equations
   inlet_flow  = a1 * percent_open
   outlet_flow = a2 * SQRT(volume)
   $volume = inlet_flow - outlet_flow
   200 < volume < 5000

to:

(:html:) <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01//EN" "https://www.w3.org/TR/1999/REC-html401-19991224/strict.dtd"> <html> <head> <META http-equiv=Content-Type content="text/html; charset=UTF-8"> <title>Exported from Notepad++</title> <style type="text/css"> span {

	font-family: 'Courier New';
	font-size: 10pt;
	color: #000000;

} .sc0 { } .sc2 {

	font-style: italic;
	color: #008000;

} .sc3 {

	font-weight: bold;
	font-style: italic;
	color: #800000;

} .sc5 {

	font-weight: bold;
	font-style: italic;
	color: #0080FF;

} .sc6 {

	font-weight: bold;
	font-style: italic;
	color: #004000;

} .sc24 { } </style> </head> <body> <div style="float: left; white-space: pre; line-height: 1; background: #FFFFFF; ">Parameters

  </span><span class="sc0">percent_open</span><span class="sc24">
  </span><span class="sc0">a1</span><span class="sc24"> </span><span class="sc6">=</span><span class="sc24"> </span><span class="sc3">0.25</span><span class="sc24">    </span><span class="sc2">! m^3/sec

a2 = 0.14 ! m^1.5/sec Variables

   </span><span class="sc0">inlet_flow</span><span class="sc24">   </span><span class="sc2">! m^3/sec

outlet_flow ! m^3/sec volume ! m^3 Equations

   </span><span class="sc0">inlet_flow</span><span class="sc24">  </span><span class="sc6">=</span><span class="sc24"> </span><span class="sc0">a1</span><span class="sc24"> </span><span class="sc0">*</span><span class="sc24"> </span><span class="sc0">percent_open</span><span class="sc24">
   </span><span class="sc0">outlet_flow</span><span class="sc24"> </span><span class="sc6">=</span><span class="sc24"> </span><span class="sc0">a2</span><span class="sc24"> </span><span class="sc0">*</span><span class="sc24"> </span><span class="sc0">SQRT(volume)</span><span class="sc24">
   </span><span class="sc0">$volume</span><span class="sc24"> </span><span class="sc6">=</span><span class="sc24"> </span><span class="sc0">inlet_flow</span><span class="sc24"> </span><span class="sc0">-</span><span class="sc24"> </span><span class="sc0">outlet_flow</span><span class="sc24">
   </span><span class="sc3">200</span><span class="sc24"> </span><span class="sc6"><</span><span class="sc24"> </span><span class="sc0">volume</span><span class="sc24"> </span><span class="sc6"><</span><span class="sc24"> </span><span class="sc3">5000</span><span class="sc24">

</div></body> </html> (:htmlend:)

Restore

June 16, 2015, at 06:05 AM by 45.56.3.184 -

Changed lines 20-22 from:

   a1 = 0.25    ! m^3/sec
   a2 = 0.14    ! m^1.5/sec

to:

   c1 = 0.25    ! m^3/sec
   c2 = 0.14    ! m^1.5/sec

Deleted line 25:

Restore

June 16, 2015, at 06:03 AM by 45.56.3.184 -

Changed lines 17-28 from:

  a2 = 0.14    ! m^1.5/sec

 Variables
  inlet_flow   ! m^3/sec
  outlet_flow  ! m^3/sec
  volume       ! m^3

 Equations
  inlet_flow  = a1 * percent_open
  outlet_flow = a2 * SQRT(volume)
  $volume = inlet_flow - outlet_flow
  200 < volume < 5000

to:

  Parameters
   percent_open
   a1 = 0.25    ! m^3/sec
   a2 = 0.14    ! m^1.5/sec

  Variables
   inlet_flow   ! m^3/sec
   outlet_flow  ! m^3/sec
   volume       ! m^3

  Equations
   inlet_flow  = a1 * percent_open
   outlet_flow = a2 * SQRT(volume)
   $volume = inlet_flow - outlet_flow
   200 < volume < 5000

Restore

June 16, 2015, at 06:03 AM by 45.56.3.184 -

Deleted lines 16-18:

 Parameters
  percent_open ! %
  a1 = 0.25    ! m^3/sec

Restore

June 16, 2015, at 06:02 AM by 45.56.3.184 -

Changed lines 19-21 from:

  c1 = 0.25    ! m^3/sec
  c2 = 0.14    ! m^1.5/sec

to:

  a1 = 0.25    ! m^3/sec
  a2 = 0.14    ! m^1.5/sec

Changed lines 28-29 from:

  inlet_flow  = c1 * percent_open
  outlet_flow = c2 * SQRT(volume)

to:

  inlet_flow  = a1 * percent_open
  outlet_flow = a2 * SQRT(volume)

Restore

June 16, 2015, at 06:01 AM by 45.56.3.184 -

Added line 18:

  percent_open ! %

Deleted line 20:

  percent_open ! %

Restore

June 16, 2015, at 06:00 AM by 45.56.3.184 -

Changed lines 17-40 from:

 Model tank
  Constants ! valve (c1) and outflow (c2) constants
   c1 = 0.25    ! m^3/sec
   c2 = 0.14    ! m^1.5/sec
  End Constants

  Parameters
   percent_open ! %
  End Parameters

  Variables
   inlet_flow   ! m^3/sec
   outlet_flow  ! m^3/sec
   volume       ! m^3
  End Variables

  Equations
   inlet_flow  = c1 * percent_open
   outlet_flow = c2 * SQRT(volume)
   $volume = inlet_flow - outlet_flow
   200 < volume < 5000
  End Equations

 End Model

to:

 Parameters
  c1 = 0.25    ! m^3/sec
  c2 = 0.14    ! m^1.5/sec
  percent_open ! %

 Variables
  inlet_flow   ! m^3/sec
  outlet_flow  ! m^3/sec
  volume       ! m^3

 Equations
  inlet_flow  = c1 * percent_open
  outlet_flow = c2 * SQRT(volume)
  $volume = inlet_flow - outlet_flow
  200 < volume < 5000

Restore

June 16, 2015, at 05:59 AM by 45.56.3.184 -

Changed line 16 from:

Tank Model in APMonitor

to:

Tank Model in APMonitor

Changed lines 18-20 from:

  Constants
   ! valve (c1) and outflow (c2) constants

to:

  Constants ! valve (c1) and outflow (c2) constants

Restore

June 16, 2015, at 05:57 AM by 45.56.3.184 -

Added line 18:

Changed lines 44-45 from:

Tank Model in MATLAB

to:

Tank Model in MATLAB

Changed lines 73-74 from:

 if (volume < low_volume) & (percent_open < (c_outflow * low_volume^0.5)/c_inflow),

to:

 low_open = c_outflow * low_volume^0.5)/c_inflow;
 if (volume < low_volume) & (percent_open < low_open),

Changed lines 79-80 from:

 if (volume > high_volume) & (percent_open > (c_outflow * high_volume^0.5)/c_inflow),

to:

 high_open = c_outflow * high_volume^0.5)/c_inflow;
 if (volume > high_volume) & (percent_open > high_open),

Changed lines 84-85 from:

Tank Model in gProms

to:

Tank Model in gProms

Changed lines 126-127 from:

Tank Model in Modelica

to:

Tank Model in Modelica

Changed lines 136-138 from:

  inlet_flow = c1 * percent_open "Inlet flow as a linear function of valve  position";
  outlet_flow = c2 * volume^0.5 "Outlet flow as a square root function of volume";
  der(volume) = inlet_flow - outlet_flow "Mass balance (assuming constant density)";

to:

  inlet_flow = c1 * percent_open "Inlet flow";
  outlet_flow = c2 * volume^0.5 "Outlet flow";
  der(volume) = inlet_flow - outlet_flow "Mass balance";

Restore

June 16, 2015, at 05:50 AM by 45.56.3.184 -

Added lines 1-136:

(:title Comparison of Dynamic Modeling Language Syntax:) (:keywords modeling language, differential algebraic equations, nonlinear control, dynamic estimation, parameter estimation, dynamic optimization, engineering optimization, MATLAB, Python, differential, algebraic:) (:description Comparison of APMonitor, MATLAB, gProms, Modelica:)

Tank Model

The same dynamic tank model is written in the following 4 modeling languages for a direct comparison between the syntax for the solution of differential and algebraic equations.

APMonitor
MATLAB
gProms
Modelica

Tank Model in APMonitor

 Model tank

Constants

   ! valve (c1) and outflow (c2) constants
   c1 = 0.25    ! m^3/sec
   c2 = 0.14    ! m^1.5/sec
  End Constants

  Parameters
   percent_open ! %
  End Parameters

  Variables
   inlet_flow   ! m^3/sec
   outlet_flow  ! m^3/sec
   volume       ! m^3
  End Variables

  Equations
   inlet_flow  = c1 * percent_open
   outlet_flow = c2 * SQRT(volume)
   $volume = inlet_flow - outlet_flow
   200 < volume < 5000
  End Equations

 End Model

Tank Model in MATLAB

 function xdot = tank(t,x)

 global u

 % Input (1):
 % Inlet Valve State (% Open)
 percent_open = u;

 % State (1):
 % Volume in the Tank (m^3)
 volume = x;

 % Parameters (2):
 % Inflow Constant (m^3/sec)
 c1 = 0.25;
 % Outflow Constant (m^1.5/sec)
 c2 = 0.14;

 % Intermediate variables
 inlet_flow = (c1 * percent_open);
 outlet_flow = (c2 * volume^0.5);

 % Compute xdot (dx/dt)
 xdot(1,1) = inlet_flow - outlet_flow;

 % adjust xdot to remain within constraints
 low_volume = 200;
 if (volume < low_volume) & (percent_open < (c_outflow * low_volume^0.5)/c_inflow),
   xdot(1,1) = 0;
 end

 high_volume = 5000;
 if (volume > high_volume) & (percent_open > (c_outflow * high_volume^0.5)/c_inflow),
   xdot(1,1) = 0;
 end

Tank Model in gProms

 MODEL Tank

  DECLARE
    TYPE
      Vol  =  500.0  :  200.0  :  5000  UNIT = "m^3"
  END

  PARAMETER
    # parameters can be specified at run-time
    #   with Tank.c1 := 0.25;
    #        Tank.c2 := 0.14;
    c1           AS REAL
    c2           AS REAL

  VARIABLE
    # Volume in the Tank (m^3)
    volume       AS Vol

    # Inlet flow (m^3/sec)
    inlet_flow   AS REAL

    # Outlet flow (m3/sec)
    outlet_flow  AS REAL

    # Inlet Valve State (% Open)
    percent_open AS REAL

  EQUATION

    # Inlet flow is a linear function of valve position
    inlet_flow = c1 * percent_open ;

    # Square root pressure drop flow relation
    outlet_flow = c2 * SQRT ( volume ) ;

    # Mass balance (assuming constant density)
    $volume = inlet_flow - outlet_flow ;

 END # Model Tank

Tank Model in Modelica

 model Tank
  parameter Real c1=0.25 "Inflow Constant";
  parameter Real c2=0.14 "Outflow Constant";
  Real percent_open "Percent Open";
  Real inlet_flow "Inlet Flow";
  Real outlet_flow "Outlet Flow";
  Real volume "Tank Volume";
 equation
  inlet_flow = c1 * percent_open "Inlet flow as a linear function of valve  position";
  outlet_flow = c2 * volume^0.5 "Outlet flow as a square root function of volume";
  der(volume) = inlet_flow - outlet_flow "Mass balance (assuming constant density)";
 end Tank;

Restore

APMonitor