## Main.CompareModelingLanguages History

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(:title Comparison of Syntax:)

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<!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>

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June 16, 2015, at 06:08 AM by 45.56.3.184 -
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  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; "><span class="sc5">Parameters</span><span class="sc24">  </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  </span><span class="sc24"> </span><span class="sc0">a2</span><span class="sc24"> </span><span class="sc6">=</span><span class="sc24"> </span><span class="sc3">0.14</span><span class="sc24"> </span><span class="sc2">! m^1.5/sec </span><span class="sc5">Variables</span><span class="sc24">  </span><span class="sc0">inlet_flow</span><span class="sc24"> </span><span class="sc2">! m^3/sec  </span><span class="sc24"> </span><span class="sc0">outlet_flow</span><span class="sc24"> </span><span class="sc2">! m^3/sec </span><span class="sc24"> </span><span class="sc0">volume</span><span class="sc24"> </span><span class="sc2">! m^3 </span><span class="sc5">Equations</span><span class="sc24">  </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">


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June 16, 2015, at 06:05 AM by 45.56.3.184 -
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   a1 = 0.25    ! m^3/sec
a2 = 0.14    ! m^1.5/sec

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

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

June 16, 2015, at 06:03 AM by 45.56.3.184 -
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 Parameters
percent_open ! %
a1 = 0.25    ! m^3/sec

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

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

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

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

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  percent_open ! %

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

June 16, 2015, at 05:59 AM by 45.56.3.184 -
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### Tank Model in APMonitor

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

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

June 16, 2015, at 05:57 AM by 45.56.3.184 -
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### Tank Model in MATLAB

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 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),

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### Tank Model in gProms

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### Tank Model in Modelica

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  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";

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

(: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;