APMonitor

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

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;
 low_open = c_outflow * low_volume^0.5)/c_inflow;
 if (volume < low_volume) & (percent_open < low_open),
   xdot(1,1) = 0;
 end

 high_volume = 5000;
 high_open = c_outflow * high_volume^0.5)/c_inflow;
 if (volume > high_volume) & (percent_open > high_open),
   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";
  outlet_flow = c2 * volume^0.5 "Outlet flow";
  der(volume) = inlet_flow - outlet_flow "Mass balance";
 end Tank;