LIBRARY

Examples.QuadTankPlant

Quadruple-tank process (Johansson) with two pumps: the lower tanks 1 and 2 are fed by their own pump and by the tank above; the fraction of each pump flow reaching the lower tank is gamma. Levels in cm, pump voltages in V. Translated from the DyadControlSystems quadtank tutorial (non-minimum-phase setting gamma1 = gamma2 = 0.2). The square roots are regularized so the model is smooth near empty tanks.

Usage

MPCComponents.Examples.QuadTankPlant(k1=1.6, k2=1.6, g=9.81, A=4.9, a=0.03, gamma1=0.2, gamma2=0.2, h10=2.0, h20=1.0, h30=8.0, h40=3.0)

Parameters:

Name	Description	Units	Default value
k1		–	1.6
k2		–	1.6
g		–	9.81
A		–	4.9
a		–	0.03
gamma1		–	0.2
gamma2		–	0.2
h10	Initial levels	–	2.0
h20		–	1.0
h30		–	8.0
h40		–	3.0

Connectors

• u1 - This connector represents a real signal as an input to a component (RealInput)

• u2 - This connector represents a real signal as an input to a component (RealInput)

• y1 - This connector represents a real signal as an output from a component (RealOutput)

• y2 - This connector represents a real signal as an output from a component (RealOutput)

• y3 - This connector represents a real signal as an output from a component (RealOutput)

• y4 - This connector represents a real signal as an output from a component (RealOutput)

Variables

Name	Description	Units
h1		–
h2		–
h3		–
h4		–

Behavior

Behavior of this component cannot be rendered because it includes path variables.

Source

"""
Quadruple-tank process (Johansson) with two pumps: the lower tanks 1 and 2 are fed by their own pump
and by the tank above; the fraction of each pump flow reaching the lower tank is `gamma`. Levels in cm,
pump voltages in V. Translated from the DyadControlSystems quadtank tutorial (non-minimum-phase setting
`gamma1 = gamma2 = 0.2`). The square roots are regularized so the model is smooth near empty tanks.
"""
component QuadTankPlant
  "Pump 1 voltage"
  u1 = RealInput() {
    "Dyad": {"placement": {"diagram": {"x1": -100, "x2": 0, "y1": 210, "y2": 310}}}
  }
  "Pump 2 voltage"
  u2 = RealInput() {
    "Dyad": {"placement": {"diagram": {"x1": -100, "x2": 0, "y1": 730, "y2": 830}}}
  }
  "Level of tank 1"
  y1 = RealOutput() {
    "Dyad": {"placement": {"diagram": {"x1": 1000, "x2": 1100, "y1": 110, "y2": 210}}}
  }
  "Level of tank 2"
  y2 = RealOutput() {
    "Dyad": {"placement": {"diagram": {"x1": 1000, "x2": 1100, "y1": 320, "y2": 420}}}
  }
  "Level of tank 3"
  y3 = RealOutput() {
    "Dyad": {"placement": {"diagram": {"x1": 1000, "x2": 1100, "y1": 580, "y2": 680}}}
  }
  "Level of tank 4"
  y4 = RealOutput() {
    "Dyad": {"placement": {"diagram": {"x1": 1000, "x2": 1100, "y1": 800, "y2": 900}}}
  }
  parameter k1::Real = 1.6
  parameter k2::Real = 1.6
  parameter g::Real = 9.81
  parameter A::Real = 4.9
  parameter a::Real = 0.03
  parameter gamma1::Real = 0.2
  parameter gamma2::Real = 0.2
  "Initial levels"
  parameter h10::Real = 2.0
  parameter h20::Real = 1.0
  parameter h30::Real = 8.0
  parameter h40::Real = 3.0
  variable h1::Real(initial = h10)
  variable h2::Real(initial = h20)
  variable h3::Real(initial = h30)
  variable h4::Real(initial = h40)
relations
  der(h1) = -a / A * sqrt(max(2 * g * h1, 0) + 0.001) + a / A * sqrt(max(2 * g * h3, 0) + 0.001) + gamma1 * k1 / A * u1
  der(h2) = -a / A * sqrt(max(2 * g * h2, 0) + 0.001) + a / A * sqrt(max(2 * g * h4, 0) + 0.001) + gamma2 * k2 / A * u2
  der(h3) = -a / A * sqrt(max(2 * g * h3, 0) + 0.001) + (1 - gamma2) * k2 / A * u2
  der(h4) = -a / A * sqrt(max(2 * g * h4, 0) + 0.001) + (1 - gamma1) * k1 / A * u1
  y1 = h1
  y2 = h2
  y3 = h3
  y4 = h4
metadata {
  "Dyad": {
    "icons": {"default": "dyad://MPCComponents/QuadTankPlant.svg"},
    "doc": {"behavior": false}
  }
}
end

Flattened Source

"""
Quadruple-tank process (Johansson) with two pumps: the lower tanks 1 and 2 are fed by their own pump
and by the tank above; the fraction of each pump flow reaching the lower tank is `gamma`. Levels in cm,
pump voltages in V. Translated from the DyadControlSystems quadtank tutorial (non-minimum-phase setting
`gamma1 = gamma2 = 0.2`). The square roots are regularized so the model is smooth near empty tanks.
"""
component QuadTankPlant
  "Pump 1 voltage"
  u1 = RealInput() {
    "Dyad": {"placement": {"diagram": {"x1": -100, "x2": 0, "y1": 210, "y2": 310}}}
  }
  "Pump 2 voltage"
  u2 = RealInput() {
    "Dyad": {"placement": {"diagram": {"x1": -100, "x2": 0, "y1": 730, "y2": 830}}}
  }
  "Level of tank 1"
  y1 = RealOutput() {
    "Dyad": {"placement": {"diagram": {"x1": 1000, "x2": 1100, "y1": 110, "y2": 210}}}
  }
  "Level of tank 2"
  y2 = RealOutput() {
    "Dyad": {"placement": {"diagram": {"x1": 1000, "x2": 1100, "y1": 320, "y2": 420}}}
  }
  "Level of tank 3"
  y3 = RealOutput() {
    "Dyad": {"placement": {"diagram": {"x1": 1000, "x2": 1100, "y1": 580, "y2": 680}}}
  }
  "Level of tank 4"
  y4 = RealOutput() {
    "Dyad": {"placement": {"diagram": {"x1": 1000, "x2": 1100, "y1": 800, "y2": 900}}}
  }
  parameter k1::Real = 1.6
  parameter k2::Real = 1.6
  parameter g::Real = 9.81
  parameter A::Real = 4.9
  parameter a::Real = 0.03
  parameter gamma1::Real = 0.2
  parameter gamma2::Real = 0.2
  "Initial levels"
  parameter h10::Real = 2.0
  parameter h20::Real = 1.0
  parameter h30::Real = 8.0
  parameter h40::Real = 3.0
  variable h1::Real(initial = h10)
  variable h2::Real(initial = h20)
  variable h3::Real(initial = h30)
  variable h4::Real(initial = h40)
relations
  der(h1) = -a / A * sqrt(max(2 * g * h1, 0) + 0.001) + a / A * sqrt(max(2 * g * h3, 0) + 0.001) + gamma1 * k1 / A * u1
  der(h2) = -a / A * sqrt(max(2 * g * h2, 0) + 0.001) + a / A * sqrt(max(2 * g * h4, 0) + 0.001) + gamma2 * k2 / A * u2
  der(h3) = -a / A * sqrt(max(2 * g * h3, 0) + 0.001) + (1 - gamma2) * k2 / A * u2
  der(h4) = -a / A * sqrt(max(2 * g * h4, 0) + 0.001) + (1 - gamma1) * k1 / A * u1
  y1 = h1
  y2 = h2
  y3 = h3
  y4 = h4
metadata {
  "Dyad": {
    "icons": {"default": "dyad://MPCComponents/QuadTankPlant.svg"},
    "doc": {"behavior": false}
  }
}
end

Test Cases

No test cases defined.

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