Modelica Example - First Order Equation

// Solve the first-order differential equation with initial value

within ModelicaByExample.BasicEquations.SimpleExample;

model FirstOrderInitial "First order equation with initial value"

  Real x "State variable";

initial equation //initialization equation of variable x 

  x = 2"Used before simulation to compute initial values"; 

equation

  der(x) = 1-x "Drives value of x toward 1.0";

  //variable differential equation

annotation(experiment(StartTime=0,StopTime=8));

//Define the simulation start time and simulation end time, in seconds (s)

end FirstOrderInitial;

//Solve first-order differential equations at steady state start

within ModelicaByExample.BasicEquations.SimpleExample;

model FirstOrderInitial "First order equation with initial value"

  Real x "State variable";

initial equation //initialization equation of variable x   

der(x) = 0"Initialize the system in steady state"; 

//The initial tangent of the variable is the horizontal line

equation

  der(x) = 1-x "Drives value of x toward 1.0";

  //variable differential equation

annotation(experiment(StartTime=0,StopTime=8));

//Define the simulation start time and simulation end time, in seconds (s)

end FirstOrderInitial;

//One-dimensional Newton cooling equation

within ModelicaByExample.BasicEquations.CoolingExample;

model NewtonCooling "An example of Newton's law of cooling"

  parameter Real T_inf "Ambient temperature" ;//Ambient temperature 

  parameter Real T0 "Initial temperature" ;//Initial temperature 

  parameter Real h "Convective cooling coefficient" ;//thermal convection coefficient 

  parameter Real A "Surface area" ;//Surface area 

  parameter Real m "Mass of thermal capacitance" ;//Object mass 

  parameter Real c_p "Specific heat" ;//The specific heat capacity of the object 

  Real T "Temperature" ;//Object temperature

initialequation 

  T = T0 "Specify initial value for T";

  //object temperature

equation

  m*c_p*der(T) = -h*A*(T - T_inf) "Newton's law of cooling";

end NewtonCooling;

//带类型定义的一维冷却牛顿方程

within ModelicaByExample.BasicEquations.CoolingExample;

model NewtonCoolingWithTypes "Cooling example with physical types"

  // Types

  type Temperature=Real(unit="K", min=0);//定义新的类型；

  type ConvectionCoefficient=Real(unit="W/(m2.K)", min=0);

  type Area=Real(unit="m2", min=0);

  type Mass=Real(unit="kg", min=0);

  type SpecificHeat=Real(unit="J/(K.kg)", min=0);

  // Parameters

  parameter Temperature T_inf=298.15 "Ambient temperature";

  parameter Temperature T0=363.15 "Initial temperature";

  parameter ConvectionCoefficient h=0.7 "Convective cooling coefficient";

  parameter Area A=1.0 "Surface area";

  parameter Mass m=0.1 "Mass of thermal capacitance";

  parameter SpecificHeat c_p=1.2 "Specific heat";

  // Variables

  Temperature T "Temperature";

initial equation

  T = T0 "Specify initial value for T";

equation

  m*c_p*der(T) = h*A*(T_inf-T) "Newton's law of cooling";

end NewtonCoolingWithTypes;