直流调速系统Modelica基本模型

为了便于在OpenModelica进行仿真，形成一个完整的仿真模型，没有使用第三方的库，参照了DrModelica的例程，按照Modelica库的开源模型定义了所用的基本元件模型。

首先给出一些基本类型的定义：

type ElectricPotential     = Real;
type ElectricCurrent     = Real(quantity = "ElectricCurrent", unit = "A");
type Resistance       = Real(quantity = "Resistance", unit = "Ohm", min = 0);
type Inductance       = Real(quantity = "Inductance", unit = "H", min = 0);
type Voltage         = ElectricPotential;
type Current         = ElectricCurrent;

type Force           = Real(quantity = "Force", unit = "N");
type Angle           = Real(quantity = "Angle", unit = "rad", displayUnit = "deg");
type Torque         = Real(quantity = "Torque", unit = "N.m");
type AngularVelocity     = Real(quantity = "AngularVelocity", unit = "rad/s", displayUnit = "rev/min");
type AngularAcceleration   = Real(quantity = "AngularAcceleration", unit = "rad/s2");
type MomentOfInertia     = Real(quantity = "MomentOfInertia", unit = "kg.m2");

type Time = Real (final quantity="Time", final unit="s");

connector RotFlange_a       "1D rotational flange (filled square)"
Angle phi           "Absolute rotational angle of flange";
flow Torque tau         "Torque in the flange";
end RotFlange_a;        //From Modelica.Mechanical.Rotational.Interfaces

connector RotFlange_b       "1D rotational flange (filled square)"
Angle phi           "Absolute rotational angle of flange";
flow Torque tau         "Torque in the flange";
end RotFlange_b;        //From Modelica.Mechanical.Rotational.Interfaces

connector Pin           "Pin of an electrical component"
Voltage v           "Potential at the pin";
flow Current i         "Current flowing into the pin";
end Pin;              //From Modelica.Electrical.Analog.Interfaces

connector PositivePin       "Positive pin of an electrical component"
Voltage v           "Potential at the pin";
flow Current i         "Current flowing into the pin";
end PositivePin;          //From Modelica.Electrical.Analog.Interfaces

connector NegativePin       "Negative pin of an electrical component"
Voltage v           "Potential at the pin";
flow Current i         "Current flowing into the pin";
end NegativePin;          //From Modelica.Electrical.Analog.Interfaces

connector InPort        "Connector with input signals of type Real"
parameter Integer n = 1    "Dimension of signal vector";
input Real     signal
"Real input signals";
end InPort;            // From Modelica.Blocks.Interfaces

connector OutPort        "Connector with output signals of type Real"
parameter Integer n = 1    "Dimension of signal vector";
output Real     signal
"Real output signals";
end OutPort;          // From Modelica.Blocks.Interfaces

基于上述自定义类型，定义一些基本元件的模型：

partial model Rigid           // Rotational class Rigid
"Base class for the rigid connection of two rotational 1D flanges"
Angle phi               "Absolute rotation angle of component";
RotFlange_a rotFlange_a  "(left) driving flange (axis directed into plane)";
RotFlange_b rotFlange_b  "(right) driven flange (axis directed out of plane)";
equation
rotFlange_a.phi = phi;
rotFlange_b.phi = phi;
end Rigid;                // From Modelica.Mechanics.Rotational.Interfaces

model Inertia    "1D rotational component with inertia"
extends Rigid;
parameter MomentOfInertia J = 1    "Moment of inertia";
AngularVelocity     w          "Absolute angular velocity of component";
AngularAcceleration a          "Absolute angular acceleration of component";
equation
w = der(phi);
a = der(w);
J*a = rotFlange_a.tau + rotFlange_b.tau;
end Inertia;              //From Modelica.Mechanics.Rotational

partial model TwoPin          // Same as OnePort in Modelica.Electrical.Analog.Interfaces
"Component with two electrical pins p and n and current i from p to n"
Voltage v                "Voltage drop between the two pins (= p.v - n.v)";
Current i                "Current flowing from pin p to pin n";
PositivePin p;
NegativePin n;
equation
v = p.v - n.v;
0 = p.i + n.i;
i = p.i;
end TwoPin;

model DCMotor                 "DC Motor"
extends TwoPin;
extends Rigid;
OutPort SensorVelocity(n=1);
OutPort SensorCurrent(n=1);
parameter MomentOfInertia J"Total Inertia";
parameter Resistance R"Armature Resistance";
parameter Inductance L"Armature Inductance";

parameter Real Kt"Torque Constant";
parameter Real Ke"EMF Constant";

AngularVelocity    w          "Angular velocity of motor";
AngularAcceleration a          "Absolute angular acceleration of motor";
Torque tau_motor;
RotFlange_b    rotFlange_b;    // Rotational Flange_b

equation

w = der(rotFlange_b.phi);
a = der(w);
v = R*i+Ke*w+L*der(i);
tau_motor =  Kt*i;
J*a = tau_motor + rotFlange_b.tau;
SensorVelocity.signal[1] = w;
SensorCurrent.signal[1] = i;
end DCMotor;

class Resistor               "Ideal linear electrical Resistor"
extends TwoPin;            // Same as OnePort
parameter Real R(unit = "Ohm")     "Resistance";
equation
R*i = v;
end Resistor;                // From Modelica.Electrical.Analog.Basic

class Inductor               "Ideal linear electrical Inductor"
extends TwoPin;            // Same as OnePort
parameter Real L(unit = "H")       "Inductance";
equation
v = L*der(i);
end Inductor;              // From Modelica.Electrical.Analog.Basic

class Ground               "Ground node"
Pin p;
equation
p.v = 0;
end Ground;                // From Modelica.Electrical.Analog.Basic

model PWMVoltageSource
extends TwoPin;
InPort Command(n=1);

parameter Time T = 0.003;
parameter Voltage Vin = 200;

equation

T*der(v)+ v = Vin*Command.signal[1]/10;

end PWMVoltageSource;

block Controller

InPort command(n=1);
InPort feedback(n=1);
OutPort outPort(n=1);

Real error;
Real pout;
parameter Real Kp=10;
parameter Real Max_Output_Pos = 10;
parameter Real Max_Output_Neg = -10;

//  parameter Real Ki=1;

algorithm

error := command.signal[1] -  feedback.signal[1];
pout := Kp * error;

if pout > Max_Output_Pos then
outPort.signal[1] := Max_Output_Pos;
elseif pout < Max_Output_Neg then
outPort.signal[1] := Max_Output_Neg;
else
outPort.signal[1] := pout;
end if;

end Controller;

block CommandSignalGenerator

OutPort outPort(n=1);
Real acc;

equation

if time <= 1 then
acc =60;
elseif time <3 then
acc = 0;
elseif time <4 then
acc = -60;
else
acc = 0;
end if;

der(outPort.signal[1]) = acc;

end CommandSignalGenerator;

基于上述元件模型，给出一个直流调速系统实例：

model DCMotorControlSystem

Ground       ground1;
Inertia      inertia1(J = 3, w(fixed = true));
DCMotor      motor1(J = 1,R = 0.6,L = 0.01,Kt=1.8, Ke= 1.8,rotFlange_b(phi(fixed = true)));
CommandSignalGenerator  sg1;
Controller   con1;
PWMVoltageSource PowerSource1;
equation
connect(sg1.outPort, con1.command);
connect(con1.feedback, motor1.SensorVelocity);
connect(con1.outPort, PowerSource1.Command);
connect(PowerSource1.p, motor1.p);
connect(motor1.rotFlange_b, inertia1.rotFlange_a);
connect(PowerSource1.n, ground1.p);
connect(ground1.p, motor1.n);
end DCMotorControlSystem;

模型检查通过后，就可以运行仿真命令并观察各个标量的波形。

simulate( DCMotorControlSystem, stopTime=5 )