《机电传动控制》——直流电机调速仿真作业

Posted 2020-07-26

通过将原有直流电机调速例子运行之后 可以看到电流的稳定性不好，到达稳定的时间较长，超调量较大，稳态误差不够小，震荡明显。

原有的Controller只有比例控制，很粗糙，当增益较低时，稳态误差较大，当增益变大时，会引起电机电流和加速度的振荡。

 

经过考虑决定用PID调节，三个调节参数为比例调节Kp，积分调节Ki，微分调节Kd

Kp增大会减小电流值达到稳定的时间，但会增大超调量，降低系统稳定性；

Ki消除稳态误差，但会降低系统稳定性，减慢动态响应；

Kd能减小超调量，减小调节时间；

 

最终选择参数为Kp＝７.５　Ki＝０.１　Kd＝４５

最终得到的电机电流与电机速度变化曲线如下：

可见超调量为Ｍｐ=７．６９%　　　Ｔｐ＝０.０１９５ｓ，比较理想。

 

完整代码：

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"

 

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 error_i;

Real error_d;

Real pout;

parameter Real Kp=7.5;

parameter Real Ki=0.1;

parameter Real Kd=45;

parameter Real Max_Output_Pos = 10;

parameter Real Max_Output_Neg = -10;

 

 

 

algorithm

 

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

error_i:=error_i+error;

error_d:=error-pre(error);

pout := Kp * error+Ki*error_i+Kd*error_d;

 

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;

parameter Integer n = 1 "Dimension of signal vector";

input Real signal[n] "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[n] "Real output signals";

end OutPort; // From Modelica.Blocks.Interfaces

 

 

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;

 

 

simulate( DCMotorControlSystem, stopTime=5 )

 

 

plot({motor1.i,motor1.w})