In
this week, group members build the model of dc motor with Simulink. The next
part of the blog will talk about the process and results.
The
electric circuit of the DC motor is shown in the following figure:
As
we can see in the figure, the DC motor contains an inductor, a resistor,armature and rotor.
We
applied Newton's law and Kirchoff's law to the motor system to generate the
following equations:
Kti-Jdw/dt-Bw=0 (1)
V-iR-Ldi/dt-Kvw=0 (2)
Kt
is torque constant.
R
is electric resistance.
L
is electric inductance.
J
is moment of inertia of the rotor.
Kv
is electromotive force constant
B
is motor viscous friction constant.
We
need to know the w and i of the DC motor. By integrating equations (1) and (2)
we get the following equations (3) and (4):
w=1/J∫(Kti-Bw) (3)
i=1/L(V-iR- Kvw) (4)
The physical parameters for our example are:
Kt=0.01N*m/Amp
R=1 Ohm
L=0.5H
J=0.01kg*m^2
Kv=0.01V/rad/sec
B=0.1N*m*s
Next
is the result of simulation of DC motor.
This
is the mathematic model of the DC motor with Simulink.
This figure is the output value of current i(t).
This
figure shows the variation of angular velocity w.
Then
we build the model of dc motor by using Simscape. The circuit is:
In this section, we build the DC motor
model by using the physical modeling blocks of the Simscape extension to
Simulink. The blocks represent actual physical components. Therefore, we don't
need to build mathematical equations from physical principles to build
complex multi-domain models. The following blocks are added to the model :
DC motor
block, H-Bridge block and controlled PWM Voltage block from the Simscape/
SimElectronics
DC Voltage
Source block from the Simscape/Foundation Library/Electrical/Electrical sources
Current Sensor block from the
Simscape/Foundation Library/Electrical/Electrical Sensors library
Three PS-Simulink
Converter blocks and a Solver Configuration block from the Simscape/Utilities
library
Electrical Reference block from the
Simscape/Foundation Library/Electrical/Electrical Elements library
Ideal Rotational Motion Sensor block from
the Simscape/Foundation
Library/Mechanical/Mechanical Sensors
library
Mechanical Rotational Reference block from
the Simscape/Foundation Library/Mechanical/Rotational Elements library
Three
scope blocks from Simulink/Commonly Used Blocks
Then, connect and label the components so that they appear as in the figure above. Next the parameters of DC Voltage Source block, Controlled PWM Voltage block and H-Bridge block are set. We also set the Motor block parameters according to the data. Finally, we run the simulation and plot the results. The plots shown the motor current, motor RPM and motor position.
This
figure is the output value of current i(t).
This
figure is the output value of the rotate speed of the dc motor.
This
figure is the output value of the position of the dc motor.
In our design, we add a potentiometer to control the speed of the DC motor next is the modelling circuit: