Modelling of DC Motor by Using SIMULINK and SIMSCAPE

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:

K_ti-Jdw/dt-Bw=0                (1)

V-iR-Ldi/dt-K_vw=0               (2)

K_t is torque constant.

R is electric resistance.

L is electric inductance.

J is moment of inertia of the rotor.

K_v 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∫(K_ti-Bw)                 (3)

i=1/L(V-iR- K_vw)                (4)

The physical parameters for our example are:

K_t=0.01N*m/Amp

R=1 Ohm

L=0.5H

J=0.01kg*m^2

K_v=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: