THIS DOCUMENT MAINLY CONTAINS THE HOW TO MODLE DC SERVO MOTOR BY USING THE MATLAB SIMULINK AND HOW IT WILL BEHAVE IS SHOWN IN THE MATHEMATICAL EQUATIONS AND THE PLOTTINGS ARE ALSO KEPT IN THIS DOCUMENT SO BY THIS IT IS USEFUL TO STUDY THE CHARACTRISTICS OF A DC SERVO MOTOR

1. Modeling of DC Servo Motor Using
MATLAB-SIMULINK
Subject: Control Systems Name& Roll No: PEDIREDLA SANJAYKUMAR
18981A0241
1. Introduction to DC Servomotor:
A DC servo motor is used as an actuatorto drive a load .Actually dc motors
are mostly used in the many application’s due to they had a high of starting
torque to inertia and they had a dynamic control on it.
DC motors are actually constructed by using the stator and rotor and it also had a
controlling system in that like a gear box to control the speed of the motor
according to the signal and pulse given to that motor. And it has a feedback
generator for generating the feedback and to control the speed and torque of the dc
servo motor .DC servo motors vary in size and have a much horsepower and more
generally used in large power servo mechanism. The output torque of the motor is
proportional to the applied control voltage. And its direction is determined by the
polarity of the control voltage. Among the dc servo motors there are different types
of motors are available like series motor, shunt motor, and the permanent magnet
excitation motor. And major applications in the aircraft control system.
Servomotors that allows for precise control of angular position according to the

2. signal given to the motor. And their speed is controlled by the gears mechanism
and this mechanism will produce feedback to the system. There are two methods to
control the speed by a armature control and field control method in the armature
control method field current is constant and armature current will be varied and
same as the vice versa of a field control method also.
2. MathematicalModelling :
The behaviour of the dc servo motor can be explained by the following
equations
𝑬𝒂 = 𝒊𝜶𝑹 + 𝑳
𝒅𝒊
𝒅𝒕
+ 𝑬 𝒃
𝑳
𝒅𝒊
𝒅𝒕
= 𝑬𝒂 − 𝒊𝜶𝑹 − 𝑬 𝒃
Where 𝑬 𝒃 = 𝒌 𝒃
𝒅𝜽
𝒅𝒕
𝒅𝒊𝒂
𝒅𝒕
=
𝟏
𝑳
[ 𝑬𝒂− 𝒊𝜶𝑹 − 𝑬 𝒃]
Also
𝝉 = 𝑱
𝒅𝜽 𝟐
𝒅𝒕 𝟐
+ 𝑩
𝒅𝜽
𝒅𝒕
𝑱
𝒅𝜽 𝟐
𝒅𝒕 𝟐
= 𝝉 − 𝑩
𝒅𝜽
𝒅𝒕
𝒅𝜽 𝟐
𝒅𝒕 𝟐
=
𝟏
𝑱
[𝝉 − 𝑩
𝒅𝜽
𝒅𝒕
]
Where
𝝉 = 𝑲 𝑻 𝒊 𝒂
3. Modelling Using MATLAB-SIMULINK
The dc motor can be modelled by using the mat lab Simulink. In the mat lab
there will be an option called Simulink and after that by clicking on the
Simulink blocks and simuscape all the blocks can be inserted into the
workspace and by joining all the blocks and by giving the parametric equations

3. and values. And then we can run the program. Then we can get the plotted
graph.
The equations for the electrical side of the dc servo motor is
𝑬𝒂 = 𝒊𝜶𝑹 + 𝑳
𝒅𝒊
𝒅𝒕
+ 𝑬 𝒃
Where ( 𝑬 𝒃=𝒌 𝒃
𝒅𝜽
𝒅𝒕
)
𝑬𝒂 = 𝒊𝜶𝑹 + 𝑳
𝒅𝒊
𝒅𝒕
+ 𝒌 𝒃
𝒅𝜽
𝒅𝒕
Where Eb is the motors back EMF constant.
The equations for the mechanical side of the dc servo motor is
𝝉 = 𝑱
𝒅𝜽 𝟐
𝒅𝒕 𝟐
+ 𝑩
𝒅𝜽
𝒅𝒕
Where ( 𝝉 = 𝑲 𝑻 𝒊 𝒂)

4. 𝐾 𝑇 𝑖 𝑎 = 𝐽
𝑑𝜃2
𝑑𝑡2
+ 𝐵
𝑑𝜃
𝑑𝑡
Where 𝜏 is the applied torque and 𝐾 𝑇 is the torque constant that relates the torque
to the armature current.
4. Simulation results: [Response forunit stepinput]
The result for the servo dc motor has been plotted by the help of matlab Simulink
software .and the graph is plotted between the time response and e value .The
result is plotted like this. And this plotted graph shows that with the linear
increasing of the time period the time constant (𝜏) has become constant.