Example H2.2
MATLAB code for example 2.2 from the book "Regeltechniek voor het HBO"
Making a block diagram of a 'independently energized' DC motor
- Date : 31/03/2022
- Revision : 1.0
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Table of Contents
Electrical part
We are going to draw up the block diagram of a so-called independently energized dc motor. That is a motor for which the magnetic field in the air gap between rotor and stator is constant. When the motor is connected to the supply voltage 
, a current i flows and rotation occurs. However, the angular velocity ω then generates a voltage e that is directly proportional to this (
) and opposes the voltage . If we call the ohmic resistance of the rotor circuit 
and the self-induction of the rotor windings 
, we can write for the 'electrical part' of the motor:
, a current i flows and rotation occurs. However, the angular velocity ω then generates a voltage e that is directly proportional to this () and opposes the voltage . If we call the ohmic resistance of the rotor circuit and the self-induction of the rotor windings , we can write for the 'electrical part' of the motor:
and also:
Also, the angular velocity ω of the shaft is the derivative of the shaft angle θ :
. Translating to the s-domain: 
.Mechanical part
The torque m delivered by the motor - because of the independent excitation - is directly proportional to the current i and this torque is used to increase the angular velocity and overcome the bearing friction (see also §2.5.3). This can be expressed as follows.
and also:
So this is the 'mechanical part' of the motor; if desired, the fixed torque resulting from what is driven, the so-called load torque, must also be taken into account. Of course c, J and 
are constants. From these two simultaneous equations, the block diagram is drawn in figure 2.36 using:
are constants. From these two simultaneous equations, the block diagram is drawn in figure 2.36 using:Using equation 2.8, we now obtain as the total transmission function:
Two things stand out in this expression:
- the system inherently has a feedback due to the generated reverse voltage in the rotor of the motor;
- the electrical and mechanical parameters are "intertwined" with each other and determine jointly the coefficients of the transmission function, i.e. of the dynamic behavior. In other words, the time constant of the electrical and mechanical system separately is no longer assignable.