## Wednesday, November 16, 2011

### Understanding the DC Motor Part I

It took me quite some time to understand the permanent magnet direct current motor or people like to just call it DC motor. In order to properly control a DC motor, they should understand the motor nature first before applying the control algorithm. The dangerous part is, a motor can get over current easily, not only spoiling the driver but the motor itself will get burned.

The figure below shows a typical DC motor. Amateur hobbyist like to apply the motor voltage directly to the motor and expect the performance of the motor to be the same every time. This is not the case. Applied voltage, Va, is not directly related to the motor speed, omega. In fact, the motor is a third order system with Type 1.

In layman term, third order means, in between the applied voltage and the angle, there are motor current and motor speed. Type 1 means, if the applied voltage is removed, the angle of rotation of the motor will not go back to the original position. To understand the nature or characteristics of the motor, read on.
 Typical motor. Photo credit: Cytron.com.my
First, we should understand the built up of the motor, or the motor schematic. Not exactly how a motor was constructed but rather, what can be used to represent a motor. The figure below (motor schematic) is a good representation of a DC motor.

Motor is built up of winding coil, therefore it is represented with the motor inductance, La. With long motor coil, there is expected to have resistance, Ra. Most important part of the motor is the back electromotive force, EMF. The concept of EMF is quite hard go grasp at the beginning but it is quite simple. Back EMF is actually "virtual". In other word, it cannot be measured directly. But the motor terminal can give a good estimate of the back EMF.

Another part of the DC motor is the mechanical part. The motor is always used to move a load, depicted as J and the load sure to have viscous friction and Coulomb friction, depicted with B and T1 respectively. Coulomb friction is sometimes represented with a constant value for simplicity. Which means, the torque will always go against the movement, either it is moving or in static. While the viscous friction appears only when the motor is moving, in fact, the faster the motor is moving, the higher the torque of the viscous friction is (approximated with a linear relationship).

After understanding this motor schematic, we should move on to the motor model. Model is the most important part to understand the motor. Using a model, one could predict how a motor react to certain applied voltage, either it is linear or in pulse width modulation form.
 Motor Schematic

I am not going to go too deep in the motor model derivation. To derive the motor model, two first principle rules are needed namely the Kirchoff Voltage Law and Newton's Law. It is also useful to use La Place transformation.

The Kirchoff Voltage Law can be used to derive the electrical characteristics while the Newton's Law can be used to derive the mechanical characteristics. Besides that, one should understand the the motor current is proportional with the motor produced torque and the back EMF is proportional with the motor speed. Using all this information, the motor can be put in the form depicted in picture below.
 Motor Model (click to enlarge)

Perhaps in Part II, I will explain more about this motor model and how to derive it. Later on, I will discuss on a motor control method to properly control a motor.

Check out the full series

Part I
Part II
Part III
Part II, III - Interlude
Part IV

#### 1 comment:

Aaron Hampson said...

Thank you for the page. Really easy to understand. A big help for my dissertation. Aaron