Armature Controlled DC Motor

A motor is an actuator, converting electrical energy in to rotational mechanical energy. A motor requiring a DC power supply for operation is termed a DC motor. DC motors are widely used in control applications like robotics, tape drives, machines and many more.

Separately excited DC motors are suitable for control applications because of separate field and armature circuit.{{Cite web|title=Armature Circuit - an overview {{!}} ScienceDirect Topics|url=https://www.sciencedirect.com/topics/engineering/armature-circuit|access-date=2021-01-08|website=www.sciencedirect.com}} Two ways to control DC separately excited motors are: Armature Control and Field Control.{{Cite web|title=Armature & Field Control of DC Motors {{!}} Motor Speed Control|url=https://www.carotron.com/articles/armature-field-control/|access-date=2021-01-08|language=en-US}}

A DC motor consists of two parts: a rotor and a stator.{{Cite web|date=2017-10-11|title=Difference Between Stator & Rotor|url=https://circuitglobe.com/difference-between-stator-and-rotor.html|access-date=2021-01-08|website=Circuit Globe|language=en-US}} The stator consists of field windings while the rotor (also called the armature) consists of an armature winding.{{Cite web|date=2016-01-05|title=Armature Winding|url=https://circuitglobe.com/armature-winding.html|access-date=2021-01-08|website=Circuit Globe|language=en-US}} When both the armature and the field windings are excited by a DC supply, current flows through the windings and a magnetic flux proportional to the current is produced. When the flux from the field interacts with the flux from the armature, it results in motion of the rotor. Armature control is the most common control technique for DC motors. In order to implement this control, the stator flux must be kept constant. To achieve this, either the stator voltage is kept constant or the stator coils are replaced by a permanent magnet. In the latter case, the motor is said to be a permanent magnet DC motor and is driven by the armature coils only.

Equations governing the operation of motor are made linear by simplifying the effects of the magnetic field from the stator to only its flux, $\backslash Phi$, and a term that describes the effect of the stator field on the rotor, $K\_\backslash phi$. $K\_\backslash phi$ is unlikely to be a constant and may be a function of $\backslash Phi$:

$T\; =\; K\_\backslash phi\backslash Phi\backslash Iota$ (1)

where $T$ is motor torque and $\backslash Iota$ is armature current. When field flux is constant, equation (1) becomes

$T\; =\; K\text{'}\backslash Iota$ (2)

where $K\text{'}=\; K\_\backslash phi\backslash phi$ as $\backslash Phi$ is constant.

In addition, the motor has an intrinsic negative feedback structure, hence at the steady state, the speed ω is proportional to the reference input Va.

These two facts, in addition to the cheaper price of a permanent magnet motor with respect to a standard DC motor (because only the rotor coils need to be wound), are the main reasons why armature controlled motors are widely used. However, several disadvantages arise from this control technique, of which major is the flow of large currents during transients. For example, when started speed ω is zero initially, hence back EMF (electromotive force) governed by the following relation, would be zero.

$E\_b=K\_\backslash phi\backslash phi\backslash omega$ (3)

Also, armature current is given by $I\; =\; \backslash left\; (\; \backslash frac\{V-E\_b\}\{R\_a\}\; \backslash right\; )$(4)

which will be very high causing increase in heating of machine and it may damage the insulation.Stephen J. Chapman, Electric Machinery Fundamentals.

File:Fig.2.- Block diagram of separtely excited DC motor.png

Essential Equations for transfer function:

$E\_b=K\_\backslash phi\backslash phi\backslash omega$ in Laplace domain $E\_b(s)\; =K\_\backslash phi\backslash phi\backslash omega(s)$(5)

$I\; =\; \backslash left\; (\; \backslash frac\{V-E\_b\}\{R\_a\}\; \backslash right\; )$ in Laplace domain $I(s)\; =\; \backslash left\; (\; \backslash frac\{V(s)-E\_b(s)\}\{R\_a\}\; \backslash right\; )$ (6)

$T\; =\; K\_\backslash phi\backslash Phi\backslash Iota$ in Laplace domain $T(s)\; =\; K\_\backslash phi\backslash Phi\backslash Iota(s)$ (7)

$T-T\_L\; =\; J\{d\backslash omega\; \backslash over\; dt\}\; +\; F\backslash omega$ in Laplace domain $T(s)-T\_L(s)\; =\; J\{d\backslash omega(s)\; \backslash over\; dt\}\; +\; F\backslash omega(s)$ (8)

Various parameters in figure are described as

• $K\_a\; =\; \{1\; \backslash over\; R\_a\}$ is the rotor gain.
• $\backslash tau\_a\; =\; \{L\; \backslash over\; R\_a\}$ is the electrical time constant.
• $\backslash Tau\_m$ is the motor torque.
• $K$ is a constant depending on field flux.
• $K\_m\; =\; \{1\; \backslash over\; F\}$ is mechanical gain.
• F is viscous friction coefficient.
• $\backslash tau\_m\; =\; \{J\; \backslash over\; F\}$ is the mechanical time constant, where J is moment of inertia of the load.
• $\backslash omega(s)$ is the resulting angular velocity.

The transfer matrix of the system may be written as

(9)

where $W\_1(s)\; =\; \backslash frac\{K\_aK\_\backslash phi\; K\_m\; \backslash phi\}\{(1\; +\; \backslash tau\_a\; s)(1\; +\; \backslash tau\_m\; s)\; +\; K\_aK\_m(K\_\backslash phi\; \backslash phi)^2\}$ (10)

$W\_2(s)\; =\; \backslash frac\{K\_m(1\; +\; \backslash tau\_as)\}\{(1\; +\; \backslash tau\_a\; s)(1\; +\; \backslash tau\_m\; s)\; +\; K\_aK\_m(K\_\backslash phi\; \backslash phi)^2\}$ (11)Luca Zaccarian, DC motors: dynamic model and control techniques.

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Category:Electric motors