Class 27 - Modeling of Servo Motors

System Modeling Coursework

P.R. VENKATESWARANFaculty, Instrumentation and Control Engineering,

Manipal Institute of Technology, ManipalKarnataka 576 104 INDIAPh: 0820 2925154, 2925152

Fax: 0820 2571071Email: [email protected], [email protected]

Web address: http://www.esnips.com/web/SystemModelingClassNotes

Class 27: Modeling of servo motors

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http://www.esnips.com/web/SystemModelingClassNotes

July – December 2008 prv/System Modeling Coursework/MIT-Manipal 2

WARNING!

•

I claim no originality in all these notes. These are the compilation from various sources for the purpose of delivering lectures. I humbly acknowledge the wonderful help provided by the original sources in this compilation.

•

For best results, it is always suggested you read the source material.


Contents

•

What is servo mechanism•

Applications of servomechanism

•

Construction of AC servo motor•

Transfer function of AC servo motor


Servo explanation

•

When the objective of the system is to control the position of an object then the system is called servomechanism.

•

Servomotors are used to convert an electrical signal (control voltage) applied to them into an angular displacement of the shaft.

•

They can either operate in a continuous duty or step duty depending on construction.


Characteristics of servo motors

•

Linear relationship between the speed and electric control signal

•

Steady state stability•

Wide range of speed control

•

Linearity of mechanical characteristics throughout the entire speed range

•

Low mechanical and electrical inertia and •

Fast response


Types of servo motors

•

DC servo motors–

Generally used for large power applications such as in machine tools and robotics

–

High torque to inertia ratio that gives them quick response to control signals

–

Low electrical time constants (0.1 to 6ms) and low mechanical time constants(2.3 to 40ms)

•

AC servo motors–

Generally suited for low power applications such as instrument servo (e.g.) control of pen in X-Y recorders) and computer related equipment (disk drives, tape drivers, printers).

–

Lower cost, higher efficiency and less maintenance

–

Characteristics are nonlinear and more difficult to control


AC Servo motor

•

It is basically a two phase induction motor except for certain special design features. A two phase servomotors differs in the following two ways from a normal induction motor.–

The rotor of the servomotor is built with high resistance, so that its X/R (Inductive Resistance/Resistance) ratio is small which results in linear speed torque characteristics.

–

The excitation voltage applied to two stator windings should have a phase difference of 900


Construction of AC servo motor


Constructional features of AC servo motors

•

The stator consists of two pole –

pairs (A-B and C-D) mounted on the inner periphery of the stator, such that their axes are at an angle of 900

in space. Each pole-pair

carries a winding. One winding is called the reference winding and the other is called control winding.

•

The exciting current in the winding should have a phase displacement of 900.

•

The supply used to drive the motor is single phase and so a phase advancing capacitor is connected to one of the phase to produce a phase difference of 900.


Constructional features of AC servo motors

•

The rotor construction is usually squirrel cage or drag cup type. The squirrel cage rotor is made of laminations. The rotor bars are placed on the slots and short circuited at both ends by end rings.

•

The diameter of the rotor is kept small in order to reduce inertia and to obtain good accelerating characteristics.

•

The drag cup construction is employed for very low inertia applications. In this type of construction, the rotor will be in

the form of hollow cylinder made of aluminum. •

The aluminum cylinder itself acts as short circuited rotor conductors. (Electrically both the type of rotors are identical)


Working of AC Servomotor

1.

The stator windings are excited by voltages of equal rms magnitude and 900

phase difference. This results in

exciting currents i1

and i2

that are phase displaced by 900

and have equal rms

values.2.

These currents give rise to a rotating magnetic field of constant magnitude. The direction of rotation depends on the phase relationship of the two currents (or voltages)

3.

The exciting currents shown in the figure produce a clockwise rotating magnetic field and a phase shift of 1800

in i1

will produce an anticlockwise rotating magnetic field.


Working of AC Servomotor

4.

The rotating magnetic field sweeps over the rotor conductors. The rotor conducts experience a change in flux and so voltages are induced in rotor conductors.

5.

This voltage circulates current in the short circuited rotor conductors and the currents create rotor flux.

6.

Due to the interaction of stator and rotor flux, a mechanical force (or torque) is developed on the rotor and so the rotor starts moving in the same direction as that of the magnetic field.


Working of AC servo motor in control systems


Working of AC servo motor in control systems

•

The reference winding is excited by a constant voltage source with a frequency range of 50 to 1000Hz.

•

By using frequencies of 400Hz or higher, the system can be made less susceptible to low-frequency noise.

•

Due to this feature, ac devices are extensively used in aircraft and missile control system in which the noise and disturbance often create problems.


Control signal

•

The control winding is excited by the modulated control signal and this voltage is of variable magnitude and polarity. The control signal of the servo loop (or the system) dictates the magnitude and polarity of the voltage.

•

The control signals in control systems are usually of low frequency, in the range of 0 to 20Hz. For production of rotating magnetic field, the control phase voltage must be of the same frequency as the reference phase voltage and in addition the two voltages must be in time quadrature.

•

Hence the control signal is modulated by a carrier whose frequency is same as that of reference voltage and then applied to control winding.

•

The ac supply itself is used as carrier signal for modulation process. The 900

phase difference between the control-phase and reference- phase voltage is obtained by the insertion of a capacitor in reference

winding.


Waveforms of control signal, modulated wave and carrier signal

•

ec

= control signal

•

ecar

= E cosωc

t = carrier signal

•

ecm

= modulated control

signal


Output Waveforms

•

The type of modulation is amplitude modulation and so the information is available on the envelope of the modulated signal.

•

It can be observed that the envelope of the modulated wave is identical to control signal.

•

The polarity of ec

dictates the phase of ecm

with respect to that of carrier.

•

If ec

is positive then ecm

and ecar

have the same phase otherwise they have 1800

phase difference.


Speed Torque characteristics of ac servomotor


Speed Torque characteristics

•

The speed torque curves of a typical ac servomotor plotted for fixed reference phase voltage E cosωc

t and different values of constant input voltages ec

≤E

are shown.•

All these curves have negative slope. Note that the curve for ec

=0 goes through the origin, this means that when the control phase voltage becomes zero, the motor develop a decelerating torque and so the motor stops.

•

The curves show a large torque at zero speed. This is a requirement for a servomotor in order to provide rapid acceleration.


Transfer function of AC servo motor

•

LetTm

–

Torque developed by servomotorθ

–

Angular displacement of rotor

ω

–

angular speedTl

–

Torque required by the loadJ –

Moment of Inertia of load and the rotor

B –

Viscous –

frictional coefficient of load and the rotorK1

-

slope of control –

phase voltage vs

torque characteristicK2

–

slope of speed –

torque characteristic


Torque equations

•

With respect to the characteristics of the servo motor, for speeds near zero, all the curves are straight lines parallel to the characteristic at rated input voltage (ec

=E) and are equally spaced for equal increments of the input voltage. Under this assumption, the torque developed is given as:

Torque developed by the motor, Tm

= K1

ec

– K2

dθ/dt

•

The load torque is given by

dtdB

dtdJTl

θθ+= 2

2


Equilibrium condition

•

At equilibrium, load torque is equal to load torque. Therefore,

•

On taking laplace

transform of equation with zero initial conditions, we get,

Js2θ(s)+Bsθ(s)=K1

Ec

(s)-K2

sθ(s)[Js2+Bs+ K2

s ]θ(s)=K1

Ec

(s)

dtdKeK

dtdB

dtdJ c

θθθ212

2

−=+


Transfer function

)1(

)1(

)/()()(

)(

2

21

2

1

+=

++

+=

++=

ssK

sKB

Js

KBKKBJss

KsEs

m

m

c

τ

θ

tconstimeMotorKB

J

tconsgainMotorKB

KKwhere

m

m

tan

tan

2

2

1

=+

=

=+

=

τ


References

•

Control Systems – A. Nagoor

kani, RBA

Publications, Chennai


And, before we break…

•

When deeds speak, words are nothing–

African Proverb.

Thanks for listening…

Class 27 - Modeling of Servo Motors

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