modeling of servo motors

8/6/2019 Modeling of Servo Motors

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System Modeling Coursework

P.R. VENKATESWARANFaculty, Instrumentation and Control Engineering,

Manipal Institute of Technology, ManipalKarnataka 576 104 INDIA

Ph: 0820 2925154, 2925152Fax: 0820 2571071Email: [email protected], [email protected]

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

Class 27: Modeling of servo motors

mailto:[email protected]


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

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 thecompilation from various sources for the purpose of delivering lectures. I humbly acknowledge the

wonderful help provided by the original sources inthis compilation.

• For best results, it is always suggested you read thesource 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 calledservomechanism.

• 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 stepduty 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 powerapplications such as in machinetools and robotics

–

High torque to inertia ratio that

gives them quick response tocontrol signals

–

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

constants(2.3 to 40ms)

•

AC servo motors

–

Generally suited for low powerapplications such as instrumentservo (e.g.) control of pen in X-Y recorders) and computer relatedequipment (disk drives, tapedrivers, printers).

–

Lower cost, higher efficiency andless maintenance

– Characteristics are nonlinear andmore difficult to control




AC Servo motor

•

It is basically a two phase induction motor except

for certain special design features. A two phaseservomotors 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 thattheir 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 phasedisplacement of 900.

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




Constructional features of AC servo motors

• The rotor construction is usually squirrel cage or drag cuptype. The squirrel cage rotor is made of laminations. Therotor bars are placed on the slots and short circuited at bothends 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 rotorconductors. (Electrically both the type of rotors areidentical)




Working of AC Servomotor

1. The stator windings are excited by voltages of equal rmsmagnitude 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 onthe phase relationship of the two currents (or voltages)

3. The exciting currents shown in the figure produce aclockwise 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 influx 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 andso 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 to1000Hz.

• By using frequencies of 400Hz or higher, the systemcan 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 thenoise and disturbance often create problems.




Control signal

•

The control winding is excited by the modulated control signal andthis voltage is of variable magnitude and polarity. The control signalof 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, inthe range of 0 to 20Hz. For production of rotating magnetic field, thecontrol phase voltage must be of the same frequency as the referencephase voltage and in addition the two voltages must be in timequadrature.

•

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 carriersignal

• ec

= control signal

•

e

car = E cosω

c t

= carrier signal

• ecm

= modulated control

signal




Speed Torque characteristics of ac servomotor




Speed Torque characteristics

• The speed torque curves of a typical ac servomotor plottedfor fixed reference phase voltage E cosω

c t and different

values of constant input voltages ec

≤E are shown.

• All these curves have negative slope. Note that the curve fore

c =0 goes through the origin, this means that when the

control phase voltage becomes zero, the motor develop adecelerating torque and so the motor stops.

• The curves show a large torque at zero speed. This is arequirement for a servomotor in order to provide rapidacceleration.




Transfer function of AC servo motor

• Let

Tm

– Torque developed by servomotor

θ

–

Angular displacement of rotor

ω

–

angular speed

Tl

– Torque required by the load

J –

Moment of Inertia of load and the rotor

B –

Viscous –

frictional coefficient of load and the rotor

K 1

-

slope of control –

phase voltage vs

torque characteristic

K 2

–

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 tothe 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

= K 1

ec

– K 2

dθ/dt

•

The load torque is given by

dt

d B

dt

d J T l

θ θ +=

2

2




Equilibrium condition

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

Therefore,

• On taking laplace transform of equation with zero initialconditions, we get,

Js2

θ(s)+Bsθ(s)=K 1 Ec

(s)-K 2 sθ(s)[Js2+Bs+ K 2

s ]θ(s)=K 1

Ec

(s)

dt

d K eK

dt

d B

dt

d J c

θ θ θ 212

2

−=+




References

•

Control Systems –

A. Nagoor

kani, RBA

Publications, Chennai




And, before we break…

•

When deeds speak, words are nothing

– African Proverb.

Thanks for listening…

modeling of servo motors

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