Answer 1

A closed loop control system can be represented by the general block diagram shown in figure.

The function of the error detector is to give out signal proportional to the difference of input and output.The most commonly usederror detectors in servo systems are potentiometers and a pair of synchros.

A synchro is an electromagnetic transducer commonly used to convert angular position of shaft into an electrical signal.It is commercially known as a selsyn or an autosyn.It basically consists of a synchro transmitter (generator) and a synchro receiver(control transformer).

Synchro generator

Its construction is similar to that of a three phase alternator.

An ac voltage V_r(t)=V_rsinw_ct

is applied to the rotor winding through slip rings.

This voltage causes a flow of magnetising current in the rotor coil which produces a sinusoidally time varying flux directed along its axis and distributed nearly sinusoidally in the air gap along the stator periphery.Because of the transformer action,voltages are induced in each of the stator coils.As the air gap flux is sinusoidally distributed,the flux linking any stator coil is proportional to the cosine of the angle between rotor and stator coil axes and so is the voltage induced in each stator coil.Thus the synchro transmitter acts as a single phase transformer in which the rotor coil is the primary and the stator coil forms three secondaries.

Let V_s1n,V_s2n,V_s3n be the voltages induced in the stator coils S₁,S₂,S₃ with respect to neutral.When the rotor axis make an angle theta with the axes of the stator coils S₂.

V_s1n=KV_rsinw_ctcos(q+120)

V_s2n=KV_rsinw_ctcos(q)

V_s3n=KV_rsinw_ctcos(q+240)

The three terminal voltages of stator are:

V_s1s2=1.73KV_r sin(q+240)sinw_ct

V_s2s3=1.73KV_r sin(q+120)sinw_ct

V_s3s1=1.73KV_r sin(q)sinw_ct

When theta(q)=0,it is seen that maximum voltage is induced in the stator coil s2 and terminal voltage Vs3s1 is zero.This position of the rotor is defined as the electrical zero of the transmitter and is used as reference for specifying the angular position of the rotor.

The output of the synchro transmitter is applied to the stator of a synchro control transformer.Circulating currents of the same phase but of different magnitudes flow through the two sets of stator coils.The control transformer flux axis being in the same position as that of the synchro transmitter rotor,the voltage induced in the C.T rotor is proportional to the cosine of the angle between the two rotors:

e(t)=KVrcosØ sinw_ct

Ø=angular displacement between the two rotors(error angle).

when Ø=90 ,e(t)=0,ie voltage induced in the C T rotor is zero.This is electrical zero of the C.T rotor.

The synchro transmitter-control transformer pair acts as an error detector giving a voltage signal at the rotor terminals of the control transformer proportional to the angular difference between the transmitter and control transformer shaft positions.

Synchro and stepper motor

There are two distinctly different ways of using stepper motors in control systems.One is the open loop mode and other is the closed loop mode.

The stepper motor is a digital  device whose output in shaft angular displacement is completely determined by the number of input pulses.Consequently,there is no need for a feedback device to determine the position of motor  shaft and ,therefore,of the load connected to the motor shaft.We can use an open step servo system with the same accuracy as that of a closed loop analog system.

If  we need to operate the stepper motor in closed loop(positional feedback)mode,we need to use synchros for error detection.Here the motor is used like conventional servomotor.A signal from the output is fed back and is used to operate a gate controlling the pulses from a pulse generator.This is shown in the figure below:

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