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# User Manual & Technical Reference Transfer Function of Dc Servo Motor

## INTRODUCTION

In the DC servomotor that includes two windings; a stationary field winding on the stator and a second winding for the rotating armature. This type of motor can be controlled by varying either the field current or the armature current. Most modern servomotors are somewhat different in construction. The field winding is replaced with two or more powerful rare-earth magnets on the stator. Since the field strength of these motors is constant, they can only be controlled by varying the armature current, in a permanent magnet motor the output torque, is directly proportional to the armature current, The constant of proportionality is referred to as the torque constant of the motor and is represented . The transfer function relating motor torque to armature current can be expressed as follows: DC servomotor that includes two windings; a stationary field winding on the stator and a second winding for the rotating armature. This type of motor can be controlled by varying either the field current or the armature current. Most modern servomotors are somewhat different in construction. The field winding is replaced with two or more powerful rare-earth magnets on the stator. Since the field strength of these motors is constant, they can only be controlled by varying the armature current, In a permanent magnet motor the output torque, is directly proportional to the armature current, The constant of proportionality is referred to as the torque constant of the motor and is represented The transfer function relating motor torque to armature current can be expressed as follows:

## Specification

 Armature voltage Va 0 - 50V DC Field Voltage Vf 0 - 50VDC AC voltage 0 – 20 VAC.

## DC servomotor

 Armature winding voltage 50V DC Field winding voltage 50V DC Power 120W Armature current (Ia) 2.6A(max) Moment of inertia (J) g/cm2.

## Front Panel Description

 DC voltmeter DC Ammeter AC voltmeter AC Ammetera

 Pot = Adjust the armature voltage from 3V to 50V. Pot = Adjust the armature voltage from 3V to 50V. A and AA = Connect to the motor armature terminal respectively.

 Pot = Adjust the field voltage from 0V to 50V. Switch ‘S2' = Switch ON/OFF the field voltage. F and FF = Connect to the motor field terminal respectively.

 AC voltage = Adjust the AC voltage from 0V to 20V. AC output (P&N) = AC output voltage.

## Principle of Operating

A DC servomotor is used in a control system where an appreciable amount of shaft power is required. The DC servomotor are either armature-controlled with fixed field, or field-controlled with fixed armature current. DC servomotor used in instrument employ a fixed permanent-magnet field, and the control signal is applied to the armature terminals.

Tm = KmΦfia - (i)

Km = Proportionality constant

Tm = Motor torque Nf = Field flux ia = Armature current

In addition to the torque when conductor moves in magnetic field, voltage is generated across its terminals which opposes the current flow and hence called as Back e.m.f denoted as eb

eb= KmΦωm- (ii)

This back e.m.f is directly proportional to the shaft velocity Tm. Equations (i) and (ii) form the basic equation of d.c. servo motor operation.

## Basic Classification

Basically d.c. servo motors are classified as:

• Variable magnetic flux motors.
• Constant magnetic flux motors.

In variable magnetic flux motors magnetic field is produced by the field windings which are connected to the external supply. These are also called as separately excited or field controlled motors.

## TRANSFER FUNCTION OF DC SERVO MOTOR

The constant magnetic flux motors are also known as permanent magnet d.c. motors. These motors have relatively linear torque-speed characteristics.

Derivation of transfer functions for

• Field controlled d.c. servo motor
• Armature controlled d.c. servo-motors.

## Assumptions

(1) Constant armature current is fed into the motor.

(2) Nf % If. Flux produced is proportional to field current. Nf = Kf If

(3) Torque is proportional to product of flux and armature current.

Tm % N Ia . Tm = K` N Ia = K’ Kf If Ia Tm = Km Kf If

Where

Km = K`

Ia = constant

Apply kirchoff’s law to field circuit.

```L fdif / dt + Rf If = ef
```

Now shaft torque Tm is used for driving load against the inertia and frictional torque.

Finding Laplace Transforms of equations (1), (2) and (3) we get,

Tm (s) = Km Kf If(s) Ef (s) = (SLf + Rf) If (s) Tm (s) = Jms 2m (s) + Bms2m (s)

Eliminate If (s) from equations (4) and (5)Input = Ef(S)

Output = Rotational displacement 2m (S)

## Assumptions

(i) Flux is directly proportional to current through field winding.

Nm = Kf If = constant

(ii) Torque produced is proportional to product of flux and armature current.

T = K`m N Ia T = K`m Kf If Ia

(iii) Back e.m.f is directly proportional to shaft velocity Tm, as flux N is constant.

```         as ωn = dθ(t) / dt
Eb = kbωm(d) = Kbsθm(s)
```

Apply Kirchhoff’s law to armature circuit:

Where Jm = Jm/Bm and