CONTROL SYSTEM LAB
Transfer Function of DC
Servo Motor
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Contents
INTRODUCTION ... 3 Specification... 6 DC Servo Motor... 6Front Panel Description ... 6
Armature volt adjustment... 6
Field Volt Adjustment ... 7
PRINCIPLE OF OPERATING... 7
TRANSFER FUNCTION OF DC SERVO MOTOR ... 9
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INTRODUCTION
In the dc motor 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 motor 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
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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:
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Pictorial View
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Specification
Armature voltage Va 0 - 50V DC Field Voltage Vf 0 - 50VDC AC voltage 0 – 20 VAC. DC Servo MotorFront Panel Description
DC voltmeter DC Ammeter AC voltmeter AC Ammeter
Armature volt adjustment
Armature winding voltage 50V DC Field winding voltage 50V DC
Power 120W
Armature current (Ia) 2.6A(max) Moment of inertia (J) g/cm2.
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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.
Field Volt Adjustment
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 motor is used in a control system where an appreciable amount of shaft power is required. The DC motors are either armature-controlled with fixed field, or field-controlled with fixed armature current. DC motors used in instrument employ a fixed permanent-magnet field, and the control signal is applied to the armature terminals.
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Km = Proportionality constant Tm = Motor torque Nf = Field flux ia = Armature currentIn 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
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: (i) Variable magnetic flux motors.
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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 (i) Field controlled d.c. servo motor
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ii. Field Controlled DC Servo motor
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.
Now shaft torque Tm is used for driving load against the inertia and frictional torque.
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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)
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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.
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Also Tm = {Jms + sBm} 2m (s) 2 Equating equations of Tm,
