lab10b_servo trainer 2 response calculating and measurements

8/18/2019 Lab10b_SERVO TRAINER 2 Response Calculating and Measurements

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ME 413: System Dynamics & ControlME 413: System Dynamics & ControlME 413: System Dynamics & ControlME 413: System Dynamics & Control

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MeasurementsMeasurementsMeasurementsMeasurements

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SERVO TRAINER (2)

RESPONSE CALCULATING ANDMEASUREMENTS

OBJECTIVES

The objective of this experiment is to determine the gain,1

G and time constant, τ , of

the servo-motor transfer function with differing inertial loads where the servo motor

transfer function is given by

( )

( )

1

1

ω

=

τ +

Y s G

V s s (1)

where ( )ω

Y s = the speed sensor output voltage and ( )V s = the motor drive input

voltage.

THEORY

Figure 1 shows the servo-control system where the clutch is disengaged. When theservo-control system is used as a feedback control system the motor speed, ω , is

controlled (or actuated) by adjusting the applied voltage to the motor drive amplifier,

V . Likewise, the shaft speed is sensed by a transducer, which produces output voltage,

ωy , which is proportional to the shaft angular velocity, ω . The overall system may be

represented schematically as shown in Figure 2.

ShaftBearings

LoadGenerator Motor

( )V t

L R

Flywheel with inertia,I

( )l V t

Speed sensor(volts)

ωy

AngularVelocity, ω

Figure 1 Servo control system: Clutch disengaged.


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1τ +

i k

s ω

k ( )V s ( )Ω s

( )ω

Y s

Figure 2

The transfer function representing the above system is

( ) ( ) ( )1

1 1ω

= =

τ + τ +

i w k k G

Y s V s V s s s

(2)

where1 ω

= i G k k is the steady state gain of the transfer function from the input drive

voltage, ( )V s , to the sensed shaft position, ( )ω

Y s . In equation (2),i

k and ω

k are

the motor and the velocity sensor gain constants respectively, while τ represents thetime constant of the first order system.

For a step input signal of magnitude U , the output shaft position ( )ω

Y s would be

( )

1

1

Step Input

ω

=

τ +

G U Y s

s s (3)

and the response of the system is obtained by taking the inverse Laplace transform

of equation (3), that is

( ) ( )1 1ω− τ

= −t y t UG e (4)

where the response is shown in Figure (3), where it can be seen that:

τ t

( )ω

y t slope of the tangent at origin

1UG

( )

( )1 1

ω

− τ= −

t y t UG e

2 τ 3τ 4τ 5τ

1UG 0.632

Figure 3 Step response of a first order system.


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• the steady state value, would reach the steady state gain time the

magnitude of the input signal voltage, in other words,1ω

=,ss y UG .

• The time constant, τ is defined as the time required for the step response

of the system to reach 0.632 of its final value.(i.e. 0.632 1UG ).

APPARATUS

• CE110 Servo Trainer

• CE120 Controller

• Chart Recorder

PROCEDURE

Part 1: Motor Drive Input to Speed Sensor Output GainCharacteristics

The steady state gain relating the motor drive input voltage to the speed sensoroutput voltage may be calculated by combining the results of Part 1 and 2 ofExperiment 1. Alternatively, the characteristic may be measured directly as detailedin the following procedure.

► Connections

Connect the equipment as shown in Figure 5(E2.1) (Do not make the dottedconnection).

► Initial Control settings:

CE 110 Servo Trainer

• Clutch disengaged.

•

Rear access panel firmly closed.

• Smallest inertial load mounted. (No additional discs).

CE 120 Controller

• Potentiometer in the center position and reading 0V.

► Steps

• Increase the potentiometer voltage in steps of 1V to 9V,recording the corresponding speed sensor output (to do this

disconnect the potentiometer/voltmeter connection and makethe dotted connection), in Table E2.1.


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• Repeat the process for voltages − 1 to − 9V.

Figure 5(E2.1)


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Table E2.1 Motor drive voltage/Speed sensor characteristics(Clutch disengaged)

Motor Drive

Voltage (V)(Positive)

Speed Sensor

Output(V)

Motor Drive

Voltage (V)(Negative)

Speed Sensor

Output(V)

1 − 1

2 − 2

3 − 3

4 − 4

5 − 5

6 − 6

7 − 7

8 − 8

9 − 9

•

Repeat the procedure with the clutch engaged and enter theresults in Table E2.2.

Table E2.2 Motor drive voltage/Speed sensor characteristics(Clutch engaged)

Motor DriveVoltage (V)(Positive)

Speed SensorOutput

(V)

Motor DriveVoltage (V)(Negative)

Speed SensorOutput

(V)

Dead-ZoneSize=

0Dead-Zone

Size= 0

2 − 2

3 − 3

4 − 4

5 − 5

6 − 6

7 − 7

8 − 8

9 − 9

10 − 10

Part 2: Measurement of Time Constant► Connections

Connect the equipment as shown in Figure 6(E2.2).

► Initial Control settings:

CE 110 Servo-Trainer

• Clutch disengaged.

• Rear access panel firmly closed.

•

No additional inertial loads mounted.


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CE 120 Controller

• Potentiometer output: 5V.

• Function Generator: square wave.

•

Frequency 0.05 Hz and level 1V

► Steps

The square wave from function generator applies to a step change of 1V in either

direction about the operating input of 5V. The transitions in the square wave signalprovide step changes in the input. The output of the speed sensor will therefore be aseries of step responses.

• Connect the output of the speed sensor to a chart recorder andplot the step response (suggested chart speed 10 mm/sec or faster).

• Repeat the above procedure with each of the inertial loadsinstalled. i.e.,

i) Small inertial load: one inertial load.ii) Medium inertial load: two inertial loads.

iii) Large inertial load: three inertial loads.

Figure 6(E2.2)


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REQUIREMENTS

1.

For Part 1: Plot the results (motor drive voltage in the x-axis and the speedsensor output in y-axis) to obtain the required characteristics and measure

the slope in order to obtain the steady state gain1

G .

2.

For Part 2: From the step responses calculate the time constant τ and the

servo-motor transfer function.

3. Comment on the shape of the motor drive voltage to speed sensor output

voltage characteristic.

4.

Discuss why the time constant for various inertial loads increases as the sizeof the load increases.

References

[1] CE110 Servo Trainer Manual, TQ Education and Training Ltd

lab10b_servo trainer 2 response calculating and measurements

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