ME 413: System Dynamics & Control
Servo Trainer Trainer (2 (2 ) Response Calculating and Measurements
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ME 413: System Dynamics and Control Lab Manual
SERVO TRAINER (2) RESPONSE CALCULATING AND MEASUREMENTS OBJECTIVES The objective of this experiment is to determine the gain,
G1
and time constant,
τ , of
the servo-motor transfer function with differing inertial loads where the servo motor transfer function is given by
Yω (s ) G1 = V (s ) τs + 1 where
Yω (s ) =
the speed sensor output voltage and
(1)
V (s ) =
the motor drive input
voltage.
THEORY Figure 1 shows the servo-control system where the clutch is disengaged. When the servo-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, y ω , which is proportional to the shaft angular velocity, ω . The overall system may be represented schematically as shown in Figure 2.
Shaft Bearings
Flywheel with inertia, I
Load Generator
Angular Velocity,
Speed sensor ω (volts)
y
Motor
L
ω
Figure 1
Vl (t)
R V (t )
Servo control system: Clutch disengaged.
Servo Trainer (2): Response Calculating and Measurements
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ME 413: System Dynamics and Control Lab Manual
Ω (s )
ki τs + 1
V (s)
kω
Yω (s)
Figure 2
The transfer function representing the above system is
Yω (s ) =
ki kw τs + 1
V (s ) =
G1 V (s ) τs + 1
(2)
G1 = kik ω is the steady state gain of the transfer function from the input drive voltage, V (s ) , to the sensed shaft position, Yω (s ) . In equation (2), ki and k ω are the motor and the velocity sensor gain constants respectively, while τ represents the where
time constant of the first order system. For a step input signal of magnitude U , the output shaft position Yω (s ) would be
Yω (s ) =
U s
G1 τs + 1
(3)
Step Input
and the response of the system is obtained by taking the inverse Laplace transform of equation (3), that is −t τ y ω (t ) = UG1 1 − e (4)
(
)
where the response is shown in Figure (3), where it can be seen that:
yω (t ) slope of the tangent at origin
UG1
(
yω (t ) = UG1 1 − e
−t τ
)
0.632 UG1
τ
Figure 3
4τ 5τ 2τ 3τ Step response of a first order system.
Servo Trainer (2): Response Calculating and Measurements
t
2
ME 413: System Dynamics and Control Lab Manual
•
the steady state value, would reach the steady state gain time the magnitude of the input signal voltage, in other words, y ω,ss = UG1 .
•
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 UG1 ).
APPARATUS
• • •
CE110 Servo Trainer CE120 Controller Chart Recorder
PROCEDURE Part 1:
Motor Drive Input to Speed Sensor Output Gain Characteristics
The steady state gain relating the motor drive input voltage to the speed sensor output voltage may be calculated by combining the results of Part 1 and 2 of Experiment 1. Alternatively, the characteristic may be measured directly as detailed in the following procedure.
► Connections Connect the equipment as shown in Figure 5(E2.1) (Do not make the dotted connection).
► 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.
•
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 make the dotted connection), in Table E2.1.
► Steps
Servo Trainer (2): Response Calculating and Measurements
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ME 413: System Dynamics and Control Lab Manual
•
Repeat the process for voltages
− 1 to − 9V.
Figure 5(E2.1)
Servo Trainer (2): Response Calculating and Measurements
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ME 413: System Dynamics and Control Lab Manual
Table E2.1
Motor drive voltage/Speed sensor characteristics (Clutch disengaged)
Motor Drive Voltage (V) (Positive) 1 2 3 4 5 6 7 8 9
•
Motor Drive Voltage (V) (Negative) −1 −2 −3 −4 −5 −6 −7 −8 −9
Speed Sensor Output (V)
Repeat the procedure with the clutch engaged and enter the results in Table E2.2.
Table E2.2
Motor drive voltage/Speed sensor characteristics (Clutch engaged)
Motor Drive Voltage (V) (Positive) Dead-Zone Size= 2 3 4 5 6 7 8 9 10
Part 2:
Speed Sensor Output (V)
Speed Sensor Output (V) 0
Motor Drive Voltage (V) (Negative) Dead-Zone Size= −2 −3 −4 −5 −6 −7 −8 −9 − 10
Speed Sensor Output (V) 0
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.
Servo Trainer (2): Response Calculating and Measurements
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ME 413: System Dynamics and Control Lab Manual
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 signal provide step changes in the input. The output of the speed sensor will therefore be a series of step responses.
•
Connect the output of the speed sensor to a chart recorder and plot the step response (suggested chart speed 10 mm/sec or faster).
•
Repeat the above procedure with each of the inertial loads installed. 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) Servo Trainer (2): Response Calculating and Measurements
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ME 413: System Dynamics and Control Lab Manual
REQUIREMENTS
1. For Part 1: Plot the results (motor drive voltage in the x-axis and the speed sensor output in y-axis) to obtain the required characteristics and measure the slope in order to obtain the steady state gain G1 . 2. For Part 2: From the step responses calculate the time constant servo-motor transfer function.
τ
and the
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 size of the load increases.
References [1]
CE110 Servo Trainer Manual, TQ Education and Training Ltd
Servo Trainer (2): Response Calculating and Measurements
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