lab11a_servo trainer 3 proportional control of servo trainer speed
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ME 413: System Dynamics & ControlME 413: System Dynamics & ControlME 413: System Dynamics & ControlME 413: System Dynamics & Control
Servo TrainServo TrainServo TrainServo Trainerererer ( ( ( (3333)))) Proportional Control of Proportional Control of Proportional Control of Proportional Control of
Servo Trainer SpeedServo Trainer SpeedServo Trainer SpeedServo Trainer Speed
Name:
__________________________________
ID #:
__________________________________
Section #:
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Due Date:
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Instructor
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ME 413: System Dynamics and Control Lab Manual
Servo Trainer (3): Proportional Control of Servo Trainer Speed 1
SERVO TRAINER (3)
PROPORTIONAL CONTROL OF
SERVO TRAINER SPEED
OBJECTIVES
The objective of this experiment is to implement a proportional controller of the Servo
Trainer speed and to investigate the closed transient response, and the steady state
errors.
THEORY
The block diagram representation of the configuration for this experiment is shown in
Figure 1.
pk 1
1τ +
G
s
Error Signal,
( )E sPID Controller block
Motor Input
CE110 Servo system
Speed sensor output
( )ωY s
Reference input,
( )rY s
Figure 1 Block diagram representation
The closed loop transfer function may be given by
( )
( )
1
1
1 1
1
11
1
ω
τ + = =
τ + + +
τ +
pp
r pp
Gk
k GY s sGY s s k Gks
(1)
Equation (1) can be written in standard first order system as
( )
( )
1 1
1
11
1
ω = =τ + τ
+ +
p p
r cl
p
k G k GY s
Y s ss
k G
(2)
ME 413: System Dynamics and Control Lab Manual
Servo Trainer (3): Proportional Control of Servo Trainer Speed 2
where
11
ττ =
+cl
pk G
(3)
is the theoretical closed loop time constant. On the other hand, the error signal ( )E s can be expressed as
( ) ( ) ( )ω
= −r
E s Y s Y s (4)
Substituting ( )ωY s from Equation (1) into Equation (4) gives
( ) ( ) ( )
( )
1
11
ω
= −τ + +
���������
p
r r
p
Y s
k GE s Y s Y s
s k G (5)
Simplifying the above equation gives
( ) ( )
1
1
1
τ +=
τ + + r
p
sE s Y s
s k G (6)
The steady state error
sse is given by
( )[ ] ( )0 0
1
1
1→ →
τ += =
τ + + ss r
s sp
se lim sE s lim s Y s
s k G (7)
For a constant reference signal (step input) of magnitude
ry , the steady state error
sse may be written as
( )[ ]0 0→ →
= =ss
s se lim sE s lim s
1
1
1
τ + τ + +
r
p
s y
s k G s1
1
=
+
r
p
y
k G (8)
APPARATUS
• CE110 Servo Trainer
• CE120 Controller
• Chart Recorder
ME 413: System Dynamics and Control Lab Manual
Servo Trainer (3): Proportional Control of Servo Trainer Speed 3
PROCEDURE
Part 1: Steady State Errors
► Connections
Connect the equipment as shown in Figure 2(E3.1) that corresponds to the block
diagram of Figure 1.
Figure 2(E3.1)
► Initial Controller settings:
CE 110 Servo Trainer
• Clutch disengaged.
• Large inertial load installed.
ME 413: System Dynamics and Control Lab Manual
Servo Trainer (3): Proportional Control of Servo Trainer Speed 4
• Rear access door firmly closed.
CE 120 Controller
• Potentiometer turned fully anti-clockwise (i.e., set to 0V output)
• PID Controller: Proportional gain set to 10 and switched in,
while Derivative and Integral blocks switched out.
► Steps:
• Investigate whether the steady state error is proportional to the reference signal,
ry .
• Increase the reference speed as given by the potentiometer
output in steps of 1V from 2V to 10 V and record the
corresponding errors signals in Table E3.1.
• Use Equation (8), the value of =pk 10 and
1=G 1 to calculate
the theoretical values of sse for various values of
ry and enter
the results in Table E3.1.
• Investigate whether the steady state error is inversely
proportional to the controller gain pk .
• Set the potentiometer to give a reference speed signal, ry , of
5V.
• Vary the controller gain from 1 to 10 in steps of 1 and record
the corresponding error signal reading in Table E3.2.
• Use Equation (8) to calculate the theoretical values of sse for
each value of pk and enter the results in Table E3.2.
Table E3.1 Steady state errors for various reference speeds
(Clutch disengaged)
Potentiometer Setting (Reference Speed
ry )
(V)
Measured Steady
State Error Signal
(V)
Theoretical sse
11
=+
r
ss
p
ye
k G
[ =pk 10 and
1=G 1]
(V)
2
3
4
5
6
7
8
9
10
ME 413: System Dynamics and Control Lab Manual
Servo Trainer (3): Proportional Control of Servo Trainer Speed 5
Table E3.2 Steady state errors for various controller gains
(Clutch disengaged)
Potentiometer Setting
Controller gain, pk
Measured Steady
State Error Signal
(V)
Theoretical sse
11
=+
r
ss
p
ye
k G
[ =ry 5 and
1=G 1]
(V)
1
2
3
4
5
6
7
8
9
10
Part 2: Transient Response
► Connections
Connect the equipment as shown in Figure 3(E3.3), this corresponds to the block
diagram of Figure 4.
► Initial Control settings:
CE 110 Servo-Trainer
• Clutch disengaged.
• Large inertial load installed.
• Rear access door firmly closed.
CE 120 Controller
• Potentiometer set to 5V.
• Function Generator set to: square wave.
• Frequency 0.05 Hz offset 0V, and level 1V.
• PID Controller: Proportional Controller 1=pk , integral and
derivative blocks switched out.
► Steps:
In this part of the experiment we investigate how the transient response of the Servo
Trainer is affected by the proportional controller gain pk .
• Use the square wave output to generate a series of step
changes in reference speed and plot the corresponding speed
ME 413: System Dynamics and Control Lab Manual
Servo Trainer (3): Proportional Control of Servo Trainer Speed 6
response using the chart recorder (suggested time base 10
mm/sec) for proportional gains =pk 0.5, 1, 2, 4.
• Calculate the closed loop time constant, τcl, from the graph and
compare the results with the theoretical values obtained using
equation (3).
• Enter the results in Table E3.3.
• Notice that for the large inertial load the following approximate
values may be used; τ=1.5 and 1G =1.
Figure 3(E3.3)
ME 413: System Dynamics and Control Lab Manual
Servo Trainer (3): Proportional Control of Servo Trainer Speed 7
pk 1
1τ +
G
s
Figure 4
Table E3.3 Comparison of Measured Closed Loop Time Constants with
Theoretical Values
(Clutch disengaged)
Controller gain, pk
Measured Closed
Loop Time
Constant
(sec)
Theoretical sse
11
ττ =
+cl
pk G
[ τ = 1.5 and 1
=G 1]
(sec)
0.5
1
2
4
ME 413: System Dynamics and Control Lab Manual
Servo Trainer (3): Proportional Control of Servo Trainer Speed 8
REQUIREMENTS
1. Enter the results into the appropriate tables.
2. For Part 1: Discuss the steady state error results and in particular give reasons for any sufficient differences between the measured and the
theoretical values of steady state errors.
3. For Part 2: Calculate the closed loop time constant, τ
cl, from the graph and
compare the results with the theoretical values obtained using equation (3).
4. Discuss the step response results and the differences between the measured and theoretical closed-loop time constants.
References
[1] CE110 Servo Trainer Manual, TQ Education and Training Ltd
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