Mech 371 Manual v2010
38
Department of Mechanical & Industrial Engineering Concordia University MECH 371 Analysis and Design of Control Systems Laboratory Manual T. Wen, W. Xie, H. Hong, G. Huard 11/30/2010
Transcript of Mech 371 Manual v2010
Department of Mechanical & Industrial Engineering Concordia University
MECH 371 Analysis and Design of Control Systems
Laboratory Manual
T. Wen, W. Xie, H. Hong, G. Huard 11/30/2010
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Table of Contents
Lab 1: Familiarization with Lab Equipments .............................................................. 2
Lab 2: Determination of DC Motor Parameters, Gain of Preamplifier,
Servo-Amplifier and Tachometer … ........................................................... 12
Lab 3: Time Response of Basic Closed-Loop System and Effect of
Tachometer Feedback .............................................................................................. 22
Lab 4: Frequency Response of Basic Closed-Loop DC Motor System ...... 29
Lab 5: DC Motor Position Control with Cascade PID Compensation ....... 33
Labs are scheduled on an alternative week basis (every two weeks). Therefore,
formal lab reports must be submitted every two weeks during your lab period.
Please submit your fifth lab report directly to your lab instructor at his/her
office, two weeks after you have performed the lab.
No late lab reports will be accepted.
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Lab 1: Familiarization with Lab Equipments & Instruments
Objectives
To familiarization students with MS150 DC Motor Control Modules, instruments such as
function generator and oscilloscope and to calibrate potentiometers, Op Amp and pre-amplifier.
Introduction
In this lab each station (MS150 System) is equipped with a DC motor, with a tachometer to
measure angular velocity, turning potentiometer (designated as input pot and output pot ) to give
and measure angular position, and power amplifier (also known as pre-amp and servo-amp) to
drive the motor. The command signal can be provided by the function generator or input pot, and
the output of angular position or velocity can be measured by the oscilloscope. Figure 1-1 shows
the MS150 system.
PS150E DCM150F
SA150D
Scope
Function Generator
Figure 1-1 MS150 DC Motor Control System
GT150X
IP150H
OP150K
PA150C
OA150A
AU150B
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Power Supply PS150E provides the ±15 volt
DC power supplies through two sets of
sockets. These sockets are used to operate
small amplifiers and provide reference
voltage. The Ammeter is used for monitoring
motor overload. The AC outputs are not used
in our experiments. The front panel is shown
in Figure 1-2.
Potentiometers: showing in Figure 1-3. The
module includes an Input Potentiometer
IP150H (input position transducer), an
Output Potentiometer OP150 K (output
position transducer), and an Attenuator Unit
AU150B containing two smaller
potentiometers, which are used to adjust gains
in the forward and feedback paths. The
input and output pots are fitted with discs
graduated (in degrees) on their
shafts. However, the output pot can be rotated continuously over 360º, whereas the input pot has
a limited rotation of about ± 150°. Both these 'angular position transducers' are normally supplied
with +15 and –15 volts, so that their outputs can vary linearly from zero to almost either of these
limits as their shafts are rotated in either direction from a central (zero) position. Normal
operation is symmetrical about this zero position. Note that in the output pot, a zero-voltage
transition also occurs at the + or –180° position, hence requiring operation which ensures output
angular displacements within these limits. Assuming that the total voltage applied across the
output pot is 30 volts, and the rotation is 360°, the position-to-voltage transducer sensitivity K0
will be 30 / 360 ≈ 0.083 volt / deg., or approx. 4.8 volts/radian. The input and output
potentiometers should be calibrated to obtain their sensitivity constants and/or to confirm
whether Ki ≈ Ko.
Figure 1-2 Power Supply: PS150E
Figure 1-3 Potentiometers
A : Input Pot IP150H B : Output Pot OP150K C : Attenuator AU150B
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The pots in the Attenuator unit are provided with knobs and scale graduations from 0 to 10.
These pots can be used as voltage dividers and to obtain the very small voltages.
Operational Amplifier OA150A is
an op-amp normally connected as a
unity-gain summing-inverter by
means of the 3-position switch
mounted on it. It is used as the
angular-position-error detector.
Since the unit is a summing
amplifier, the feedback signal
polarity must be reversed with
respect to the reference signal, in
order that the output will represent
the error. The unit has three
summing input terminals, and the
output is available at two (or three)
output sockets. The unit also has a
zero-set control and a selector
switch, which selects the feedback
(normally resistive) within the unit.
The selector switch is normally
switched to the leftmost position
indicating resistive feedback with unity gain. The op-amp must be zeroed before use. ZERO
PROCEDURE: With no input applied (input terminals left open circuited), the Zero-Set
control should be carefully adjusted until the output is zero. The Preamplifier PA150C, DC
motor DCM150F, Servoamplifier SA150D, Tachometer DTX150X will be introduced in next
lab session.
Experiment Procedure
In these experiments, we will begin with the power source and display, calibration of
potentiometers (attenuator, input pot and output pot) then Op-amp. Please preview
Experimental Results at P#11, pay attention to these questions during each Experiment.
Exp#1 DC voltage measurement using DMM and Oscilloscope
The objective here is to get variable voltage (signal) output from a fixed power source through
potentiometer (attenuator in our case), monitor and measure it using DMM and Oscilloscope. [In
this case, +15, -15 volt supply should be used as input]
1. Display and measure DC voltage by Oscilloscope and check the reading by DMM: The
oscilloscope used in our lab is a 2 channel storage oscilloscope. It can display and measure two
different signal sources simultaneously. DMM is 8085A.
Figure 1-4 Op-Amp OA150A
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Figure 1-6 Attenuator Calibration Scheme
Top Pot
Bottom Pot
Figure 1-5 Attenuator Calibrate Connection
-15 V in
+15 V in V 1 out
V 2 out
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1) Make connection as show in Figure 1-5. DMM set to: DC, V, scale to 20, connect
V/KΩ/S to terminal #2 of AU150B. com to terminal #1 of AU150B.
2) Scope Ch1 red terminal connect to output of attenuator (terminal #2 in AU150B), Ch1
black terminal to the common ( #1 of AU150B). Ch2 red to #5 in AU150B. Note only
one ―ground‖ in scope is connected to circuit common.
3) To make signal display correctly on the screen by adjusting the time scale (SEC/DIV)
and voltage scale (VOLTS/DIV) knob. On the bottom of screen, it display: CH1 1.00V,
CH2 2.0V, M 100ms. The signal can be displayed or not displayed by press button above
the knob.
4) Push the MEASURE button to see the side Measure menu.
5) Push the top menu box button to select Source. Select CH1 for the first measurements,
second button to select type: MEAN.
6) Push the second menu box button again to select CH2, select Type: MEAN. The CH1
and CH2 mean values are shown in the menu and are updated periodically. If it is a
question mark or not display, clockwise turn the Time scale until it is in auto run mode.
2. Adjust top pot knob from 0 position to 10 position and record voltage from CH1 mean, check
with DMM and fill out the following table.
3. Repeat Step 2 by adjusting the bottom pot knob, and record from CH2 mean.
Top knob Position
Voltage input (#3) V in
Voltage output(#2) V out CH1
K1 (gain) Vout/Vin
0 15 v
1 15 v
2 15 v
3 15 v
4 15 v
5 15 v
6 15 v
7 15 v
8 15 v
9 15 v
10 15 v
Bottom knob Position
Voltage input (#6) V in
Voltage output(#5) V out CH2
K2 (gain) Vout/Vin
0 -15 v
1 -15 v
2 -15 v
3 -15 v
4 -15 v
5 -15 v
6 -15 v
7 -15 v
8 -15 v
9 -15 v
10 -15 v
Exp#2 Calibration of Input, Output Potentiometers
1) Apply +15 and – 15 volts to the Input and Output pots (150H and 150K) exactly as shown
in Figure 1-7, noting the physical 'cross-connection' with respect to the pot terminal polarities*.
Rotate the pot shafts until each output is zero volts.
[Note that the Output pot shaft can be rotated only by turning the motor shaft which is
between DCM150F and GT150X. DO NOT FORCE THE SHAFT WHICH IS
CONNECTED TO THE OUTPUT POTENTIOMETER]. Check that the graduated disc
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attached to the pots indicates zero degree position, and the voltage output of each pots should be
zero volt, if not, record the angle and use it as an offset. Don’t force to adjust disc to
zero.. *Note: This 'cross-connection' is necessary in the final setup (close loop control setup), since both pots are
rotated in the same direction, their outputs will be with opposing polarities. Thus, if the outputs are summed (as is
done in the lab by the operational amplifier module 150A), the op-amp output indicate the error in angular position
between the two potentiometers. The op-amp thus serves as the error detector. If the two pots are physically
identical, then setting both to the same angular position should result in zero output from the op-amp. The
generation of the error signal is observed in the next step.
2) Rotate input pot shaft in steps and record the output voltage from IP150H #3(CH1 mean), fill
out the following table.
3) Repeat step #2 for output pot, rotate motor shaft (not Disc) to change the disc position.
Figure 1-7 Input and output pot calibration setup
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Output Pot
Position (150K)
(Degree)
Voltage from
#3 Vo CH2
(volt)
-170
-120
-90
-60
-30
-10
0
10
30
60
90
120
170
*turning the pot clockwise for positive polarity
Input Pot position
(150H) ( Degree)
Voltage From #3
Vi CH1
(volt)
-120
-100
-80
-60
-40
-20
-10
0
10
20
40
60
80
100
120
Figure 1-8 Input and Output pot Calibration Scheme
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Exp#3 Observation of the Error Signal
1. Zero Op-Amp (Figure 1-9): Connect a common
(0 volt) signal to one of the op-amp inputs (leave the
other two inputs open). Then adjust the ―zero set‖
knob so the output of the op-amp is zero.
2. Remove the common signal from #1 of Op-amp.
Connect the input and output potentiometer as in
figure 1-10. Rotate the input pot shaft approximately
to Vi= 2.5V position. Use DMM to check Vi.
3. With the input potentiometer position left
undisturbed, from start point position (0 degree),
vary the output pot position by slowly turning the
motor shaft and observe the change in Op-amp
output. Fill out the following table.
Figure 1-10 Op-Amp Calibration and Error Signal connection
+15V 0V
-15V
CH2
Figure 1-9 Zero Op-Amp
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Input
pot
Vi
Output
Pot
Position
(Deg)
Output
Pot
Vo
CH1
Op-Amp
Output
Ve
CH2
Erro (Cal)
Ve=
-(Vi+Vo)
Difference
of Ve(cal)
and
Ve(real)
-170
-150
-120
-90
-60
-30
-10
2.5 0
10
30
60
90
120
150
170
Figure 1-11 Op-Amp as a Summing and Error Signal Block
Diagram
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Experiment Results
Exp#1 Calibration of Attenuator
1) What is the model of oscilloscope used in your station? Explain how to measure a DC
voltage of 0.5 V by this scope?
2) Obtain the calibration curves showing the Pot Coefficient k =Vout/ Vin versus scale
reading(knob position). The plots yield the correct value of k1 and k2 to be used.
3) If we need a variable voltage out 0 ~ 0.5v, but we only have a power supply which can
give fix +15v output. Can we use two attenuators to do so (the second attenuator must
output 0~0.5v by adjusting knob position 0~10). How to connect it, Referring Figure 1-5,
Figure 1-6 and draw your connection similar as Figure 1-6.
4) Can you explain which terminal is input, which is output if we use AU150B as a voltage
divider. Do we need a ground for it, explain why.
Exp#2 Calibration of Input, Output Potentiometers
1) Obtain the calibration curve of output voltage versus input angle in both directions from
zero, and hence calculate the sensitivities Ki and Ko of the two pots in volts/rad. If the two
values are close to each other, the average value may be calculated.
2) What is the ―cross connection‖ mean in experiment.
3) Can you explain which is input signal, which is output signal for IP150H. How can you
give input, what is the unit, how and where can you get output, and what is the unit.
4) Can you explain which is input signal, which is output signal for OP150K. How can you
give input, what is the unit, how and where can you get output signal, and what is the unit
Exp#3 Observation of the Error Signal
1) Explain how to check if the op-amp is zero or not. Can you use DMM to do so. Please
explain in detail.
2) From above experimental results table, explain how to make connection to get a signal
subtraction.
3) Referring Figure 1-10 and 1-11, please use one attenuator to adjust (decrease) the error
signal and measure it use scope ch2. Draw the connection similar as Figure 1-10 (add
attenuator unit AU150B to Figure 1-10, redraw the connection).
4) Referring Figure 1-10 and 1-11, if we switch the connection of IP150H (#1 to +15, #2 to
-15). What is the effect on Ve error signal.
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Lab 2: Determination of DC Motor Parameters, Gain of Preamplifier, Servo-Amplifier and Tachometer
Objectives
To familiar with the DC motor module, amplifiers and tachometer. To verify DC motor
parameters, calibrate the gain of pre-amplifier, servo-amplifier and tachometer.
Introduction
Preamplifier PA150C is a low-power control
amplifier which is used to provide the "deadband
compensation" voltage, as well as a fixed forward-
path gain Kp. The module has two summing input
terminals and two output terminals. An additional
input terminal labelled "Tacho" may also be
present. A positive voltage applied to either input
yields an amplified positive voltage at the upper
output socket(3),the socket(4) staying near zero; a
negative voltage applied to either input yields an
amplified positive voltage at the lower output
socket(4), the socket(3) staying zero. The two
output terminals provide the positive voltage drive
required as input for the servoamplifier. Thus, if
the output terminals are connected to the
servoamplifier input terminals, the motor will
reverse direction whenever the preamplifier
input voltage changes polarity.
With zero input, the voltages at both output sockets must be equal, and this condition must be
achieved by adjusting the Zero Set control on the preamplifier. PROCEDURE: Power on
preamplifier. With the input terminals left open circuited, adjust the Zero Set knob until
the differential voltage between the two output sockets is zero, i.e., until the voltages at the
two output sockets are equalized. The preamplifier must remain reasonably balanced for
proper operation. Maximum output is about 12 volts, and the linear voltage gain is about 10 to 15
V/V.
'Deadband' occurs due to the presence of mechanical static-friction (Coulomb-friction) effects in
the commutator brushes and in the bearings. The term 'deadband' which essentially is "the no-
response of the motor until the servoamplifier[motor] input voltage Vm, exceeds a certain value
Vd " [see Figure 2-2 (a)] occurs in both rotational directions. The 'deadband' prevents the
modeling of the servomotor as a linear element. In the experimental equipment, the motor is
'linearized', by providing the servoamplifier input with a bias voltage Vb which is approximately
Figure 2-1 Preamplifier PA150C
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equal to the deadband voltage. The required bias is obtained from a pre-amplifier which has the
transfer characteristic shown in Figure 2-2(b). The bias voltage Vb is somewhat less than Vd in
order to prevent motor response due to spurious noise signals which may be present in the
preamplifier output. At balance, identical output voltages of 1 to 1.5 volts should be obtained.
Servoamplifier SA150D is the power-
amplifier which drives the motor. Its panel
shows a simplified schematic of the amplifier.
The left side of the panel contains two input
terminals which accept only positive input
signal voltages: A positive input voltage
[exceeding the deadband voltage], when
applied to one input terminal will rotate the
motor in one direction, a similar positive
voltage applied to the other terminal will
produce reverse rotation. Negative inputs will
have no effect. The panel also contains a set
of ± 15v terminals which can be used by other
units. The servoamplifier is already connected
to the power supply unit by a cable, and does
not require further power connections.
DC Motor DCM150F & Reduction Gear
Tacho Unit GT150X consists of a DC
motor mechanically coupled to a
tachogenerator on high speed input end,( tachometer sensitivity is 0.025 Volts per radian-sec-1
and its output polarity can be reversed by appropriate patching), through a 30:1 reduction gear (a
90° worm gear assembly), to an output shaft on the other end. The output shaft is coupled to the
Figure 2-2 (a) Motor Deadband Vd (b) Preamplifier Bias Vb
Figure 2-3 Servoamplifier SA150D
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Output Potentiometer through a coupling link. A top panel display can be switched to indicate
speed in r/min or to monitor an external DC voltage. The motor is operated in the armature-
controlled mode, through appropriate patch-cord connections made on the servoamplifier. The
motor is already connected to the Servoapmplifier by cables, and does not require further power
connections.
The armature-controlled DC Motor is used in the laboratory equipment. The motor is driven by
a servoamplifier [the combination of the two being called a 'Servomotor‘]. The overall transfer
function can be written as follows :
(2-1)
where is the output angular velocity, Vm is the servomotor input voltage, Km is the
servomotor gain constant and is an equivalent electro-mechanical time constant. The two
characteristic constants in (2-1) can be experimentally determined. The block diagram is shown
in Figure 2-5.
Figure 2-4 DC Motor DCM150F coupled Tacho- gear GT150X
Figure 2-5 Block Diagram: SA150D+DCM150F+ GT150X
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Experiment Procedure
In these experiments, we will learn to balance the preamplifier, connect modules, calibrate the
amplifier gain, determine the bias, motor deadband, and servomotor time constant.
Exp#1 Determination of Preamplifier Bias and Gain
1) Balance the Preamplifier and
determine Preamplifier Bias:
Power PA150C, connect a common
signal (0V) to the inputs (input 1 and
2). Monitor (using the oscilloscope
and its measurement feature, scope
vertical position and scale should be
same) both outputs (3 and 4), adjust
the Balance Control (zero set knob)
until both outputs have the same
voltage. This voltage should be in the
range of 1.0 to 1.5 volts and is the
"bias" voltage which is intended for
overcoming part of the system
Deadband. The zero set knob should not be disturbed
after balancing. Record the bias value.
2) Set up the circuit to obtain a small voltage signal: as shown in Figure 2-7 using the Attenuator modules.
Note that the pots in the Attenuator are connected in
cascade so that very small DC voltages required as
input for the gain determination can be easily obtained.
Set top pot 0.5 volt (after get 0.5V at #2, don‘t touch
the top knob any more), then bottom pot will yield an
output of 0 to 0.5 volt over its entire knob-rotation
range at socket 5. If -15V connect to # 3, then # 5 can
obtain an output of 0 ~ -0.5V.
3) Preamplifier Gain: Disconnect the common
signal from the pre-amp and connect the signal from
the bottom pot #5 as show in figure 2-8. Apply various
voltages to the preamplifier input #1 and scope CH1.
Connect PA150C output #3 to scope CH2. Leave input
#2 and output #4 unconnected. Vary input signal from
0~0.5 by turning bottom knob, (Oscilloscope setting: fisrt side menu: source: CH1, Type: mean.
Second side menu: Source: CH2, Type: mean, properly adjust voltage and time scale to get
Figure 2-6 Balance PA150C
Figure 2-7 Using AU150B
get small variable Signal
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reading from Scope), record data at the following table. Then disconnect +15V and connect
-15V to AU150B socket 3, thus a variable signal (varies from 0~ -0.5V) can be obtained at #5 on
AU150B and at input #1 on PA150C, the amplified signal output to PA150C output #4, leave
input 2 and output 3 unconnected, record data at the following table.
Input terminal #
Input Voltage CH1 Volt
Output Terminal #
Output Voltage CH2 Volt
1 0 (real reading here) 3
1 0.1 3
1 0.2 3
1 0.3 3
1 0.4 3
1 0.5 3
1 0 4
1 -0.1 4
1 -0.2 4
1 -0.3 4
1 -0.4 4
1 -0.5 4
Figure 2-8 Preamplifier Calibration Connection
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Exp#2 Servomotor Deadband and Gain Determination
1) Set up the circuit shown in Figure 2-9. Apply 0 ~ 3 volts (using top attenuator AU150B #3
connect to +15v, #2 to input #1 of PreAmp PA150C). Scope CH1 to input #1 of Servo-amp
SA150D. Note that the motor does not respond until the input voltage exceeds a certain threshold
value Vd, which is the deadband voltage for one direction.
Gradually increase the voltage allowing the motor to start to turn. Continue to increase the
input voltage to 1.5V (read from CH1 of scope), read the LED display (rpm), CH2 volts and
record all values on the following table.
Continue to increase input voltage to 2.5V (read from CH1), read LED display (rpm), CH2
volts, and record all values on the table.
2) Then apply the negative 0 ~ -3V input voltage to terminal #1 of the Pre-amplifier PA150C
(Switch top attenuator #3 to -15v, CH1 switch to terminal #2 of Servo-amp SA150D ). Also
note that the motor responds similarly but in the opposite direction. Repeat step 1. Record all
values same as above.
Figure 2-9 Servomotor Gain and Deadband Connection
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Servo – Amp Input Tachometer Output
Terminal #
Vm Volts (CH1)
n RPM
Rad/S
Vt Volts (CH2)
Kt Volts.S/rad
# 1
1.5 V
#1
2.5 V
#2
1.5 V
#2
2.5 V
Exp#3 Servomotor Time Constant determination:
1. How to use Function Generator and measure low frequency signal by Scope:
1) The function generator is used to apply a square-wave input to the servo-amplifier. It
can generate three different signals: Sine, Square, and Saw signal. We can adjust the
Frequency, Amplitude, Offset (pull out offset knob to adjust DC offset) and Duty of
these signals.
2) Directly connect Function Generator 50 Ω output to Scope CH1. Set Oscilloscope to
operate in Scan Mode(100ms/div to 5 sec/div) which produce a scrolling trace. Adjust
the position knob of CH1 and CH2 of DSO to have zero vertical position.
3) Check signal on Scope by run/stop, freeze display, press Cursor, voltage, two
horizontal cursor will display, put first cursor to 0 position and second to final step
position, the Delt volt in side menu is the Amplitude of this signal. You can check
frequency also by switch ―Type‖: Voltage to Time, two vertical cursors will display.
Put two cursors at a whole period position, the Delt is the period time and the under is
the frequency reading.
4) You can also check signal by counting grids by adjusting voltage scale. Setting scope
to 200mv/div, if voltage changed in 2 grids, the amplitude is 0.4 v. If it changed in 3
grids, it is 0.6v.
5) Use function generator to obtain a square wave with a frequency of ≈ 0.3 Hz, Slowly
adjust the 'DC offset' and 'Amplitude' controls on generator such that the minimum
value of the square wave is zero and its maximum 0.4 volts.
2. Use the circuit shown in Figure 2-10. Connect Servo-Amp terminal #1 to scope CH1.
The tachometer output to CH2 will display the rising exponential curve of the (first-
order) servomotor. Power on motor and fine adjust offset to make sure motor run in one
direction and full stop periodically.
3. Adjust oscilloscope amplitude (volts/div) and time base (sec/div) controls until the
positive-going half-cycle of the square wave appears as a 'step' in the display [see Figure
2-11]. Press Run/Stop ** button in Scope to display the rising wave form. Use the
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voltage and time cursors to graphically determine the servomotor time constant by
reading off the time corresponding to 63.2 % of the 'final' value*. Capture the display and
mark the time constant and final value, fill out the following table.
* How to get Time Constant using Cursor measurement: 1) From Scope, Press Cursor: Type: Voltage, Source: CH1, Turn vertical position to
move 2 horizontal cursors, read Delta, Vm (volt). Then switch to Source CH2, using cursor to read Delta, Vt (volt).
2) Refer to Figure 2-11, find the cursor of 63.2% of Vt( e.i. if Vt=0.38v, the 63.2% of Vt is 0.240 v, move second cursor to delt=0.24v) . Adjust “Horizontal Position” knob to move waveform to a marked (known) position (center of screen or any vertical grid line), Switch cursor type to “Time”, two vertical cursor display, set first cursor to initial position, second to marked (known) position. The Delta is the time constant. Capture a graph of this waveform and measurement.
4. Connect CH1 to terminal #2 of Servo-Amp and adjust Function Generator Offset down
to -0.4V ~0V (don‘t touch ―Amplitude‖) to make sure motor run in reverse direction and
full stop periodically. Repeat the steps #3). Fill out above table‘s second row.
5. Repeat Step #2, switch CH1 to #1 of Servo-Amp, increase AM PL of Function
Generator to 0~ 0.8 V, Adjust Offset also to make sure motor run in one direction and
stop periodically. This will yield data same direction as step #2 but for big input voltage.
V Function Gen. Vm (CH1) Tachometer (Vt CH2) Time Constant
0~0.8 V
-0.8V ~0V
6. Repeat Step #4, (keep amplitude, only adjust DC offset), fill out above table‘s second
row.
** Alternate method to get one shot wave form:
1) Scope setting: Ch1: 2v, Ch2: 2v, M: 50 ms, adjust ―Horizontal Position to set M Pos:
0.0 s, Trigger level set to +1v for rising wave or -1v for falling wave.
2) Press Scope ―Trigger Menu‖: Type: Edge, Source: CH1, Slope: Rising (Falling
depending on waveform), Mode: Auto, Couple: DC.
3) Run motor by turn power. Press Scope: Single Seq. A rising (or falling waveform)
will display and freeze on screen. Now you can use cursor to measure it.
V Function Gen. Vm (CH1) Tachometer (Vt CH2) Time Constant
0~0.4 V
-0.4V ~0V
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Figure 2-10 Servomotor Time Constant Connection
Figure 2-11 Servomotor Time Constant Scope display
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Experiment Results
Exp#1 Determination of Preamplifier Bias and Gain
Obtain a plot of output voltage (terminal 3) versus input voltage from 0~ +0.5 V (input terminal
#1). Next, on the same graph, plot other output (terminal #4) versus Vin from 0 ~ -0.5V (input
terminal #1). A V-shaped characteristic will result if the preamplifier has been well balanced.
Find Kp from these plots.
Exp#2 Servomotor Deadband and Gain Determination
1) From the table, calculate and Kt,
(Rad/s),
.
2) Plot versus Vm in both input terminal #1 and #2 in one graph. The
, is the slope of
fitted line. Find Vd from this plot.
Exp#3 Servomotor Time Constant Determination
1) From the recorded table and plot, get average time constant.
2) Find servomotor gain from the final value and input square-wave amplitude. Refer to (2-1)
and Figure 2-5,
, when t∞, S0,
. Compare this Km with
obtained from Exp#2.
3) Using above obtained parameters to simulate the DC motor in Matlab Simulink. Compare
your result with experimental one.
Pre-Lab 3: Following the block diagram Figure 3-3, Draw a connection in Figure 3-4. Submit
connection diagram during next lab.
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Lab 3: Time Response of Basic Closed-Loop System And Effect of Tachometer Feedback
Objectives
To observe the time response of the closed-loop DC motor position control system, investigate
the performance of second order system, and effect of tachometer feedback on the second-order
system response.
Introduction
Basic angular position control system:
The block diagram of the basic system which is investigated is shown in Figure 3-1. The speed
reducing gear coupled at the output shaft of the motor is represented as a block having the
transfer function (1/SN), to indicate speed reduction as well as angular velocity - to - position
conversion. Ki and Ko are the transfer functions of the Input and Output potentiometers, Kp is
the pre-amp gain, and Km is the servo-motor gain respectively, which were obtained by
calibration in the previous lab.
The op-amp 150A is used to sum multi-signals as ―Reference Comparator‖ or ―Error Detector‖.
The error voltage Ve is the difference between desired voltage Vi and real voltage Vo (or
).
150 X Gear Box
Figure 3-1 Basic Angular Position Control System
23
The close loop transfer function of the system of Figure 3-1 (including Ki) may be obtained as:
(3-1)
Where the Natural Frequency is
(3-2)
, and the Damping Ratio is
(3-3)
Transient time response specifications to a step input are defined as follows (refer to Figure 3-2):
0 2 4 6 8 10 12 14 16 18 200
0.2
0.4
0.6
0.8
1
1.2
1.4
tr
tp
T
X1
X2
X3
P.O
2%
ts
Figure 3-2 Time Response of Basic Angular Position control System
O.S
24
Period Time:
where the damped natural frequency is .
Rise time, tr: the time required for the response to rise from 0 ~ 100% of its final value for a
underdamped second-order system.
Peak Time: time taken to reach the first maximum,
Percent Overshoot (P.O.): the maximum peak value of the response curve measured from
unity.
(3-4)
Settling Time: the time required for the response curve to reach and stay within a range about
the final value of size specified by absolute percentage of the final value (usually 2% or 5%).
, (2% settling time)
The time-domain specifications are quite important since most control systems must exhibit an
acceptable time response. Except for certain applications where oscillations cannot be tolerated,
it is desirable that the transient response be sufficiently fast and be sufficiently damped. Thus, for
a desirable transient response of a second-order system, the damping ratio must be between 0.4
and 0.8. Small values of yield excessive overshoot in the transient response and a
system with a large value of responds sluggishly. An overshoot in the range of 2 to
6% is considered to be the optimum, a ‗range‘ being necessary because setting the P.O. may
involve a ‗trade-off‘ with other specifications.
Note that an increase in KM, while providing an increase in the natural frequency (ie. speed of
response or rise-time), will also result in a reduction in the damping ratio, thereby increasing the
tendency towards instability (ie. larger overshoot and settling time). Thus, a 'trade-off‘ exists
between, say, the rise-time and the settling time. Furthermore, in the experimental setup, all of
the above system parameters are constant and any adjustment capability can only be obtained
through an effective variation in the forward-path gain. In the experimental setup, such a gain-
variation is obtained by an attenuator which is ahead of the pre-amplifier (see Figure 3-3) to
effectively reduce the gain of that amplifier (ie. 0< overall forward-path gain ≤ KM , in our case,
KM=K1KpKm , where K1 is the potentiometer constant which was calibrated in previous lab and
ranged from 0 to 1)
Basic angular position control system with velocity feedback:
The restrictive trade-off situation between and in the basic system described above may be
somewhat improved by using additional 'derivative feedback'. In obtaining the derivative of the
output position signal, it is desirable to use a tachometer instead of physically differentiating the
output signal. In our lab, the angular velocity of the motor (Tachometer feedback or
Velocity feedback or Rate feedback) is introduced. In the laboratory system, a ‗tachogenerator‘
25
(Tachometer) is physically coupled to one end of the motor. It produces a DC voltage output
, which is used as an additional negative feedback signal as shown in Figure 3-3.
This system can be shown to have the same transfer function given by Eqn. (3-1) where
remains unchanged but with now given by:
(3-5)
The Damping Ratio is now multiplied by the factor (1 + KMK2Kt). Thus, can now be
independently set for any given In the laboratory setup, an attenuator (with pot constant
k2) is used in cascade with the tachometer output, so that an effective adjustment range for Kt
from zero to its full value is possible. For the basic system, optimum* step response should
normally occur with the pot coefficients k1=0.4 and K2 = 0.02, respectively. It can be seen that
velocity-feedback improves stability by introducing extra damping.
Experiment Procedure
Pre-lab: Please review Lab#1 and Lab #2 and connect a basic angular position control system
with velocity feedback as shown in Figure 3-3. The lab equipments layout is shown in Figure 3-
4. All the +15V and -15V and 0V voltage will be connected in the lab later. The power supply
PS150E, servo-amplifier SA150D and DC motor DMC150-F are internal connected. Please note
that input pot IP150H and output pot OP150K must be cross connected (referring Figure 1-8).
Make sure Ve is a voltage difference and not a voltage sum. The reference voltage of IP150H
Figure 3-3 Basic Angular Position Control System with Velocity Feedback
Ki
150H
150A
K1
150B
top
150D
+150F
150X
Kt
150X
K2
150B Bottom
Ko
150K
Kp
150C
26
and OP150K is ±15V. Draw your connection on Figure 3-4 and submit it to your lab
demonstrator after finishing exp#1 connection.
Exp #1 Basic Closed-loop System Set Up
Notes: Throughout the following experiments, it will be assumed that the op-amp and the
pre-amp remain zeroed and balanced respectively and that the supplies to the input/output
pots are cross-connected so that the op-amp is the difference between the input and output
position signals.
OA150A
PA150C SA150D
DCM150F
GB150X
OP150K
K1
K2
PS150E
AU150B
GB150X
IP150H
Figure 3-4 Pre-lab connection for block diagram of Figure 3-3
27
1) With no power applied, set up the circuit in Figure 3-4 (Figure 3-3 is the block diagram for
this). Set the input and output pots to their mid-positions, indicating approximately zero output
voltages. Also set the two pots in the Attenuator unit to K1 =0.5, K2 = 0.
2) Offset the reference input pot by about 30° and turn the power on, the output pot will then
rotate to follow the reference pot position if the system is functioning as a negative feedback
system. If it does not, then the feedback signal polarities of either position or velocity or both are
incorrect and must be reversed as required until the system shows the proper position following
response. (Letting K2=0, check position feedback first. Switch +15,-15 connect of IP150H to
make sure system is controllable and stable. Then add K2=0.5, if system is unstable, switch the
polarities of GB150X.)
3) Replace input pot by function generator and connect to terminal #1 of OP150K. Set square
wave, 4V pk-pk, frequency 0.3 Hz. Connect scope CH1 to Vi, (terminal #1 of OP150K), CH2 to
Vo (terminal #2 of OP150K). Set the DSO time base to produce a scrolling trace (scan mode).
Now observe the responses to step input with various settings of K1 and K2 which are the two
control pots in the Attenuator module. Note that K1 effectively sets the forward-path gain (from
zero to 1) while K2 sets the magnitude of the tachometer feedback signal.
4) With K2 remaining at zero (thereby removing the velocity-feedback loop): increase K1 in
steps and observe the change in the transient response. Capture input and output in one plot for
same K2=0 but with K1=0.1, 0.2, 0.4. Try to measure Tp, T and P.O for each case. (using
run/stop and Cursor to do). Refer to Figure 3-2.
Exp #2 Closed-loop System with Tachometer Feedback
1) Keep same as above steps 1)—3).
2) With K1 set at maximum (=1), observe the change in transient response as the tachometer
(velocity) feedback is gradually introduced by increasing K2. Using RUN/STOP , capture plot for
same K1=1 but with K2=0.1, 0.2, 0.3 or 0.05(if the system shows too sluggish). Also try to
measure Tp, T and P.O for each case.
Exp #3 Closed-loop System Time Response
1) Keep same as Exp#1 steps 1)—3).
2) Select k1 and K2 which yields what you consider to be the 'best' step-response
(approximately 5% of overshoot). From the displayed 'best' response curve, use the DSO cursors
to graphically determine the Percentage Overshoot and use it to estimate the damping ratio.
Capture of this 'best' response for the report.
3) Repeat step 2) for choosing approximately 10% or more of overshoot. Make sure the system
is stable
28
Experiment Results
Exp#1 Basic Closed-loop System Set Up
Write a summary of your observations in your report. Calculate , and from your
recorded T, Tp, and P.O for each case. Comment on your results.
Exp#2 Closed-loop System with Tachometer Feedback
Write a summary of your observations in your report. Calculate , and from your
recorded T, Tp, and P.O for each case. Pay attention to . Comment on your results.
Exp #3 Closed-loop System Time Response
1) Estimate two from your best response experiment by equation (3-4). Compare them with
value calculated using equation (3-5)
where the selected values of K1 and K2 have been introduced to take into account the effective
modified values of the gain KM= Kp*Km and the tachometer sensitivity Kt. Tabulate the results
of your comparison. N = 30 is the output shaft gear ratio. You can find all the other parameters in
your former experiment results.
2) Use Matlab Simulink to simulate the system as in Figure 3-3. K1 and K2 are the two values
used in the lab (Exp#3, step #3, one is 5% of overshoot, other is 10% of overshoot). N = 30 is the
output shaft gear ratio. You can find all other parameters in your former experiment results. Plot
the simulated results and check the P.O. in graphs. Compare them with your experimental plot.
29
Lab 4: Frequency Response of Basic Closed-Loop DC Motor System
Objectives
To study the frequency response of a basic closed-loop DC motor system by observing its natural
response, and compare the experimental response with computer simulation response.
Introduction
The frequency response means the steady state response of a system to a sinusoidal input. The
resulting output for a closed loop DC motor system is sinusoidal in the steady state; it differs
from the input waveform only in amplitude and phase angle. Consider the DC motor described
by Equation (3-1),
(4-1)
0 10 20 30 40 50 60-4
-3
-2
-1
0
1
2
3
4
Figure 4-1 Frequency response of closed loop system
t T
30
The input (t) is sinusoidal and is given by:
If the system is stable, then the output can be given by
Where
We can present frequency response characteristics in graphical forms, Bode Diagrams or
Logarithmic Plots. A Bode Diagram consists of two graphs: one is a plot of the logarithm of the
magnitude of a sinusoidal transfer function ( ), or called dB; the other is a plot of
the phase angle (deg) or phase shift; both are plotted against the frequency in logarithmic scale.
An example of input and output sinusoidal waveform is shown in Figure 4-1.
The output/input magnitude ratio:
100
101
102
-180
-135
-90
-45
0
Phase (
deg)
Bode Diagram
Frequency (rad/sec)
-40
-30
-20
-10
0
10
20System: DC
Frequency (rad/sec): 10.6
Magnitude (dB): 10.3
System: DC
Frequency (rad/sec): 15
Magnitude (dB): 0.00225
Magnitu
de (
dB
)
Figure 4-2 Bode diagram of closed loop DC motor System
Mp (in dB)
31
M (dB) =
(4-2)
Phase shift: (degree) =
(4-3)
Figure 4-2 shows the Bode Diagram of closed loop DC motor system. We can estimate the
underdamped natural frequency and damping ratio by the asymptotic lines from Bode
diagram.
, (4-4)
Experiment Procedure
1) Set up the circuit shown in Figure 3-3, make sure system is controllable and stable, use
function generator to replace input pot 150H. Get step response by setting K1, K2 to your value
which yielded your 'best' step-response. Set the oscilloscope to read DC at 1 volt/div and adjust
the sec/div setting until the waveform is scrolling, 100-500mS/div. Turn on the 'invert' for Ch2 of
scope. Adjust the function generator controls to obtain a sine wave output of approximately 1
Hz, 4 volts peak-to-peak, symmetrical about the zero volt baseline.
2) Keep the peak-to-peak input voltage magnitude constant, vary the frequency from 0.1 Hz to
approximately 10 Hz in steps. Sweep frequency from 0.1 to 10 Hz, find the resonance peak,
more readings will have to be taken near the peak so that it is well defined in a plot. Conversely,
less readings may be taken in regions where the response is 'flat'. At each frequency fin, 'freeze'
the signal and use cursors to find the input period T, pk-pk amplitude , pk-pk amplitude ,
and the phase-shift time t between input and output waveforms. Tabulate the results.
Fin (Hz)
T (sec)
t (sec)
(pk-pk) (volt)
(pk-pk) (volt)
(rad/S)
M ( dB)
Phase (deg)
0.1
1
2
3
…
…….
f peak
……..
……
…
..
7
8
9
10
IP150H
32
Experiment Results
1) Calculate the output/input Magnitude Ratio M (dB) and the Phase shift Ф (degrees) at each
frequency and put them into the table above. For an input and an output which lags
the input, the Ф (degrees) and M (dB) may be calculated by (4-3) and (4-4). Plot the Magnitude
Ratio M (dB) and the Phase-lag Ф (degrees) against the radian-frequency ω=2πf, using two-
cycle, semi-logarithmic graph paper. Example M and Ф plots are shown in Figure 4-2. Typical
data points are also shown to emphasize the need to take more readings at frequencies where
rapid changes occur. Note: A distinct peak will not be obtained if the system is set for near
critical damping.
2) Estimation of undamped natural frequency ωn and damping ratio ζ from the resulting
frequency response plot. The magnitude (dB) – frequency data points plotted on semi-log graph
paper can be used to obtain system parameters such as ζ and ωn, as shown in Figure 4-2. Use
asymptotic lines to estimate the ωn and the peak (if any) to find the ζ by (4-4). Compare the
result of ζ with the corresponding value calculated earlier in Lab#3.
3) Use Matlab M scripts to plot the Bode diagram given the system parameters as in the previous
lab. The K1 and K2 are chosen in this lab. Find the and from the Bode diagram and
compare it with above experimental results and in lab #3.
4) Use Matlab Simulink to simulate the system. Fist get step response with the K1 and K2 same
as in experiment, then use Chirp signal input and Spectrum Analyzer output. Compare the result
with 3) and experimental results.( You can find Spectrum Analyze in Simulink Extra library).
33
Lab 5: DC Motor Position Control with Cascade PID Compensation
Objectives
To investigate PID controller and cascaded PID with tachometer feedback, compare the
experimental response with computer simulation response.
Introduction
'Compensation' is the modification of system (plant) performance characteristics so that they
conform to certain desired specifications. This is accomplished by effectively changing the
transfer function (more specifically, the OLTF) of the system, by introducing a ‗compensator‘
block at some suitable point in the closed loop. The compensator is usually located near the
input comparator, since the signal levels are low there and hence the compensator can be a low-
power device. In cascade Proportional-Integral-Derivative (PID) compensation, the time-integral
and time-derivative of the comparator output are obtained and added to that output itself and the
composite signal is used as the actuating signal (refer to Figure 5-1).
In the laboratory setup, a Proportional-Integral-Derivative amplifier unit (called PID unit
PID150Y) is used in the forward path, following the reference comparator, for the investigation
of cascade compensation. The Proportional-Integral-Derivative unit PID150Y is a three-mode
control amplifier. It provides three operational paths (P+I) or (P+D) or (P+I+D). The block
diagram is shown in Figure 5-2. Switching possibilities can be readily seen on the simplified
schematic shown on the faceplate of the unit (see Figure 5-3).
This amplifier has the following transfer function:
Gc(S) = K [1 + (1/sTi) + sTd] (5-1)
where the proportional gain K and the integral and derivative time constants Ti and Td can be
varied over specified ranges by means of three calibrated knobs on the unit. [The gain K can be
varied from 0.11 to 11 in two decade ranges. The Integral Time Constant Ti can be set from 0.11
to 11 seconds (in two decade ranges) and the Derivative Time Constant Td can be set from 2
milliseconds to 220 milliseconds in two ranges. Also, the Integral and Derivative functions can
be independently switched on or off as required.]
34
Figure 5-1 DC Motor Position Control with Cascade PID + Velocity
Feedback Compensation
Ki
150H
150A
PID
150Y
PID
150D
+150F
150X
Kt
150X
K2
150B
Ko
150K
Kp
150C
Vc
150C
Figure 5-2 PID150Y Block Diagram
Ti
K
Td
35
Now consider the system with the PID unit in the forward path, but with the tachometer feedback
removed (with the PID module parameters K, Ti and Td set, K2=0, this will correspond to
cascade PID compensation).
Using
and , the CLTF is given by
.
The equivalent unit-feedback transfer function
may be found, assuming
by:
(5-2)
Equation (5-2) clearly shows that (a) the system ‗Type‘ has been changed to Type 2, and (b) a
pair of zeros has been introduced. ie: the system will now have zero steady state error for both
step and ramp inputs. However, its transient response will depend on the location of the roots of
the system characteristic equation [ie: closed loop poles].
Figure 5-3 PID150Y Module
Ve
Vc
Select
Switch
Multiplier
Switch
36
Experiment Procedure
Pre-lab: Please review Lab#1, Lab#2 and Lab#3, connect a basic angular position control
system with PID controller and cascade velocity feedback as shown in Figure 5-1. The lab
equipments layout is shown in Figure 3-4. All the +15V and -15V and 0V voltage will be
connected in the lab later. The power supply PS150E, servo-amplifier SA150D and DC motor
DMC150-F are internal connected. Please note that input pot IP150H and output pot OP150K
must be cross connected (referring Figure 1-8), make sure Ve is a voltage difference not a
voltage sum. The reference voltage of IP150H and OP150K is ±15V. draw the connect in Figure
3-4 and bring to lab.
Expt. #1 Dc Motor Position Control With PID Compensation
Notes: Throughout the following experiments, it will be assumed that the op-amp and the
pre-amp remain zeroed and balanced respectively and that the supplies to the input/output
pots are cross-connected so that the op-amp is the difference between the input and output
position signals. Check system is controllable and stable, then replace input pot with
function generator.
Set up the circuit shown in Figure 5.1. Set K2 to zero to eliminate the velocity feedback. Adjust
the function generator controls to obtain a square wave output of about 4 volts peak-to-peak,
symmetrical about the zero volt baseline, at approximately 0.4 Hz.
Notes: For the following each steps, record your observations (Stop/Run scope, capture display
for your report) and comment on them. Attempt a correlation of your observations with a root-
locus diagram drawn using your values of system parameters.
1. Proportional Compensation: switch out the Integral (Ti=0) and Derivative (Td=0) paths, and
switch in only the Proportional path. Observe the change in 'step' (square-wave) response of the
angular-position output as the proportional compensator gain K is varied from 0.1 to 10.
Momentarily switch the input waveform to a triangular-wave and observe the change in the
"follower" (ramp) response as K is changed. (Let: K=0.1, 0.3, 1, 10)
2. Proportional-Integral Compensation*: Switch in the Integral path. Set the proportional gain
K=0.3, and observe the effect on the output responses for square wave and triangular wave input
when Ti is set to various values, Let .
3. Proportional-Derivative Compensation*: With K=0.3, switch out the Integral path and
switch in the Derivative path instead. Observe the effect on the output responses for square wave
and triangular wave input when Td is set to various values. Decrease the proportional gain if
necessary, to reduce noise. Let .
4. Proportional-Integral-Derivative Compensation*: Next, switch in the Integral path again.
The compensation is now a "cascade PID". Observe the effect on the 'step' (square-wave)
37
response and triangular-wave response when the gain K, Ti and Td are set to various values. Let
a) (K=0.3, .
b) (K=0.3, .
c) (K=0.3, .
d) (K=0.3, , ).
Expt. #2 DC Motor Position Control With PID Compensation and Tachometer feedback
Cascade Compensation with Tachometer feedback: Velocity feedback compensation can be
introduced in addition to any of the cascade compensation schemes given in Expt#1,steps 1, 2, 3
and 4 above, by means of pot coefficient K2. Note that the tachometer feedback is now applied
directly to the preamplifier (Y150C, input#2) in an internal loop which is also called a "minor"
feedback loop. Observe the effect of increasing K2 in each of the above cases. Record your
observations and comment on them.
a) P+ Tach: (K=0.3, K2=0.1) (K=0.3, K2=0.05)
b) PI+Tach: (K=0.3, ) , (K=0.3, )
Experiment Results
Expt. #1
1). Derive the transfer Function (real position of DC motor)/ (desired position of DC
motor) from Figure 5.1 given K2=0.
2). In Expt.#1, draw a Root-Locus plot for each step 1,2, 3 and 4 using system parameters and
the value in the experiments. Comment on them.
3). In Expt.#1, Simulate block diagram Figure 5.1 for each step 1,2, 3 and 4 using system
parameters and the value in the experiments, compare it with the experimental results.
4). In Expt.#1, get step response of the transfer function from question #1 for each step 1,2, 3
and 4 using system parameters and the value in the experiments. Compare the results with
Question #3 and experimental results.
Expt. #2
1). Derive the transfer Function (real position of DC motor)/ (desired position of DC
motor) from Figure 5.1 with velocity feedback K2.
2). In Expt.#2, Simulate block diagram Figure 5.1 with K2 using system parameters and the
value in the experiments of each case, compare them with the experimental results.
3). In Expt.#2, get step response of the transfer function from question #1 for each case.
Compare the results with Expt#2 Question #2 and experimental results.
