2
1
3
4
5
6
REVISION BLOCK
DESCRIPTION
REV
DATE
INCORP. BY
OVERVIEW
A
The goal of this document is to present the TCS1 control system in a clear and understandable way and to derive the transfer functions to be used in SIMULINK.
This document format combines notes, graphs, plots, graphics, etc. all on one page. It is not a traditional report style format.
A
The method used to present this material was to:
1) Present a hybrid block diagram of the entire system on one page. The block is not 100% mathematically or functionally correct. It is meant to present the system in an understandable way.
2) Explore each block or group of blocks, understand the function, and derive the transfer function for use in SIMULINK.
NOTE: Because of the way the blocks are implemented physically (e.g. inverting summer amplifier) the negative signs on some transfer functions may not show up in the SIMULINK model. For example, an
inverting summing amplifier followed by an inverting amplifier with a gain of -1 can be simply shown as a simple summer. SO, keep in mind that if a negative sign is dropped, either the input has already been
inverted into the block or its output will be inverted in the next block.
B
C
D
TABLE OF CONTENTS
PAGE
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
BLOCK
1&2
3
4
5
6
6
7
8
9
10
11
12
12
13
13
-
B
DESCRIPTION
TITLE PAGE (THIS PAGE)
OVERALL BLOCK DIAGRAM
COMMAND RECTIFIERS, PRE-LOADS, HIGH FREQUENCY TACHOMETER COMPENSATION
TACHOMETER & TACHOMETER INPUT BUFFERS
TACHOMETER SUMMER CIRCUIT
ACCELERATION LIMITER
MOTORS & BULL GEARS
MOTOR DATASHEET
COMMAND MAGNITUDE LIMITER (SLEW or OFFSET)
POWER AMPLIFIER MOTOR DRIVER
MAIN SUMMING BLOCK (PROPORTIONAL GAIN, INTEGRATOR, SLEW FEED FORWARD)
INCREMENTAL ENCODER & FRICTION GEAR
PROPORTIONAL GAIN
INTEGRATOR WITH SHORTING AND OFFSET FEED FWD PULSES
OFFSET FEED FWD PULSE EXPLANATION
DIGITAL TO ANALOG CONVERTER
COMPUTER/DIGITALLY GENERATED CONTROL SIGNALS (SLEW, OFFSET, POSITION ERROR)
UNIT CONVERSIONS (SUMMER VOLTS to RAD/S & RAD/S to ARCSEC/S)
APPENDIX: ABSOLUTE POSITION ENCODERS
APPENDIX: TCS1 BLOCK DIAGRAM CIRCA 1980
APPENDIX: IRTF 123 - TELESCOPE SERVO CONTROL HA COMPUTER CMD & MAGNITUDE DETECT
APPENDIX: IRTF 125 - TELESCOPE SERVO CONTROL HA SEQUENCE CONTROL BOARD
APPENDIX: IRTF 127 & 128 - TELESCOPE SERVO CONTROL D/A, JOYSTICK, & INTEGRATOR
APPENDIX: IRTF 130 - TELESCOPE SERVO CONTROL TACH SUMMER & TORQUE CMD
APPENDIX: IRTF 131 - TELESCOPE SERVO CONTROL DEC TACH SUMMER & TORQUE CMD
C
University of Hawaii
DWG #
REV TITLE
TCS1-CBD
ENGINEER
Eric Warmbier
-
Institute for Astronomy
TCS1 Control Block Diagram
LAST EDIT
12/12/2007 5:57:32 PM
SIZE B
FILE: Z:\public_html\Presentation\TCS1 Control Block Diagram_12_12_07.vsd
1
2
3
4
5
6
SHEET
1 of 25
D
1
2
Adj 0 to 8V
Adj 0 to 0.5V
BUF EAST SLEW DISABLE
BUF EAST MOTION DISABLE
A
13
14 bit
PEC B0:B12,B25
-10
Digital position
error CMD.
10
SWITCH
6
7
G=5
A
Compensator
.839
(1.0)
Low Pass
0
-0.35 V
(on output)
Adj. pre-load
1
12
Ki=
SWITCH
RESET
Ki ∫ v (t ) dt
2
0
1
SWITCH
+
12
12
0
0.02
1
12
Ki=
SWITCH
9
+
+
+
+
+
9
9
338 Hz
+
+
+
+
+
.839
(.513)
Low Pass
RESET
Ki ∫ v (t ) dt
9
11
-11
Mag Limit
POSITIVE
LIMIT
7
ADJ
468 Hz
7
12
-8V
0V
FD FWD WEST
0
1
SWITCH
5
+
ADJ
Mag Limit
-
5
5
1000
1000
-11
Low Pass
5
5
11
Mag Limit
Low Pass
4.5
-4.5
Mag Limit
12
680k
4
Ki ∫ v (t ) dt
330k
Integrator
+
-1.2
-
SWITCH
+
8
AMP
0
Low Pass
Half Wave
Rectifier-
+
1
+
+
5
1
12
Ki=
+
1
G=-2
0.35 V
(on output)
Adj. pre-load
0
0.02
+
Mag Limit
1
1
240 Hz
1
12
10
G=-2
Half Wave
Rectifier+
+
1
5
0
WEST
2
2
4
Ki=
RESET
NEGATIVE
LIMIT
Integrator
B
2
2
240 Hz
Integrator
+8V
0V
FD FWD EAST
8
12
.002
12
(active low)
7
338 Hz
Low Pass
12
5
9
1.96
(1.33)
DAC
7
(active low)
0V
4
SWITCH
11
1.59 kHz
11
3
7
(active low)
5.36
SWITCH
2
8.6Hz
RESET
Ki ∫ v (t ) dt
5.36
2
1
8.6Hz
240Hz
1
10
8
AMP
0
B
Mag Limit
EAST
240Hz
Integrator
Bandpass
HA CLEAR INTEGRATOR
+8V
0V
SLEW EAST/
9
(active low)
9
9
SLEW WEST/
Low Pass
9
(active low)
C
Compensator
4
4
3.77 Hz
Low Pass
9
0.488
Low Pass
338 Hz
+
4
Low Pass
3
+
723 Hz
4.7
(4.7)
0V
3
723 Hz
338 Hz
6.26
(12.1)
(active low)
Compensator
9
9
SWITCH
Joystick
Circuit
1
6.26
(12.1)
SWITCH
-8V
0V
Bandpass
2
338 Hz
SWITCH
Low Pass
9
9
Adj 0 to -8V
Adj 0 to -0.5V
BUF WEST SLEW DISABLE
BUF WEST MOTION DISABLE
7
(active low)
OPPOSING MOTORS APPLY TORQUE IN
ONE DIRECTION ONLY
7
(active low)
SWITCH
C
Low Pass
0V
7
~180:1 friction gear ratio
(encoder to bull gear)
G=5
SWITCH
10
Incremental
Encoder
MOTOR
144:1 ratio
(motor to bull gear)
3
SLEW
E
WEST
Tach
D
MECHANICAL
-
PEC B0:B12,B25
Active low SLEW signals present when
SLEW commanded in a direction.
When SLEW is nearly complete and
deceleration is required, the SLEW
signals are removed (high) and the
control goes back to standard control.
This is based on DIP switch settings
representing when to begin
deceleration in number of counts from
the end of the SLEW. Integrator is
also shorted during this event.
Desired
Position
EAST Tach
1
2
Counter
+
3
6
Bull gear
MOTOR
5 3 8 9
.2105
3
14
D
.2105
Telescope
Mount
HA CLEAR INTEGRATOR
3
6
SLEW WEST/
SLEW WEST/
HA CLEAR INTEGRATOR
BUF EAST SLEW DISABLE
BUF WEST SLEW DISABLE
If an offset is commanded, variable
amounts of pulses are added to the
integrator of opposite polarity to
remove charge from the integrator and
reduce overshoot.
E
FD FWD EAST
FD FWD WEST
F
F
DWG #
REV SIZE
TCS1-CBD
1
2
3
4
5
6
7
8
-
D
SHEET
2 of 25
2
1
3
BLOCK GROUP #1 & #2
4
Inverting Amp with low pass.
Gain =-300k/100k
=-3
f(-3dB) =1/(2πRC)
=1/(2π*300k*2200pF)
=240 Hz
B
HOWEVER, the compensation up front
will cause lower gain overall and will
cause additional lower gain at lower
frequencies. Also, filter is not a “brick
wall” filter. Pass band will have lower
gain than calculated as the simulation
illustrates..
6
Half Wave Rectifier Output EAST=negative output (positive for WEST)
Gain adjust
A
Inverting Amp with band pass.
Gain =-300k/56k
=-5.357 in pass band
f(low) =1/(2πRC)
=1/(2π*300k*2200pF)
=240 Hz
~f(high) =1/(2πRC)
=1/(2π*56k*0.33uF)
=~8.58 Hz
5
Inverting Amp
(Gain = -2)
Positive Values Only (EAST)
Negative Values Only (WEST)
A
INVERTING
SUMMING
Adds a preload to the output
and will be adjusted to add to
the DAC output about: +0.35V
(East) or -0.35 (West).
Low pass filter
f(-3dB) =1/(2πRC)
=1/(2π*100*0.1uF)
Sets maximum output clamp,
=16 kHz
which must be less than the
series Zeners, or ~10.7V.
This is really high compared to
240 Hz upstream filter. This is
for high frequency electronic
noise induced or picked up.
B
ACTUAL GAIN
(input signal is 1V)
TRANSFER FUNCTION(S) FOR SIMULINK
C
12
-
G=-2
0
-
C
10
+
Mag Limit
+
Pass band, shorted C8,R33
0
Mag Limit
WEST
-0.35
Compensated Input Plot from Mathcad
Actual circuit
0
-
-
-12
0
G=-2
Mag Limit
+
+
D
-10
Mag Limit
D
EAST
0.35
DWG #
REV
TCS1-CBD
1
2
3
4
5
-
6
SHEET
3 of 25
2
1
BLOCK GROUP #3
3
4
5
Identical amplifier input stage for EAST & WEST.
TCS Tachometer Voltage vs. Speed
Gain= Rf/Rs
10k/47k
2.000
0.213
f(-3dB) =1/(2πRC)
1.800
=1/(2π*10k*0.022uF)
=723 Hz
1.600
A
6
y = 0.008845x + 0.005803
R2 = 0.999922
1.400
(Intercept set to Zero)
Clamp
Voltage (V)
1.200
y = 0.008764x
R2 = 0.999979
A
y = 0.008654x - 0.001271
R2 = 0.999997
East
West
1.000
Average
Linear (West)
0.800
Linear (East)
0.600
DIFFERENTIAL AMP
w/ filtering
Linear (Average)
0.400
0.200
B
0
100
150
200
250
Speed (as/s)
V
arc sec/ s
⋅
arc sec/ s rad / s
0.008764V 206264.81arc sec/ s
Tach =
⋅
arc sec/ s
rad / s
1807.704V
Tach =
rad / s
Tach =
C
50
-0.200
For the tachometer rad/s to volt conversion:
TRANSFER FUNCTION(S) FOR SIMULINK
B
0.000
Very high frequency passive filtering
f(-3dB) =1/(2πRC)
Where R is the line + source impedance
which is low.
NOTE:
This conversion is from TELESCOPE
axis rotational velocity to volts. The
mechanical model in SIMULINK
provides axis velocity in rad/s at each
motor geared output (after the 1:144
ratio).
C
Tachometer
Velocity
(rad)
D
D
DWG #
REV
TCS1-CBD
1
2
3
4
5
-
6
SHEET
4 of 25
2
1
3
BLOCK GROUP #4
VEL
CMD
4
+
Gain= -Rf/Rs
33.2k/68.1k
-0.4875
f(-3dB) =1/(2πRC)
=1/(2π*33.2k*(1uF+0.27uF)
=3.77 Hz
-1.2
-
A
4
West Tach IN
4
3.77 Hz
0.488
Low Pass
6
West Tach IN
4
4
5
+
+
A
4
East Tach IN
INVERTING SUMMING
w/ filtering
Velocity CMD
B
B
INVERTING SUMMING
Gain = -120/100
Gain = -1.2
East Tach IN
By adding together ~½ of two individual signals, the output is approximately the average.
TRANSFER FUNCTION(S) FOR SIMULINK
C
C
NOTE: Be careful with the polarity signs here. The equation will be worked through to demonstrate the polarities.
VEL
CMD
+
-
Vout = 1.2 ⋅ (−VCMD − Vsum _ amp )
Vout = 1.2 ⋅ (−VCMD − (−0.4875 ⋅ ( Etach + Wtach )))
Vout = 1.2 ⋅ (−VCMD + 0.4875( Etach + Wtach ))
Vout = −1.2(VCMD − 0.4875( Etach + Wtach ))
-1.2
West Tach IN
+
+
D
D
East Tach IN
DWG #
REV
TCS1-CBD
1
2
3
4
5
-
6
SHEET
5 of 25
2
1
3
4
BLOCK GROUP #5
A
5
+
-
5
1000
5
Op-amp supplies limit output to about +/- 12V.
5
11
-11
Mag Limit
5
1000
INTEGRATOR
Since the input to the
integrator will always be either
+/-4.5V due to the total gain of
1 million and the clamping
diodes, the current going into
the integrator will always be
+/- a constant value (4.5V/
resistor) and the result is a
signal with a +/- constant
slope. This slope is change in
velocity, which is acceleration.
The integrator uses a
capacitor.
Where the capacitor voltage
change over time:
i=Cdv/dt
i/C=dv/dt
5
4.5
Ki=
RESET
-4.5
Mag Limit
680k
Ki ∫ v (t ) dt
330k
Integrator
5
0
1
HA CLEAR INTEGRATOR
SWITCH
5
Notice the feedback and high gain of a million.
This can be represented as a slew limited amplifier with a gain of +1.
This circuit functions as an acceleration limiter.
B
INVERTING AMP
Gain = -1000
INVERTING AMP
Gain = -1000
1n5240 are 10V
Zener Diodes, so
output is limited to
about:
10+0.7=10.7V.
Roundoff to ~11V
Output is clamped
to about:
3.1+0.7+0.7 =
~4.5V
6
Therefore:
330kΩ case:
i=4.5V/330kΩ
i=13.64μA
dv/dt=13.64μA/1μF
dv/dt=13.64V/s
C
B
1010kΩ case:
i=4.5V/1010kΩ
i=4.46μA
dv/dt=4.46μA/1μF
dv/dt=4.46V/s
NOTE: In this simulation the first stage was unclamped (it just saturated) and a 3.3V
(1n746A) Zener was used. The result will be nearly identical with the exception that the
slope will be a slightly larger value. 330kΩ used for integrator in simulation.
TRANSFER FUNCTION(S) FOR SIMULINK
A
C
+/- 13.64V/s
Results,
Rate Limit
12
0
+/- 4.46V/s
1
330kΩ simulation:
dv/dt=-1V/83.5ms
dv/dt=~12V/s
-12
SWITCH
Mag Limit
Rate Limit
D
D
HA CLEAR INTEGRATOR
DWG #
REV
TCS1-CBD
1
2
3
4
5
-
6
SHEET
6 of 25
2
1
BLOCK GROUP #6
Telescope
Mount
6
MOTOR
B
The motors are driven by a current amplifier. The output of
the motor has a 144:1 gear ratio to the HA Axis. Since the
motor is driven by a current drive amplifier, the equations
for the torque involve the torque constant of the motor,
current, and gear ratio. The back EMF produced by the
motor is used as feedback for the amplifier in the amplifier
model. The back EMF reduces the maximum current
output of the amplifier. See the amplifier section for more
details. See next page for motor datasheet and parameter
values.
Imai measured 1Ω and 1.3Ω across the motors at the
junction box with the amplifiers off but still connected on
11/2/07. This suggests “A” version of motor.
5
6
SPARE, Model 12016A
MOTOR TORQUE
Torque = IKT ⋅ Gear _ Ratio
Torque = IKT ⋅ Gear _ Ratio
lb ⋅ ft ⎤
⎡
Torque = I ⎢12.8
⋅ (144)
A ⎥⎦
⎣
lb ⋅ ft ⎤
⎡
Torque = I ⎢1843.2
A ⎥⎦
⎣
lb ⋅ ft ⎤
⎡
Torque = I ⎢3.90
⋅ (144)
A ⎥⎦
⎣
lb ⋅ ft ⎤
⎡
Torque = I ⎢561.6
A ⎥⎦
⎣
MOTOR
144:1 ratio
(motor to bull gear)
Bull gear
4
ORIGINAL, Model 12016A
6
A
3
A
lb ⋅ ft ⎤ ⎡1.355 817 952 N ⋅ m ⎤
⎡
Torque = I ⎢1843.2
⋅
⎥
A ⎥⎦ ⎢⎣
lb ⋅ ft
⎣
⎦
2499.04 N ⋅ m
Torque = I ⋅
A
lb ⋅ ft ⎤ ⎡1.355 817 952 N ⋅ m ⎤
⎡
Torque = I ⎢561.6
⋅
⎥
A ⎥⎦ ⎢⎣
lb ⋅ ft
⎣
⎦
761.427 N ⋅ m
Torque = I ⋅
A
MOTOR IMPEDANCE (@25C)
MOTOR IMPEDANCE (@25C)
Z motor = Z L _ winding + Rwinding
B
Z motor = Z L _ winding + Rwinding
Z motor = s (0.008)Ω + 0.97Ω
Z motor = s (0.017)Ω + 0.4.50Ω
BACK EMF (used in amplifier section)
BACK EMF (used in amplifier section)
Back _ EMF = θ M ⋅ K b
Back _ EMF = θ M ⋅ K b
V
Back _ EMF = θ M ⋅ 5.30
rad / s
Back _ EMF = θ M ⋅ 17.4
V
rad / s
C
C
TRANSFER FUNCTION(S) FOR SIMULINK
Current (A)
Torque (N•m/A)
761.427
D
D
DWG #
REV
TCS1-CBD
1
2
3
4
5
-
6
SHEET
7 of 25
2
1
3
4
5
6
BLOCK GROUP #6 CONTINUED
6
Telescope
A
Mount
A
MOTOR
144:1 ratio
(motor to bull gear)
6
Bull gear
MOTOR
B
B
C
C
Imai measured 1Ω and 1.3Ω across the motors at the junction box with the
amplifiers off but still connected on 11/2/07. This implies model “A”.
D
D
SPARE MOTOR
CURRENT MOTOR IN USE
DWG #
REV
TCS1-CBD
1
2
3
4
5
-
6
SHEET
8 of 25
2
1
3
4
BLOCK GROUP #7
Adj 0 to 8V
Adj 0 to 0.5V
A
7
(active low)
BUF EAST SLEW DISABLE
BUF EAST MOTION DISABLE
SWITCH
7
(active low)
0V
INVERTING Summing AMP with half wave rectifier.
Only positive outputs allowed.
7
Op-amp equation when Vcmd is ≤ -5*Vrefp:
Vout=-Vrefp-0.2*Vcmd
G=5
SWITCH
7
POSITIVE
LIMIT
7
ADJ
468 Hz
Else, Vout=0.
Mag Limit
Adj 0 to -8V
Adj 0 to -0.5V
(active low)
BUF WEST SLEW DISABLE
BUF WEST MOTION DISABLE
B
SWITCH
0V
INVERTING summing amp.
This stage subtracts the exact
amount from the command
that is required to clip it and
keep it within 5*ref voltage .
The final result is the inverted
value.
A
(-5*VREFP is the actual negative
output voltage limit of Z9)
Low Pass
NEGATIVE
LIMIT
7
6
It also provides a filter.
ADJ
7
(active low)
5
7
G=5
SWITCH
B
This is just a selectable magnitude limiter with a filter.
The “BUF MOTION DISABLE” can be ignored since it is a personnel safety feature, which isn’t part of the servo analysis.
Also, it can be assumed that EAST and WEST slewing will have equal magnitude limiting.
(-5*VREFN is the actual positive
output voltage limit of Z9)
C
INVERTING Summing AMP with half wave rectifier.
Only negative outputs allowed.
TRANSFER FUNCTION(S) FOR SIMULINK
0.720
0.160
BUF EAST SLEW DISABLE
1
SWITCH
Z8A-9= 160 mV
Z8A-5= 717 mV
Z7A-5= -720 mV
Z7A-9= -150 mV
(EAST track)
(EAST slew)
(WEST track)
(WEST slew)
Else Vout=0.
(Velocity CMD input only,
excludes limit refs)
For model, use
+/- 160 mV for tracking/offset
+/- 720 mV for SLEW
ADJ
Mag Limit
NEGATIVE
LIMIT
D
Op-amp equation when Vcmd is ≥ -5Vrefn:
Vout=-Vrefn-0.2*Vcmd
Testing 11/7/07
G=5
POSITIVE
LIMIT
ADJ
-0.720
-0.160
BUF WEST SLEW DISABLE
C
0
D
0
1
G=5
SWITCH
DWG #
REV
TCS1-CBD
1
2
3
4
5
-
6
SHEET
9 of 25
2
1
3
BLOCK GROUP #8
Absolute value of power supply.
+90V
(supply voltage)
Functionally, the amplifier becomes a transconductance amplifier - with a
transfer function of 10.5 amps of equivalent output current per volt of input
command voltage. This is the nominal specified value. See test results
below. However, the amplifier output current is limited by the impedance it
is driving and its +90V supply used in the TCS. The motor impedance will
change with frequency due to the inductance and the motor will also create
a back EMF, which further reduces the available voltage to drive the motor.
The CSR amp uses an H-Bridge driver. This means that it only uses a
+90V supply but it can reverse the polarity on the motor, resulting in current
flowing the opposite direction. In regards to modeling, it would appear as if
the amplifier could supply +/- 90V to the motor.
-
C
BACK EMF
(see motor modeling)
1
0
-
D
SWITCH
Motor Drive
Current (A)
+
|ABS|
1/(Motor
Inductance)
(see motor)
|Maximum current| that the amplifier
can provide to the motor due to the
back EMF and motor impedance.
B
The voltage could be positive or negative for the back
EMF. These blocks are used as a comparison to see if
the current magnitude requested can be supplied.
Rotational Speed (rad/s)
5.30
CMD
(A/V)
-6.202532
-6.162791
-6.097561
-6.116071
-6
-6.541667
-6.18677
Monitor
(A/V)
11.66667
11.77778
11.90476
17.125
16.66667
18.47059
14.60191 WEST
17.42075 NORTH
D
DWG #
REV
TCS1-CBD
1
C
DESCRIPTION
Measurments taken at NC307 amplifiers to compare the volts to amps command conversion
and the amps to volts current monitor. FLUKE DVM put in series with actual armature wire
originating at the NC307. "+" of multimeter was hooke up to "+" armature, so current flow is
measured coming out of the amplifier.
MOTOR & FLUKE
Term 6
Term 8
Axis Tracking
AXIS
Current (A) CMD (V) Monitor (V) Speed (as/s)
WEST
4.9
-0.79
0.42
10
WEST
5.3
-0.86
0.45
6
WEST
5
-0.82
0.42
30
NORTH
2.74
-0.448
0.16
15
NORTH
2.7
-0.45
0.162
30
NORTH
3.14
-0.48
0.17
50
average
average
1
0.008s + 0.970
-
Select the lower value between desired and available:
IF desired < available, control value is positive “1”, use desired value
IF desired > available, control value is negative “0”, use max value
Date Created: 11/28/07
Author: E. Warmbier
|ABS|
+
-
Ideal amplifier model:
This model is a very simplified model of a transconductance amplifier. It does not take into account
any frequency response of any kind. However, for the purposes of the TCS model, it should be
sufficient. The switching frequency of the amplifier is 20 kHz. The response of the amplifier is DC
to 1000 Hz at rated current. The TCS control system is limited to the hundreds of hertz.
-6.2
+90V
A
SWITCH
|ABS|
TRANSFER FUNCTION(S) FOR SIMULINK
Current
CMD
(in volts)
Motor Drive Current (A)
0
+
+
B
1
|ABS|
Each of the two motors is operated by a dedicated power amplifier (CSR
Contraves, NC307). These amplifiers are classic switching amplifiers, in that
they utilize an alternating polarity square wave with an adjustable duty cycle,
to control the equivalent DC current. Their switching frequency is 20 kHz.
6
10.5 A/V
AMP
A
5
Desired command current
Current
CMD
(in volts)
8
4
2
3
4
5
-
6
SHEET
10 of 25
2
1
3
4
5
6
BLOCK GROUP #9
(proportional output ->)
A
A
INVERTING Summing Amp with filtering and output
magnitude limiting to about +/- 10.7V or ~11V.
B
B
(integrator output ->)
INVERTING Summing Amp with filtering and output magnitude limiting to about +/10.7V or roundoff to ~+/-11V. However, the +/- 11V clamp may be ignored for the
purposes of this model. There is another limiter of lower magnitude that follows this
stage. See block #7.
w/ amp
above
SLEW EAST/
TRANSFER FUNCTION(S) FOR SIMULINK
C
C
w/ amp
above
(proportional output ->)
SLEW WEST/
(integrator output ->)
D
+8V
0V
SLEW EAST/
(active low)
JOYSTICK
(ignore)
D
SWITCH
-8V
0V
SLEW WEST/
+
+
+
+
+
(active low)
Not using during servo modeling – ignore.
SWITCH
DWG #
REV
TCS1-CBD
1
2
3
4
5
-
6
SHEET
11 of 25
2
1
3
4
5
6
BLOCK GROUP #10
A
~180:1 friction gear ratio
(encoder to bull gear)
Telescope
A
Mount
10
Incremental
Encoder
B
Bull gear
The encoder input is in terms of rotation position (radians) and output is in volts
ultimately at the digital to analog converter.
1 encoder
pulse
Friction
A/D
increments
Gear
Scaling
Encoder
position
Ratio
(see block #12)
counter by 1
B
Teledyne Gurley Incrementel encoders, model 8626.
Both of the current incremental encoders have a 3600 line count and associated electronics
capable of 40x interpolation for a total of 144 000 pulses/ revolution.
⎛ 3600⋅ 40 pulses revolution 180turns 20V
bit ⎞
⎟⎟ ⋅ Radians
Output _ Voltage = ⎜⎜
⋅
⋅
⋅ 14
⋅
⎝ revolution (2π )radians 1turns 2 bits pulse ⎠
Output _ Voltage ⎛ 3600⋅ 40 pulses revolution 180turns 20V
bit ⎞
⎟⎟
= ⎜⎜
⋅
⋅
⋅ 14
⋅
(
2
)
1
2
π
Radians
revolution
radians
turns
bits
pulse
⎝
⎠
From BEI’s website gloassary: http://www.motion-control-info.com/encoder_glossary.html
Output _ Voltage
V
= 5035.762
Radians
radians
C
C
There is quantization of position due to the encoder. The encoder provides pulses,
not a continuous output. The quantization is the number of radians that must be
traveled before the next pulse. This is calculated as follows:
revolution
(2π )radians 1
radians
⋅
⋅
= 242 .41 ⋅ 10 − 9
3600 ⋅ 40 pulses revolution 180
pulse
radians
242 .41 ⋅ 10 − 9
⋅ 1 pulse = 242 .41 ⋅ 10 − 9 radians
pulse
TRANSFER FUNCTION(S) FOR SIMULINK
D
D
5035.762
Encoder
242.41E-9
quantization interval
DWG #
REV
TCS1-CBD
1
2
3
4
5
-
6
SHEET
12 of 25
2
1
3
4
5
6
BLOCK GROUP #11
11
1.59 kHz
11
1.96
(1.33)
Low Pass
A
A
This is proportional gain of the PID with a low pass filter.
Inverting amplifier with filtering:
Gain= Rf/Rs
10k/5.11k
1.96
f(-3dB) =1/(2πRC)
=1/(2π*10k*0.01uF)
=1.59 kHz
B
DEC AXIS:
HA AXIS
B
C
C
HA TRANSFER FUNCTION(S) FOR SIMULINK
DEC TRANSFER FUNCTION(S) FOR SIMULINK
D
D
DWG #
REV
TCS1-CBD
1
2
3
4
5
-
6
SHEET
13 of 25
2
1
3
4
5
6
300Ω “Short”
BLOCK GROUP #12
300Ω “Short”
Normal
Normal
A
B
A
B
TRANSFER FUNCTION(S) FOR SIMULINK
INVERTING Summing Integrator under normal operation.
Position Error Signal
(from DAC)
Very low gain inverting summer with filter when R17 via switch is active (SLEW mode).
Essentially the integrator is shorted out since 300Ω is a low value and therefore the gains become very
small.
0
1
SWITCH
C
+8V
0V
FD FWD EAST
C
(active low)
0
1
0
1
SWITCH
SWITCH
-8V
0V
FD FWD WEST
Bottom line: “I” term for the PID controller is either active or it is shorted.
+
+
+
+
+
0
0
1
1
SWITCH
SWITCH
D
D
HA CLEAR INTEGRATOR
DWG #
REV
TCS1-CBD
1
2
3
4
5
-
6
SHEET
14 of 25
1
2
3
BLOCK GROUP #12 Continued
4
5
6
MANUAL (finger pushing button), REPETITIVE +/- 60 ARCSEC OFFSETS, 11/7/07
A
A
CH1: “VOUT” TP
CH2: Integrator Output TP2
CH3: FD FWD East
B
B
Below is a portion of the Ev Irwin memo about the offset
operation and how the FD FWD is used.
From Ev Irwin Memo:
C
“In addition to using the PEC D/A signal as an input, during offset or beam switching operations, the
Integrator receives pulses of fixed amplitude but varying numbers. These pulses inject charge
into the integrator of opposite polarity as is the direction of desired position change. The
purpose of these pulses is to reduce overshoot and improve settling time. The number of pulses –
and therefore total injected charge is one-for-one equal to the commanded number of steps
required for relative position change. In other words, when the telescope is commanded to step
400 steps to the east, there is a delay while the telescope moves to the east. During that time, the
integrator integrates the error so that when the telescope finally reaches the desired new position,
there is excess charge in the integrator. To remove this charge, there would have to be an
overshoot with a negative error. The feed-forwarding pulses inject negative charge into the
integrator thereby shortening or eliminating the need for overshoot. NOTE – At first, one might
wonder why not simply short out the integrator, as is done during slew operations? Unfortunately,
during tracking, the integrator contains the amount of charge necessary to produce an output
voltage equal to the value required to track the telescope. To short the integrator, would remove
that charge, forcing the telescope to briefly stop and thereby worsening the settling time – not
improving it.”
C
FD FWD pulse initially
causes large jump in
opposite polarity of error
signal.
The scope plot seems to confirm the above statement. When the error reaches
zero (CH1) the integrator output (CH2) is approximately the same as the value
when the offset started. This is due to the charge injected by the FD FWD pulse
(CH3). If this pulse did not exist, the integrator would have a positive value on its
output due to integrating the error signal when the error reaches zero.
D
Error signal is then
integrated which brings
output back close to
initial value.
(Keep in mind that the op-amp is inverting.)
DWG #
Remember: inverting amplifier configuration.
1
2
3
4
5
REV
TCS1-CBD
-
6
SHEET
15 of 25
D
2
1
3
4
5
6
BLOCK GROUP #13
13
14 bit
PEC B0:B12,B25
A
Digital position
error CMD.
-10
10
DAC
A
Digital to analog converter.
Voltage output.
The digital to analog converter gain was lumped into the encoder
block. See block #10.
Note: no datasheet was located on the internet.
(It’s an older obsolete DAC.)
B
B
It is known from operation and the above schematic that the
DAC uses +/- 15V supplies, outputs +/-10V, and is 14 bits.
Given this information, the resolution can be calculated as:
10 − (−10)V
= 1.22mV / bit
214 bits
This value is used as the quantization interval for the
quantization block in Simulink.
C
C
In addition, the DAC can only output +/- 10V. A limiter can be
placed on the output.
DEC TRANSFER FUNCTION(S) FOR SIMULINK
1.22E-3
quantization interval
10
D
PEC B0:B12,B25
Digital position
error CMD.
-10
DAC
D
Mag Limit
DWG #
REV
TCS1-CBD
1
2
3
4
5
-
6
SHEET
16 of 25
1
2
3
4
5
6
BLOCK GROUP #13 CONTINUED
A
B
A
B
The SIMULINK modeling of this will be much simpler than the large
amounts of digital circuitry that were required to create these signals.
SEE BLOCK #12 for more information on the offset pulses.
(“FD FWD EAST” and “FD FWD WEST”)
More work needs to done here. As of 11/27/07 two things are
unknown:
1) Position error magnitude at which a slew ends
2) Offset pulse characteristics
C
The model currently uses values that work well in the simulation.
C
D
D
DWG #
REV
TCS1-CBD
1
2
3
4
5
-
6
SHEET
17 of 25
2
1
3
4
5
6
CONVERSIONS
CONVERSION FOR SIMULINK
The tachometer summer circuit has a scaled, averaged, tachometer output in volts. In the
SIMULINK simulation, it is convenient to display this in arcsec/sec. See conversion
derivation for rad/s to arcsec/s used below. This is the feedback that the control system
uses.
A
tach summer out
(volts)
548.78
radian/sec
A
arc sec
arc sec/ s _ conversion
1
1
1
1
= Output(V ) ⋅
⋅
⋅
⋅
⋅
Tach _ conv Diff _ Amp summer _ gain Num _ tach _ input
rad / s
sec
radians
1
1
1 206264.81arcsec/s
1
= Output(V ) ⋅
⋅
⋅
⋅ ⋅
1808V 0.213 0.488 2
rad / s
sec
rad / s
radians
548.78arc sec/ s
= Output(V ) ⋅
sec
V
B
B
C
C
CONVERSION FOR SIMULINK
D
radians/sec
206264.81
In Simulink, some of the outputs will be displayed on a scope.
Radians/second are used in the model for radial velocity, but
arcsec/sec is what the telescope control displays and uses.
Converting it makes it easier to understand and compare to actual
telescope data.
arcsec/sec
radians radian 180 deg 60arc min 60arc sec
=
⋅
⋅
⋅
sec
sec π ⋅ radian
deg
arc min
radians
arc sec
= 206264.81
sec
sec
D
DWG #
REV
TCS1-CBD
1
2
3
4
5
-
6
SHEET
18 of 25
1
2
3
4
5
6
APPENDIX: ABSOLUTE POSITION ENCODERS
The current RA absolute position encoder (APE) is located in the North Pier. It is an inductosyn
encoder with one half mounted on the yoke, and the other half mounted to the pier.
A
A
The DEC APE is located in the west arm of the yoke. It is also an induction type encoder
(identical to the RA encoder) with one half mounted to the telescope central section, and the
other half mounted on the yoke.
Both of the current APEs have a resolution of 0.1 arcsec.
B
B
C
C
D
D
DWG #
REV
TCS1-CBD
1
2
3
4
5
-
6
SHEET
19 of 25
5
MCC TRACK WEST PULSES
COMPUTER SLEW EAST (SOUTH) COMMAND
COMPUTER SLEW WEST (NORTH) COMMAND
EXCESS POSITION ERROR
A
RAMPDOWN
DISTANCE
SWITCH
MEMORY
IRTF 123 HA
IRTF 124 DEC
Y
X
(MCB)
EAST (SOUTH) TELESCOPE MOTION PULSES
19.9028 PULSES/ARC-SEC ≈ 0.05 ARC-SEC/PULSE
19.9472 PULSES/ARC-SEC ≈ 0.05 ARC-SEC/PULSE
B
INCREMENTAL
ENCODER
COUNT UP/DN CONTROL
POSITION
ERROR
WINDOW
LOGIC
IRTF 125 HA
IRTF 126 DEC
BITS 0 - 23
MANUAL
SLEW
CLEAR
PEC
LOADER
IRTF 122
POSITION
ERROR
UP/DOWN
COUNTER
(PEC)
(24 BITS)
IRTF 125 HA
IRTF 126 DEC
EXCESS
POSITION
ERROR
TELEDYNE
GURLEY
MODEL 8626
144,000 PULSES
PER ENCODER
REVOLUTION
BIT 23 (MSB)
DIGITAL
TO
ANALOG
CONV.
BITS 0 - 12
24 BIT PARALLEL COMMAND
IRTF 122
8
A
WEST (NORTH) TELESCOPE MOTION PULSES
DIVIDE BY 2
LOGIC
(BINARY SHIFT)
IRTF 123 HA
IRTF 124 DEC
C
COMPUTER
INTERFACE
X-Y
DIGITAL
SWITCH
IRTF 123 HA
IRTF 124 DEC
HARDWARE
CONTROLLED
SLEW LOGIC
MASTER CONTROL BUS
ARITHMETIC
SUBTRACTION
LOGIC
IRTF 123 HA
IRTF 124 DEC
7
ANTICOINCIDENCE
SCANNER
IRTF 125 HA
IRTF 126 DEC
COUNTDOWN
B
COMPUTER
COMMAND
MAGNITUDE
ANALYSIS
LOGIC
IRTF 123 HA
IRTF 124 DES
IRTF 123 HA
IRTF 124 DEC
*OR* COMMAND / 2
SLEW
MODE
MINIMUM
COMMAND
SWITCH
MEMORY
IRTF 123 HA
IRTF 124 DEC
LOAD AND COUNT
COMMAND MINUS DECEL. DISTANCE
COMMAND > MINIMUM COMMAND SETTING FOR SLEW
DISTANCE
BEFORE
RAMPDOWN
COUNTER
BEGIN DECEL.
SELECT
COMMAND ≥ 2 TIMES DECELERATING DISTANCE
COMPUTER
COMMAND
TIMING
AND
MODE
SEQUENCE
CONTROL
IRTF 125 HA
IRTF 126 DEC
6
(MANUAL MODE AND
COMPUTER SLEWS ONLY)
4
MCC TRACK EAST PULSES
3
OPERATION COMPLETE
2
(MANUAL MODE AND
COMPUTER SLEWS ONLY)
1
APPENDIX: TCS1 BLOCK DIAGRAM CIRCA 1980
C
0V = NULL
BULL
GEAR
ERROR NULL
=10000000000000
HARDWARE CONTROLLED SLEW LOGIC CONTROLS TELESCOPE
DURING COMPUTER INITIATED SLEW OPERATIONS. IT INITIATES
ACCELERATION, CALCULATES THE DECELERATION POINT, AND
RETURNS THE SERVO TO LINEAR MODE.
OPPOSING DRIVES
EAST
(SOUTH)
DRIVE
MOTOR
WEST
(NORTH)
DRIVE
MOTOR
0 TO ±10 VOLT ANALOG POSITION ERROR SIGNAL
DC
TACH
DC
TACH
WEST
DRIVE
TACH
SIGNAL
(NORTH)
EAST
DRIVE
TACH
SIGNAL
(SOUTH)
INLAND
D
HIGH FREQ WEST DRIVE MOTOR
TACH SIGNAL
F
MCC2 JOYSTICK SIGNAL
MANUAL
SLEW
JOYSTICK
BUFFER,
DUAL SLOP
GENERATOR
COMPUTER SLEW
EAST (SOUTH) COMMAND
COMPUTER SLEW
WEST (NORTH) COMMAND
PRODUCES WEST (NORTH)
TORQUE COMMAND ONLY
+
TELESCOPE EAST (SOUTH) SLEW LIMIT SWITCH
-8V
+8V
TELESCOPE WEST (NORTH) STOP LIMIT SWITCH
INTEGRATOR
TORQUE SPLITTER
COMPENSATION
NETWORK
LOW FREQUENCY TACH SUM
E
SUMMING
AMP
EAST
(SOUTH)
DRIVE
TACH
SIGNAl
3HZ
HIGH
FREQ
FILTER
LOW
FREQ
FILTER
-
SUMMING
AMP & PREC
RECTIFIER
HIGH FREQ EAST DRIVE MOTOR
TACH SIGNAL
+
WEST DRIVE
TACH SIGNAL
+
EAST DRIVE
TACH SIGNAL
+
+
-
SUMMING
AMP & PREC
RECTIFIER
SWITCH
-
PRECISION
RAMP
AMPLIFIER
PRECISION
AMPLITUDE
LIMITER
SUMMING
AMP
SUMMING
AMP & PREC
RECTIFIER
+
SHORTED
DURING
SLEWS
+
+
+
+
+
CSR
POWER
AMP
SUMMING
AMP & PREC
RECTIFIER
+
VELOCITY LIMITED
CSR
POWER
AMP
+
ACCELERATION LIMITED
LOW
FREQ
FILTER
WEST (NORTH) DRIVE TORQUE CMD
BUFFER
AMP
WEST
(NORTH)
DRIVE
TACH
SIGNAl
+
D
E
WEST
(NORTH)
PRE-LOAD
EAST
(SOUTH)
PRE-LOAD
EAST (SOUTH) DRIVE MOTOR TORQUE COMMAND
PRODUCES EAST (SOUTH)
TORQUE COMMAND ONLY
SUMMING
AMP
F
(TELESCOPE LIMIT
SWITCH INITIATED)
DWG #
REV SIZE
TCS1-CBD
1
2
3
4
5
6
7
8
-
SHEET
D 20 of 25
1
2
3
4
5
6
7
8
APPENDIX: IRTF 123 - TELESCOPE
SERVO CONTROL HA COMPUTER CMD
& MAGNITUDE DETECT
A
A
B
B
C
C
D
D
E
E
F
F
DWG #
REV SIZE
TCS1-CBD
1
2
3
4
5
6
7
8
-
SHEET
D 21 of 25
1
2
3
4
5
6
7
8
APPENDIX: IRTF 125 - TELESCOPE SERVO
CONTROL HA SEQUENCE CONTROL BOARD
A
A
B
B
C
C
D
D
E
E
F
F
DWG #
REV SIZE
TCS1-CBD
1
2
3
4
5
6
7
8
-
SHEET
D 22 of 25
1
2
3
4
5
6
7
8
APPENDIX: IRTF 127 & 128 TELESCOPE SERVO CONTROL D/A,
JOYSTICK, & INTEGRATOR
A
A
B
B
C
C
D
D
E
E
F
F
DWG #
REV SIZE
TCS1-CBD
1
2
3
4
5
6
7
8
-
SHEET
D 23 of 25
1
2
3
4
5
6
7
8
APPENDIX: IRTF 130 - TELESCOPE SERVO
CONTROL TACH SUMMER & TORQUE CMD
A
A
B
B
C
C
D
D
E
E
F
F
DWG #
REV SIZE
TCS1-CBD
1
2
3
4
5
6
7
8
-
SHEET
D 24 of 25
1
2
3
4
5
6
7
8
APPENDIX: IRTF 131 - TELESCOPE SERVO
CONTROL DEC TACH SUMMER & TORQUE CMD
A
A
B
B
C
C
D
D
E
E
F
F
DWG #
REV SIZE
TCS1-CBD
1
2
3
4
5
6
7
8
-
SHEET
D 25 of 25