NATIONAL RADIO ASTRONOMY OBSERVATORYCharlottesville, Virginia 22901

Electronics Division Internal Report No. 127

THE 45-FOOT ANTENNA DRIVE SYSTEM

John M. Payne

MARCH 1973

NUMBER OF COPIES: 150

THE 45-FOOT ANTENNA DRIVE SYSTEM

John M. Payne

TABLE OF CONTENTS

Page

1. 0 Introduction .................................................................................................... 12. 0 Performance Summary of the Drive System ..................................... ......... 1

2. 1 Pointing Accuracy .................................................................... ......... 12. 2 Slew Speeds ....................................................................................... 12. 3 Modes of Operation ................................... ........................................ 1

3. 0 Description of Control System ........................................................... .........24. 0 Torque Requirements .......................................................................... .........25, 0 Servo Design .................... ............................................................................. 3

5. 1 General Description of Servo System ..................................... .........35. 2 Mechanical Transfer Functions .............................................. ......... 55. 3 Tachometer Loop Design ....................................................... ......... 75. 4 Position Loop Design ............................................................... .........85. 5 Performance in Wind ..........................................................................8

6. 0 Constructional Details of Servo System .............................................. .........96. 1 Power Amplifiers ...................................................................... .........96. 2 Circuitry .............................................. ............................................ 10

6.21 Tach loop chassis ....................................................... ....... 106. 22 Tachometer and position loop circuits ...................... ....... 10

7. 0 Tests with Antenna ........................................................... ............................10

LIST OF FIGURES

1. Block Diagram of Servo System2. Simplified Servo Block Diagram3. Model Of One Axis of Drive System4. Simplified Model of One Axis5. Bode Plot of eLiem6. Bode Plot of em/Vin7. Block Diagram of Position Servo8. Bode Plot of Open Tachometer Loop9. Bode Plot of Closed Tachometer Loop

10. Bode Plot of Integrator and Compensation11. Bode Plot of Open Position Loop12. Bode Plot of Closed Position Loop13. Position Loop Response to a 16 Minute Step14. Block Diagram for Wind Torques15. eLoadiWind Torque for Closed Position Loop16. Tachometer Buffer17. Control Circuits18. Elevation Error Signal During Tracking

THE 45-FOOT ANTENNA DRIVE SYSTEM

John M. Payne

1. 0 Introduction

This report describes the servo system used to drive the 45-ft antenna. The posi-

tion readout system, the digital electronics, the stand alone computer, the control panel

and the telescope interface wiring were designed and built by other groups and will be de-

scribed in other reports.

2. 0 Performance Summar of the Drive S stem

2. 1 Pointing Accuracy.

The antenna has a beamwidth of approximately 10 arc minutes at the highest operating

frequency and an RMS pointing accuracy of better than a 1/10 beamwidth is required. The

servo system was designed to have an RMS pointing error of less than 10 arc seconds in

winds up to 30 MPH.

2. 2 Slew Speeds

The maximum slew rate of the antenna drive system is 50°/min, this slew speed is

obtainable in continuous 50 MPH winds. When given a new position command the antenna

automatically slews to the new position at 50°/min.

Restrictions may be imposed on these slew speeds according to preset conditions.

For example, when a position pre-limit is reached the antenna speed is automatically re-

duced to a low value (usually 5°/min) that may be previously selected by a rotary switch in

the control chassis. When the final position limit is reached the antenna stops and will

only respond to slew commands that will drive it out of the limit.

2. 3 Modes of 0 eration

The servo system accepts either position commands or velocity commands. These

commands may originate from the interferometer control building via the radio link or

at the telescope location. The telescope has a "stand alone" computer that generates

telescope position commands from entries in right ascension and declination. In the

manual mode the telescope slews at a velocity selected by a potentiometer on the tele-

scope control pa:nel. All functions on the control panel are interlocked to insure safe

operation of the anterma,

2

3. 0 De _

A block diagram showing control of one axis of the antenna is given in Figure 1.

The drive consists of four permanent magnet DC motors driving the bull gear of the an-

tenna, each motor having a 1425:1 reduction gearbox. A further gear reduction of 12. 63

between the output of each gearbox and the bull gear results in an overall gear reduction

of 18000:1. Each motor is provided with a tachometer that provides a rate signal propor-

tional to the speed of the motor shaft. The motors work in pairs, the behavior of each

pair being identical, so the analysis in this report is applied to one pair of motors, the

various constants being adjusted to allow for this. In normal operation (winds up to 30

MPH) one motor in a pair opposes the other so eliminating backlash in the gearboxes.

Load torque is obtained by an increase in current through one motor and a decrease through

the other. In winds over 35 MPH both motors produce torque in the same direction.

Each motor is driven by a transistor amplifier operating as a current driver. This

mode of operation results in the output torque of the motor being proportional to the input

voltage to the amplifier, effects due to the inductance of motor windings and the back emf

of the motors being effectively removed by the current feedback.

The tachometer associated with each motor is used in a velocity servo loop to con-

trol the angular velocity of the motor. The servo loops must be well matched for obvious

reasons. The common input to these four velocity loops is the velocity command to the

antenna and an input of ± 5. 0 volts gives ± 509/min.

An inductosyn mounted on the telescope axis, measures the position of the telescope

and, through associated electronics, outputs this position as a digital number. This posi-

tion is compared with the commanded position (it may be from the interferometer computer

or the local calculator) in the digital subtractor, the error being a 10 bit number that is

changed to an analog voltage in the D/A converter. The least significant bit is 5 arc

seconds and the subtractor cycles 20 times a second. The resulting analog error signal

is then integrated and after compensation is used as an input to the velocity servo loop to

drive the antenna to the commanded position.

4. 0 Torque Requirements

The torque on an antenna due to wind is strongly dependent on the angle of the wind

relative to the antenna. The torques in this report assume that the wind is always from

the worst possible direction, a very conservative approach. Empirical formulas derived

3

from wind tunnel tests (reports published by Andrews and JPL) were used to caluclate the

torques in various wind speeds. The motors supplied with the antenna have a torque con-

stant of 5. 2 x 10 -2 ft lbsiamp and, when forced air cooled, may be run continuously at 30

amps according to the manufacturer. The transistor amplifiers used current limit at 30

amps and when considering a pair of motors the figures given in the table relate the various

quantities.

Torques and Currents in Different Wind Speeds

WindSpeed(MPH)

Torque(ft lbs )

Current inMotor I(amps)

Current inMotor 2(amps)

0 0 -10 +10

25 25 x 103

-3. 3 +16. 7

30 36 x 103 -0. 4 +19. 6

35 49 x 103 +3. 0 +23. 0

40 64 x 103 +7. 0 +27. 0

45 81 x 103 +13. 2 +30. 0

50 100 x 103 +23. 3 +30. 0

53 112 x 103

+30. 0 +30. 0

At 53 MPH, a steady wind from exactly the worst direction will stop the antenna. This is

a very unlikely situation, particularly for both axes simultaneously.

5. 0 Servo Design

5.1 General Descri ton of Servo S stem

Servo systems are generally classified in different types according to the number

of integrating elements used in the system. An integrator, of course, gives an output that

is proportional to the integral of the input with respect to time (in our case). The inte-

grator may be electronic or it may be mechanical. A motor, for instance, may be re-

garded as an integrator, the angle turned through by the motor shaft being proportional to

both voltage input and time. When servo engineers talk about type "0", type "1", and

type "2" systems they are simply referring to the number of integrators in the system.

The higher the type number, the better the performance of the servo and, generally, the

harder it is to stabilize. The performance of a servo system is usually measured in

terms of its ability to respond to certain inputs and disturbances. A type "1" position

servo, for instance, has a theoretical zero error to steady state position commands, a

finite error to velocity commands (position commands changing linearly with time) and

an infinite error to accelerating position commands. A type "2" system has a theoretical

zero error to position commands, a zero error to velocity inputs and a finite error to

accelerating inputs. A type "2" system is the one usually used to control antennas as

wind gusts constitute an accelerating disturbance and a theoretical zero error when

trabking is nice to have. As with all engineering the real world modifies the theoretical

performance somewhat, the main culprit being non-linearities in the servo, by far the

most noticeable being stiction in the main telescope bearing.

Figure 2, a simplified block diagram of the servo should make the operation clear.

The tachometer signal is used in a velocity servo loop, the velocity command and the

actual velocity being subtracted and the resultant error used to drive the antenna drive

motor. The open loop gain of this servo loop dictates how well the antenna will follow the

commanded velocity signal. Obviously, when the wind blows, the motor will need a

bigger input which can only come from a larger error signal which in turn must come

from the integrated position signal. The design of the tach loop is a compromise between

having a high enough gain to keep velocity errors small, a bandwidth such that structural

resonances are not excited and adequate stability. Also, the gain of each loop should not

be so high that matching the individu:' loops is difficult. The over 1 function of the

velocity loop is that of an integrator; a ste dy input volt.lge results in an angular displace-

ment of the antenna that increases linearly with time.

Any system with two integr tors must have a tot phase shift of 180° and be un-

stable so compensation is essential. We now consider what h ppens when a tracking

command is fed in, that is, a position command that is changing with time. At the start

a position error signal will appear; this is integrated and the output of the integrator drives

the antenna until the antenna is moving at the commanded rate. The output of the inte-

grator is now fixed and unchanging and its input is zero (zero position error). Any change

in conditions (wind, bearing friction) will require different input to the velocity loop and

will result in a position error being generated while the new conditions are being met.

5

In practice, the error signal is quantized, the interval in our case being 5 arc secs, so

a completely zero position error is not a practical proposition.

5. 2 Mechanical Transfer Functions

The key part of any servo design is an investigation into how each constituent part

of the system responds to inputs of varying frequency. The amplitude and phase relation

of the output to the input is derived from the transfer function. By an examination of the

open loop frequency response the designer may make predictions of the closed loop fre-

quency response and stability of the system. A model of one axis of the telescope is

shown in Figure 3. If we assume that the structure is very stiff compared to the gearbox,

i. e. K >> K, 0 = 0 and K and J may be transferred to the other side ofg/ RF e Rthe gearbox. The simplified model given in Figure 4 may then be used for one pair of

motors with certain reservations. The inertia and viscous friction associated with the

gearbox are really distributed quantities but, nevertheless, Figure 4 is certainly a good

approximation to reality.

The torque developed by the motor is proportional to current. The amplifier is

a current driver so the torque is given by

T = K1 Vin

where K is measured in ft lbsivolt. Assume a torque bias of A ft lbs, so that when1 T1

increases, T2 decreases and vice versa. Then

T = A + K1 Vin1

T2

= A - K1 Vin

Equating torques, we have

2A + K i Vin (0 1 - OL) Kg = J

m S 0

1 + B

m S 0

1(1)

2( 0

1 -

L) K

g - (0

L - 0

2) K

g = J

L S L + B

L S L(2)

2(0 -0)K - A +KV. =J S +B SO (3)L 2 g m 2 m 2

6

where S is the operator .d t

From (1) we have

A+K V +0 Ki L g 0 = 2J S + B S + KIn In

and from (2)

-A+K V. +0 K0

2 in g2 J S

2 + 13 S + Km m

As we would expect, 0 1 = 02 when A = 0. (No bias torque. )

Substituting for 0 1 and 02 in (2) we have

2K K=

Vin

Jm JL

S + (Jm BL

+ Bm JL

) S3 + (JL Kg

+B m g

BL +2K J

m

also2K

J S

2 + B S + 2KO

m

and

Om K i

(JL S

2

+ BL

S + 2K )

S + (B K BL g m

V. J J S + (Jm BL m

+ B JL

) S + (J K + B B + 2K Jin m L g m L gm 52 + (BL Kg+ 2Kg Bm) S

The values of the various constants can now be evaluated. The stiffness of a single

drive train is quoted as 5. 26 x 10 7 ft lbs rad. The moment of inertia in azimuth is

2. 75 x 10 5 ft lbs sec2 . These figures give a locked rotor resonant frequency for the an-

tenna of 4. 5 Hz. The load inertia referred to on the motor side of the gearbox will be2. 75 x 105

= -4 ft lbs sec whi(1. 8 x 103), 8. 48 x 10 ch is shared between two sets of motors."5. 26 x 107Similarly, K referred to the motor shaft is = O. 16 ft ths /rad.(1. 8 x 104)2

7

We now have the following constants:

= 0. 18 ft lbs/volt (assumes a gain of 3. 5 lavolt in amplifier)

• 24 x 10 -4 ft lbs sec2

K = 0. 16 ft lbs/radg

Jm . 1 x 1O lbs sec2

BL = 1 x 10 -4 ft lbsiradisec

B = 4 x 10 -4 ft lbs/rad/secm

The values of BL and B result from figures supplied by ESSCO and estimates based

on the type of gearbox used.

These constants result in the following transfer functions:

OL 0.32O

m1. 8 x 1O4 4. 24 x 1O + 10 - S + 0. 32)

O. 18 4. 24 x 10 -4 S2 + 10 -4 S + 0. 32V

in4. 24 x 10

-4 S

4 + 1. 7 x 10 -7 S3 + 7. 1 x 10 -5 S2 + 1. 44 x 10

-4 S

where V11

the input to the final power amplifier.

These two functions are plotted out in Figures 5 and 6. We would expectL

to be

1 1. 8 x 104 of Om (-85 dB) at low frequencies, peak at the locked rotor frequency, with

an abrupt phase change and then decrease rapidly. Figure 5 shows this to be so.

Vin shows an integrator characteristic (gain falling off at 20 dB/decade and phase

shift of -900) at low frequencies with increased phase shift as the locked rotor frequency

is approached (Figure 6).

5.3 1_,....._12,122warjdoop,Design.

Figure 7 shows a block diagram of the complete servo system. The tachometer

closed loop transfer function is 52.3 rad/sec/volt at the motor shaft or 100

y/flan/volt at

and

Om

8

the telescope axis. The Itach. loop compensation reduces the gain at the higher frequencies

but still gives an adequate phase margin. The open loop frequency response (or Bode plot)

is shown in Figure 8, and the closed loop in Figure 9. The peak in the response at around

100 radians/sec results from a 'coupled circuit" type phenomena involving the motor in-

ertia and the gearbox stiffness. These plots show the output as Seout

rather than eout

for

clarity. The peak at 100 rads/sec depends very strongly on the construction of the gearbox

and is not to be taken too seriously. The bandwidth of the tachometer loop is 12 rads/sec.

5. 4 Poson ,

As previously mentioned, the two integrators in the loop would result in an un-

stable system without compensation. The compensating network should be designed to

give maximum phase advance at the unity gain frequency of the open loop frequency

response.

Figure 10 shows the Bode plot of the integrator and compensating networks and

Figure 11 shows the open position loop response. The phase margin is 400 which is quite

acceptable.

The closed position loop is shown in Figure 12 and the response to a step posi-

tion command of 16 arc minutes is shown in Figure 13. The closed position loop band-

width is 7 radians/sec.

5. 5 Performance in Wind

The antenna will be subject to wind torques of varying frequency and magnitude

that may result in position errors in the servo system.

As described in section 5. 1, the servo error to an unchanging wind torque will be

zero. It is only that component of wind changing with time that will give rise to servo

errors. The varying component of the wind is defined by the "gust factor" and is the ratio

of the RMS of the varying wind component to the fixed component. Various references

quote a gust factor of 0. 2. The wind itself has a spectrum that is flat up to about 1 rad/sec

(references quote figures that vary between 0. 3 rad/sec and 2 rad/sec) and thereafter falls

as the square of the frequency.

Strictly speaking, wind gusts are a random phenomena and should be treated on a

statistical basis. However, examining the response of the servo system to sinusoidal

9

torque disturbances will certainly give a good indication of the performance to be expected

in gusting winds.

Wind torques may be injected into the model of the servo system as shown in

Figure 14. This block diagram relates output angle to input torque and the Bode plot of0

LoadFigure 15 shows

for a range of frequencies. This plot is, in effect, the admit-Torquetance of the servo system or the inverse of the stiffness. As we would expect, the stiffness

-2 OLis very high at low frequencies. For instance, at 10 rads/sec, = -280 dB and the

stiffness is 10 14 ft lbs/rad. Over the range of frequencies, 1 rad/sec to 10 rads/sec the

stiffness is 3 x 10 9 ft lbs/rad.

In a 30 MPH wind the RIVIS of the varying torque will be 0. 2 x 36 x 10 3 = 7. 2 x 103

ft lbs. A sinusoidal torque of this value would result in an angular error of 2. 4 x 10-6

rads

(O. 5 arc sec RMS), over the frequency range mentioned. This figure neglects any filtering

effect due to the antenna and is small in comparison to wind induced structural pointing

errors.

6. 0 Constructional Details of Serv ystem

6. 1 Power Amplifiers

Each motor is driven by a transistor amplifier manufactured by Control Systems

Research, Inc. Two amplifiers and a power supply are packaged as a unit in a 7" chassis,

individual motor currents being displayed on the front panel. The servo system auto-

matically shuts down if an amplifier overheats or the supply voltages to an amplifier are

incorrect.

The basic specifications on the power amplifiers are as follows:

Gain .... . ... .0. ................. 3. 5 A/volt

Maximum continuous current .... ..... ± 35 amps

Maximum output voltage .... ..... .... ± 50 volts

Frequency response ....... ....... ... DC - 1 kHz

The amplifiers are provided with a thermal cut out and electronic current limiting.

10 -

6. 2 Circuitry

6. 21 Tach hop chassis

The output of each tachometer is fed into a buffer amplifier to reject any

pick up on the telescope cables. The output from each tach is displayed individually on

a front panel meter calibrated in degrees per minute. The circuit is shown in Figure 16.

Any one tachometer output may be selected by a rotary switch for display on the control

console. Trimming potentiometers are provided to equalize individual tachometer gains.

6. 22 Tachometer andm_sitionlos2p circuits

The control circuits are shown in Figure 17 and are fairly self explana-

tory.

7. 0 Tests with Antenna

Tests with the completed servo system were made to confirm the important

aspects of the design. The manual velocity mode was tested first, each motor being

run separately to check polarities °, then all four motors on each axis were run together.

The position loop was connected up and found to be stable. The closed position loop

bandwidth was checked by injecting a sinusoidal signal into the integrator summing junc-

tion and examining the system response. The bandwidth was measured at approximately

1. 3 Hz which compares well with theoretical value of 1. 15 Hz. The response to a step

function in position command was measured and, again, good agreement was found with

the theoretical results.

Figure 18 shows a plot of the error signal in the elevation loop during tracking

a source. The 1 a RMS value of the error is about 5. 5 arc secs.

So far we have used the antenna in winds gusting to about 30 MPH and have been

unable to see any significant wind induced errors.

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