Acceleration feedback control (AFC) enhanced by ... Observation and Compensation Control for...

Research in Astron. Astrophys. 2012 Vol. X No. XX, 000–000

http://www.raa-journal.org http://www.iop.org/journals/raaResearch inAstronomy andAstrophysics

Acceleration feedback control (AFC) enhanced by disturbance

observation and compensation (DOC) for high precision tracking

in telescope system ∗

Qiang Wang1,2, Hua-Xiang Cai1,2,3, Yong-Mei Huang1, Liang Ge4, Tao Tang1,2, Yan-RuiSu1,2,3, Xiang Liu1,2, Jin-Ying Li1,2, Dong He1,2, Sheng-Ping Du1,2 and Yu Ling1,2

1 Institute of Optics and Electronics, Chinese Academy of Sciences, P.O. Box 350, Chengdu 610209,

China; wangqiang [email protected] Key laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China3 University of Chinese Academy of Sciences, Beijing 100039, China4 Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of

Sciences, Beijing 100012, China

Received 2015 December 16; accepted 2016 April 14

Abstract In this paper, a cascade acceleration feedback control (AFC) enhanced by dis-

turbance observation and compensation (DOC) method is proposed to improve the track-

ing precision of telescope systems. Telescope systems usually suffer some uncertain dis-

turbances, such as wind load, nonlinear friction and other unknown disturbances. Then,

to ensure the tracking precision, the acceleration feedback loop which can increase the

stiffness of system is introduced. Besides, to make further improvement on the tracking

precision, we combine the DOC method which can estimate the accurate disturbance and

compensate it. Furthermore, the analysis of track accuracy of this method is proposed.

Finally, a few comparative experimental results show that the proposed control method

has excellent performance for reducing the tracking error of telescope system.

Key words: telescopes — instrumentation: control method – instrumentation miscella-

neous: high angular resolution – instrumentation: detector — control software

1 INTRODUCTION

Telescopes are playing more and more important role in many fields, such as ground-based space obser-

vation (Valyavin et al. 2014), optical communication (Sodnik et al. 2010; Khalighi & Uysal 2014) and

quantum communication (Gisin & Thew 2010). The tracking precision is the key indicator of telescope

systems. It determines the performance of telescope system. However, it is inevitable that the telescope

systems will suffer some unknown nonlinear disturbances that will severely reduce the tracking preci-

sion and the pointing precision. For example, wind load (Qiu et al. 2014), friction(Canudas et al. 1995),

and other disturbances (Su et al. 2015). Usually, because the volume of the telescope systems is rela-

tively large, the wind load is the major outer disturbance (Qiu et al. 2014). Especially when there is no

dome, or the dome of the telescope is opened, it is an important task to restrain the influence of wind

disturbance. Obviously, the classical control structure (position and speed double loop control) may not

∗ Supported by the quantum communication project,one of the Strategic Pilot Projects, Chinese Academy ofScience.

2 Qiang W. et al.

guaranteed enough tracking precision. At present, to reduce the influence of outer disturbances, there

are mainly these control methods could be chosen: robust control (Nicol et al. 2008), adaptive control

(Yao et al. 2014), active disturbance rejection control (ADRC) (Cai et al. 2015), disturbance observation

and compensation (DOC) (He & Ge 2015) and internal model control (IMC) (Canale et al. 2009).

In recent years, with the development of science and technology in electric devices, the accelerome-

ter has become an important sensor in control system. The cascade acceleration loop has also been used

in some high precision systems, such as the telescope system (Sedghi et al. 2008; Tang et al. 2007; Ge

et al. 2015), missile control system (Chwa 2014), robots (Koch et al. 2013;Xu et al. 2000). The acceler-

ation loop can enhance the stiffness of systems, meanwhile reject the disturbance. But the ability is still

not adequate(Sedghi et al. 2008; Tang et al. 2007).

In this paper, a new control method which combines the acceleration feedback control (AFC) with

disturbance observation and compensation (DOC) method is proposed, which takes use of the acceler-

ation feedback constituting the acceleration loop for increasing the stiffness of telescope systems, and

use the DOC for estimating and compensating the outer disturbance. As we known, the DOC needs an

approximate mathematical model of the system. The compensating precision depends on the accuracy

of approximate mathematical model. However, it can be known that the wind disturbance is relatively

a kind of low frequency disturbance (Emde et al. 2003). So it is easily to get the accurate low fre-

quency characteristic of system. To illustrate the excellent performance of the proposed control method,

three comparative experiments will be given in this article. The remainder of this paper is organized as

follows: Section 2 gets the dynamic models. Section 3 and 4 introduces the controller design and the

theory analysis. The experiment results are presented in Section 5. And some conclusion can be found

in Section 6.

2 DYNAMIC MODELS

In most of the telescope systems, the control structure usually is the double loop structure (DLS) which

includes the velocity loop and the position loop. The velocity loop is used to increase the ability for

inhibiting disturbances and enhance the stiffness of system. And the position loop is used to guarantee

the tracking accuracy. However, even though the velocity loop can increase the ability for inhibiting

disturbances, it can hardly eliminate the outer unknown disturbances in essence. Therefore, it will be

difficult to further enhance the precision of system.

This section mainly analyses the performance of three control methods: the double loop structure

(DLS) ,the cascade acceleration feedback control method (AFC) and the cascade acceleration feedback

control with disturbance observation and compensation (AFC-DOC).

The telescope system is usually a two-axes structure, including the azimuth axis and the elevation

axis as Fig1.

Disturbance Observation and Compensation Control for Telescope 3

Fig. 1: The gimbal structure and servo system of a telescope

The dynamics of the tracking system is described as equation (1):

dθ(t)dt

= ω(t); ω(t)dt

= a(t);Ja(t) = u−Bω(t)− f(t, ω);u = kti, J = Jm + Jl, Tm = u

(1)

In equation (1), Jm, Jl is the motor inertia and the load inertia, respectively. θ and ω represent

the load angle and angle velocity, respectively. Tm represents the torque applied at the motor. i is the

current to the motor. f(t, ω) represent all the uncertain disturbances, include inner disturbances and

outer disturbances. B is the viscous coefficient.

According to equation (1), the transfer function G(s) from the input u to the output acceleration ais as equation (2):

G(s) =a(s)

u(s)=

s

Js+B(2)

2.1 The double loop structure (DLS)

f

ueθ

− +

refθ

( )pC s ( )C sω

( )G s 1/sθ

1/seω

−

ω

Position loop

Velocity loop

( )H s

++ref

ϖ

Fig. 2: Classical double loop structure (DLS) scheme

The classical control structure of telescope is as Fig.2, the closed-loop velocity is given by equation

(3).

ω =CωG

1s

1 + CωG1s

ωref +H 1

s

1 + CωG1s

f (3)

4 Qiang W. et al.

In equation(3), ω is angular speed. G is object. Cω is speed controller. ωref is the given speed to

speed loop. H(S) is the transfer function from disturb torque to gimbal acceleration. In low frequency

domain, H(S) is just a gain.

Similarly, according to the control scheme, the encoder reading θ will be given by equation (4).

θ =CωG

1s2

1 + CωG1s

Cp(θref − θ) +H 1

s2

1 + CωG1s

f (4)

So

θ =CpCωG

1s2

1 + CωG1s+ CpCωG

1s2

θref +H 1

s2

1 + CωG1s+ CpCωG

1s2

f (5)

Let FPSD is the power spectral density (PSD) of the disturbance. From the above equations, it can

get that the PSD of the angular position θ is:

θPSD =

∣

∣

∣

∣

H · 1s2

1 + CωG · 1s+ CpCωG · 1

s2

∣

∣

∣

∣

2

FPSD (6)

From the equation, it can be known that the performance of control system depends on the velocity

loop controller and the position loop controller, especially the velocity loop controller. When designing

the appropriate controller, there will be a minimum θPSD, which means the least effect brought by the

disturbance f .

2.2 Acceleration feedback control (AFC)

The AFC method scheme is as Fig.3.

f

ue

! "

ref

( )pC s ( )C s

( )aC s ( )G s 1/s

1/se

!

!

"

a

Position loop

Velocity loop

Acceleration loop

( )H s

ref

!refa

Fig. 3: The AFC scheme

As Fig.3. The close loop angular position θ will be given:

θ =CpCωCaG · 1

s2

1 + CaG+ CωCaG · 1s+ CpCωCaG · 1

s2

θref +H · 1

s2


s2

f

(7)

Then:

θPSD =

∣

∣

∣

∣

H · 1s2


s2

∣

∣

∣

∣

2

FPSD (8)

As equation (8), the performance of AFC depends on the acceleration loop controller, the velocity

loop controller and the position loop controller, especially the acceleration loop controller. The

disturbance rejecting ability of AFC is stronger than that of DLS.

2.3 Acceleration feedback control with disturb observation and compensation control (AFC-DOC)


f

u−

eθ

− +

refθ

( )pC s ( )C sω

( )aC s ( )G s

( )G s%

1/sθ

1/seω

−

−

−

+

+

+

ω

a

( )fdC s

Position loop

Velocity loop

Acceleration loop

( )H s

+

Disturb observationand compensation

refϖ

refa

Fig. 4: The AFC-DOC scheme

From Fig.4, it is easy to get:

a = [(aref − a)Ca − Cfd(a− uG)]G+ fHa = uG+ fH

(9)

It can be known u = (a− fH)G−1, then substitute it into the equation:

a = [(aref − a)Ca − Cfd(a− aG−1G+ fHG−1G]G+ fH (10)

For G−1 = 1/G, it can be promised easily in low frequency. So

a = CaGaref − CaGa− CfdGa+ CfdGa− CfdGfH + fH (11)

a =CaG

1 + CaG + Cfd(G− G)aref +

(1− CfdG)H

1 + CaG + Cfd(G− G)f (12)

For aref = (ωref − ω)Cω . Then, the closed velocity ω will be given:

ω =CaG

1 + CaG + Cfd(G− G)(ωref − ω)Cω ·

1

s+

(1− CfdG)H

1 + CaG + Cfd(G− G)f ·

1

s(13)

ω =CωCaG

1 + CaG + Cfd(G− G) + CωCaG · 1s

ωref ·1

s+

(1− CfdG)H


f ·1

s

(14)

Simultaneously, for ωref = (θref − θ)Cp, the closed angular position θ will be given:

θ =CpCωCaG


(θref−θ)·1

s2+

(1− CfdG)H


f ·1

s2

(15)

θ =CpCωCaG

1+CaG+Cfd(G−G)+CωCaG·1

s+CpCωCaG·

1

s2

· 1s2θref

+(1−CfdG)H

1+CaG+Cfd(G−G)+CωCaG·1

s+CpCωCaG·

1

s2

· 1s2f

(16)

From the equation (16), the PSD of the angular position θ is:

θPSD =

∣

∣

∣

∣

∣

(1− CfdG)H · 1s2

1 + CaG + Cfd(G− G) + CωCaG · 1s+ CpCωCaG · 1

s2

∣

∣

∣

∣

∣

2

FPSD (17)

6 Qiang W. et al.

3 DESIGN CONTROLLER

The telescope system is a 1.2m telescope which is shown in Fig.5. This Telescope is used for

quantum laser communication between ground and satellite meanwhile it is also used for astronomical

observation. The sensors for gimbal control include grating ruler, velocity measuring gyroscope and

accelerometer.

Fig. 5: The 1.2m quantum communication and astronomical observation telescope system

The target of controller is to eliminate the outer disturbance as far as possible. Since the disturb

observation and compensation controller needs the approximate mathematical model of system, the

dynamic characteristic of object which between the input current and output acceleration should be got.

And it can be got by a spectral analyzer. The opened loop characteristic between the input current and

the output acceleration is showed in the Fig.6.


10-1

100

101

102

103

-50

0

50

100

Frequency(Hz)

Ma

gn

itu

de

(dB

)

Experiment result

Fitcurve result

10-1

100

101

102

103

-100

0

100

Frequency(Hz)

Phase(

)

Fig. 6: The open loop response from the input current to the output acceleration

As the Fig.6 shown, by the method of curve fitting, it can get the approximate mathematical model

of system. Because of the telescope system mainly suffer some low frequency disturbances(Emde et al.

2003), the high frequency part of system mathematical model can be neglected. Therefore, the system

model can be predigested by curve fit method as:

G ≈2.25

0.011s+ 1(18)

So we can get

G−1 ≈0.011s+ 1

2.25(19)

Combining the control scheme block and the above analysis, it can be known that a low pass filter

and a gain should be designed in the controller. So

Cfd =kas+ a

s+ a(20)

A classical PI controller can be chosen in the acceleration loop.

Ca = kap(aref (t)− a(t)) + kai

t∫

0

(aref (τ)− a(τ))dτ (21)

The kap , kai is the proportional gain and the integral gain of acceleration loop controller, respectively.

When the disturb observation and compensation controller and the acceleration loop controller are

completed. The current disturb rejecting ability is tested. Fig.7 shows the measured response from the

current disturbance to the track error (Impose the disturb to the internal current loop of drive power

amplifier). As it shown, when DLS method is adopted , the disturbance rejection ratio is about -5dB

at 0.6Hz. When AFC method is adopted, the disturbance rejection ration is -35 dB at 0.6Hz. When

AFC-DOC method is adopted, the disturbance rejection ratio is about -55 dB at 0.6Hz. This indicated

that the proposed AFC-DOC method will have the best disturbance rejecting ability.

The disturbance rejection ratio is a relative value which depend on the feedback gain to the dynamic

8 Qiang W. et al.

100

-70

-60

-50

-40

-30

-20

-10

Freq(Hz)

dB

disturb rejection ability compare

DLS method

AFC method

AFC-DOC method

Fig. 7: The comparative result of disturbance rejection ability

signal analyzer. In this experiment, the closed-loop bandwidth of speed loops of three control methods

is almost the same. About 12Hz exactly.

According to the above control scheme, in the velocity loop and the position loop, the classical PI

controller will be chosen.

aref = kωp (ωref (t)− ω(t)) + kωi

t∫

0

(ωref (τ)− ω(τ))dτ

ωref = kθp(θref (t)− θ(t)) + kθi

t∫

0

(θref (τ)− θ(τ))dτ

(22)

4 PERFORMANCE ANALYSIS

From the above equations, it can be get these conclusion:

(1) when the DLS is applied , the Power Spectral Density (PSD) of position will be:

θ1PSD

=

∣

∣

∣

∣

H · 1s2

1 + CωG · 1s+ CpCωG · 1

s2

∣

∣

∣

∣

2

FPSD (23)

(2) When the control structure is the AFC, the Power Spectral Density of position will be:

θ2PSD

=

∣

∣

∣

∣

H · 1s2

1 + CaG + CωCaG · 1s+ CpCωCaG · 1

s2

∣

∣

∣

∣

2

fPSD (24)

(3) When the control structure is the AFC-DOC, the Power Spectral Density of position will be:

θ3PSD =

∣

∣

∣

∣

∣

(1− CfdG)H · 1s2

1 + CaG + Cfd(G− G) + CωCaG · 1s+ CpCωCaG · 1

s2

∣

∣

∣

∣

∣

2

fPSD (25)


If design DOC controller as:

Cfd∼= 1/G (26)

Then

θ3PSD → 0 (27)

Without no doubt, there will be

θ3PSD

= min{θ1PSD

, θ2PSD

, θ3PSD

} (28)

In equation (28), it can be seen that the PSD of the position is the least when the AFC-DOC

method is applied, which means that the system will suffer the least influence from the outer disturbance.

5 EXPERIMENT SETUP AND RESULT

The verification experiments are applied in azimuth axis of the 1.2m telescope system. The main

hardware consist of a direct drive torque motor, a angular encoder with accuracy about 0.53 arc second

in RMS value, and a pair of linear accelerometer with resolution about 0.00005g. The speed information

was got from the difference of encoder rather than a tachometer.

To verify the disturbance rejection ability, a pull and push dynamometer is chosen to introduce

some disturbances. Meanwhile, the disturbance torque is measured by the dynamometer by which we

impose the torque on the gimbal. The disturbance torque is transferred to a recording computer via a

USB cable. In Fig.4, the input of Cfd(s) is the observed acceleration disturbance which is proportional

to torque disturbance in low frequency.

Fig. 8: The pull and push dynamometer Fig. 9: Impose some periodic disturb torques via

dynamometer

Fig.8 shows the pull and push dynamometer which is chosen. In Fig.9, some periodic pull and push

disturbances are imposed on the azimuth axis of telescope system via the dynamometer.The following

three experiments are compared:

(1) The DLS: without the acceleration loop, it only needs to design the velocity loop controller and the

position loop controller.

(2) The AFC: an acceleration loop controller is added in the system. The acceleration signal can be

gotten by the accelerometer.

10 Qiang W. et al.

(3) The AFC-DOC: as Fig.4 shows, the DOC controller is in the inner of acceleration loop.

The three control methods are tested at a fixed azimuth position. Then a periodic pull and

push torque disturbance is imposed on the azimuth axis, the magnitudes are about ±300(N · m).Simultaneously, the data of periodic disturbances was recorded by a computer. From Fig.10, Fig.12,

Fig.14, the periods and magnitudes of disturbances which are applied in the system can be seen. The

result is calibrated according to the torque imposed to the gimbal in DLS method experiment.

In Fig.11, it can be known that the system will have the bigger tracking error, when the DLS method

is used. The root mean square(RMS) of track error is 2.89′′ while the RMS of disturb is 131.8Nm,

which indicates that the DLS method has the lowest inhibition ability for the outer disturbance. In

Fig.12, the RMS of track error is about 0.51′′ while the RMS of disturbance is 144.5Nm, when AFC

method is applied in the system. Comparatively speaking, the AFC-DOC has the least disturbance error.

In Fig.15, The RMS of track error is only 0.23′′ while the RMS of disturb is 140.9Nm.

Simultaneously, in Fig.14, it can be seen that the applied disturbances torque can be estimated by

the DOC method. The dash line is the torque disturbance which is estimated by the DOC method. The

solid line is the disturbance torque applied to the system which is measured by the dynamometer. This

shows that the cascade AFC-DOC method can estimate the accurate disturbance and compensate it.

Therefore, the track error is the least. In equation (28), it also shows that the PSD of the track error is

the least.

0 5 10 15-400

-300

-200

-100

0

100

200

300

Without acceleleration loop

Disturb Torque. std: 131.829506 (N.m), mean peak: 237.930234(N.m)

Time(s)

Torq

ue

(N.m

)

measured disturb

DLSmethod

Fig. 10: The measured disturbance torque in DLS

method experiment

0 5 10 15-8

-6

-4

-2

0

2

4

6

8

Without acceleleration loop

Track Error. std: 2.892891(arcsecond),mean peak: 5.513418(arcsecond)

Time(s)

Err

or(

arc

second)

Track Error

DLSmethod

Fig. 11: The track error with DLS method


0 2 4 6 8 10 12 14-400

-300

-200

-100

0

100

200

300

Cascaded AFC


Time(s)

To

rqu

e(N

.m)

measured disturb

AFC method

Fig. 12: The measured disturbance torque in AFC

method experiment

0 2 4 6 8 10 12 14-1.5

-1

-0.5

0

0.5

1

1.5

Cascaded AFC


Time(s)

Err

or(

arc

second)

Track Error

AFC method

Fig. 13: The track error with AFC method

0 5 10 15-400

-300

-200

-100

0

100

200

300

Cascaded AFC-IMC


Time(s)

To

rqu

e(N

.m)

measured disturb

observed disturb

AFC DOC method

Fig. 14: The measured and estimated disturbance

torque in AFC-DOC method experiment

0 5 10 15-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Cascaded AFC-IMC


Time(s)

Err

or(

arc

se

co

nd

)

Track Error

AFC DOC method

Fig. 15: The track error with AFC-DOC method

In Fig.16 the track error of three control methods is compared.

12 Qiang W. et al.

2 4 6 8 10 12 14-8

-6

-4

-2

0

2

4

6

Time(s)

Tra

ck E

rror(

arc

second)

Comparative experiment result

Without acceleration loop

Cascade AFC

Cascade AFC-IMC

DLS method

AFC method

AFC DOC method

Fig. 16: Compare the experiment result of track error

In tab.1, the statistic data of track error and disturb torque of three experiments is listed. The track

error is calibrated to input disturb torque of the experiment with DLS method.

DLS AFC AFC-DOCC

RMS of disturb 131.8 Nm 144.5 Nm 140.9 Nmmean |peak| of disturb 237.9 Nm 245.3 Nm 251.1Nm

RMS of track error 2.89′′ 0.51′′ 0.23′′

mean |peak| of track error 5.51′′ 1.1′′ 0.54′′

RMS of track error calibrated to disturb 2.89′′ 0.47′′ 0.22′′

mean |peak| of track error calibrated to disturb 5.51′′ 1.07′′ 0.51′′

Notes: The “mean |peak|”is the mean value of the peaks’s absolute value; Calibrating is to the value of

“DLS”method.

Table 1: the experimental result of three controllers

6 DISCUSSION

Uncertain outer disturbances have been the major factor which restrict the performance of telescope’s

tracking control systems. This is because the systems’s tracking precision is decreased when suffering

some uncertain nonlinear disturbances. Therefore, to reduce the influence from the disturbances, a

AFC-DOC method is proposed in this paper. The acceleration loop can increase the stiffness of systems.

The DOC method can estimate the accurate disturbance and compensate it. The combination of the two

control methods increase the ability of system for inhibiting outer disturbances. Finally, the experiment

results show that the proposed control method has excellent performance for improving the track

precision of telescope system.

The DOC method is restricted by the simulation precision of gimbal’s dynamic mathematical

model, and the noise of accelerometer. From Fig.14, when the outer torque change direction, the error

between real torque and estimated torque is obvious. This is mainly because of the hysteresis lag of the

pull and push dynamometer especially when static friction take effect.


Acknowledgements This work was supported by the quantum communication project, one of the

Strategic Pilot Projects, Chinese Academy of Science. We acknowledge the use of the new made

DeLingHa (QingHai province) 1.2m telescope and NanSan (XinJiang province) 1.2m telescope and

XingLong (HeBei province) 1.0m telescope. The control method is applied to those telescopes espe-

cially the new made two telescopes. Special thanks to ZuoWei Lv(as Fig.9), XiaoMing Huang and

ZhiQiang Wang.

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