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Precise Position Control of a Gimbaled Camera System

Bülent Özkan1, Erdinç N. Yıldız2, and Burcu Dönmez3 TÜBİTAK-SAGE, Defence Industries Research and Development Institute, Ankara, Turkey, 06261

In the camera systems mounted on moving platforms such as the surveillance camera of unmanned air vehicles, it is a difficult task to track nonstationary targets. Especially for maneuvering ones, the optical field of view (FOV) of the present cameras is not wide enough to keep the target image within the boundary. Thus, the use of the gimbaled structures is one of the most common ways to enlarge the effective FOV of the cameras. In this sense, the orientation control of the camera supported by the gimbals comes into the picture as a significant issue. In order to make the camera follow the intended target accurately, its orientation should be correctly controlled by means of a convenient control system constructed upon the gimbaled configuration. Here, the most usual control algorithm is the conventional single-loop control system. On the other hand, the two-loop alternatives become more advantageous when the precision requirement from the control system is increased. In this study, the single- and two-loop position control systems are evaluated in the precision control of a gimbaled camera system and relevant computer simulations are carried out. Eventually, it is observed that the two-loop control systems especially regarding the robust control structure in the inner loop yield better results than their single-loop counterparts.

Nomenclature tiB = viscous friction coefficient

id = uncertainties defined in the robust control system (i=1, 2, and 3) E = error between the desired and actual gimbal positions

je = penalties defined in the robust control system (j=1 and 2)

sf = desired bandwidth of the speed control system ( )sGc = controller transfer function ( )sGv = transfer function of the speed control system

I = driver unit output current iJ = moment of inertia of the inner gimbal about the rotation axis

K = controller of the robust control system dK = derivative gain of the controller

iK = integral gain of the controller

pK = proportional gain of the controller

tK = motor torque coefficient

tiK = equivalent stiffness of the connection cables

vK = velocity gain of the controller

viK = driver unit gain T = plant control torque

mT = control torque applied by the torque motor

1 Chief Researcher, Mechatronics Division, bozkan@sage.tubitak.gov.tr, AIAA Member. 2 Chief Researcher, Mechatronics Division, eyildiz@sage.tubitak.gov.tr. 3 Senior Researcher, Mechatronics Division, bdonmez@sage.tubitak.gov.tr, AIAA Member.

AIAA Guidance, Navigation and Control Conference and Exhibit18 - 21 August 2008, Honolulu, Hawaii

AIAA 2008-6643

Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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sT = time constant of the extraneous root added to the control system u = output of the robust controller V = controller output voltage

actW = weighting of the actuator output

cmdW = weighting of the command signal

distW = weighting of the gimbal control torque

idealW = closed-loop transfer function of the ideal control system

perfW = weighting for the deviation from the ideal system

snoiseW = weighting of the gyro signal y = input of the robust controller

cω = desired bandwidth of the position control system

nω = natural frequency of the ideal control system

sθ = angular position variable of the inner gimbal

sdθ = desired angular position of the inner gimbal ζ = damping ratio of the ideal control system

I. Introduction N the recent years, the gimbaled camera structures have become more popular in tracking moving and even maneuvering targets by means of certain flying platforms such as unmanned flying vehicles in order to enhance

the field of the regard, i.e. the effective field of view (FOV), of the camera and hence to increase the probability of target detection within the relatively short engagement period1. In this sense, one of the necessary conditions of making the platform chase the mentioned target accurately is the precise control of the gimbals of these cardanic structures. The selection of the control method to be employed is a critical issue particularly at the point of the minimization of the errors caused by the disturbances and noises2. The inaccurate control of the gimbals may result in blur on the images taken by the camera and this causes the air vehicle to miss the planned target3.

The conventional gimbal control systems are single-loop algorithms based on the position or speed control. Although not so common as single-loop ones, two-loop control systems have also been designed in order to increase the positioning accuracy4. Due to the varying stiffness of the connection cables of the camera, noise on the sensors, and base vibrations acting on the gimbaled structure, the precise control of the gimbals may not be achieved at a desired level3. For this reason, the two-loop control systems happen to be an alternative to the frequently used conventional control systems. In the mentioned algorithm, the outer loop makes the position control of the considered gimbal to compensate the steady-state position error while the inner loop tries to nullify the angular speed of the gimbal within the presumed settling time. Actually, the accuracy of this structure is better than the accuracy of the single-loop ones as presented in the forthcoming sections2.

In this study, the precise control of a certain gimbaled camera structure is dealt with. In this extent, single- and two-loop control algorithms are constructed considering classical and robust control methods and the relevant computer simulations are performed. In the single-loop control systems, the classical PID (proportional plus integral plus derivative) and PIV (proportional plus integral plus velocity) control actions are taken into account whereas the PIV rule and robust control with respect to the H∞ norm are utilized for the speed control system in the inner loop along with the outer position control loop regarding PI (proportional plus integral) action in the two-loop counterparts. Finally, the collected results are compared for both of the proposed algorithms.

II. Gimbal Model The cardanic structures utilized to enhance the effective field of regard of the cameras usually comprise two

gimbals whose axes of rotation are perpendicular to each other. On the other hand, their dynamic behaviors are similar to each other with different values of the moment of inertia, friction coefficient, and equivalent stiffness parameters. Therefore, it will be sufficient to deal with the dynamics of the either gimbal in order to design a convenient control system for the entire cardanic system.

In this study, the inner gimbal of a cardanic structure shown in Fig. 1 is taken into account. As seen, the system consists of the outer and inner gimbals along with the associated torque motors and resolvers of the gimbals and a

I

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gyro to measure the angular velocity of the inner gimbal covering the camera. The outer gimbal rotates inside a frame which also connects the structure to the air vehicle.

From here, the dynamics of the inner gimbal can be described in terms of the relevant angular position variable ( sθ ) in the following manner:

mstistisi TKBJ =++ θθθ &&& (1)

where iJ , tiB , tiK , and mT stand for the moment of inertia of the inner gimbal about its rotation axis, viscous friction coefficient, equivalent stiffness of the connection cables, and control torque applied by the torque motor, respectively.

III. Single-Loop Gimbal Control Systems As mentioned above, the single-loop control systems are designed such that they control the angular position of

the gimbal within one loop by means of direct-drive torque motors. The general structure of the considered single-loop control systems are given in Fig. 2. In this figure, sdθ , E, V, I, and T denote the desired value of the angular position variable of the inner gimbal, error between the desired and actual gimbal position, controller output voltage,

driver unit output current, and plant control torque, respectively. Also, the symbols ( )sGc ,

viK , and tK represent the controller transfer function, driver unit gain, and motor torque coefficient, respectively.

The classical PID and PIV rules are considered in the following sections5.

A. Single-Loop Gimbal Control System with the PID Type Controller In the PID type controller which is the most preferably used controller in the industry because of its simplicity

and ease of implementation, the control signal to be sent to the plant, or the system to be controlled, is generated by multiplying the error between the desired and actual values of the control variable, sum of the error within a certain interval, and error rate with the proportional (P), integral (I), and derivative (D) gains, respectively. Here, the mentioned gains are chosen in accordance with the desired behavior of the control system. In this scheme, the integral action tries to nullify the steady-state error on the control variable which results from the parameter uncertainties, disturbances, and noise effects while the derivative action handles the trends in the transient error6.

Figure 1. Gimbaled camera structure.

( )sGc

+

-

sdθPlant

sθviK tK

E V I T

Figure 2. Single-loop control system structure.

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Usually, the PID type controllers are utilized together with an “anti-windup structure” to prevent the accumulation of the error in time due to the summation effect of the integration5. The block diagram of the gimbal control system with the PID controller is given in Fig. 3.

According to the PID law, the controller transfer function can be written as follows:

( ) sKs

KKsG d

ipc ++= (2)

where pK , iK , and dK denote the proportional, integral, and derivative gains in the given order.

The closed-loop transfer function from sdθ to sθ is obtained from the block diagram in Fig. 3 as given below:

( )( ) 1sdsdsd

1snsnss

12

23

3

12

2

sd

s

+++

++=

θθ

(3)

where ip1 KKn /= , id2 KKn /= , ( ) ( )ipitviti1 KKKKKKd // += , ( ) ( )iditviti2 KKKKKBd // += , and

( )itvii3 KKKJd /= . After getting the transfer function of the closed-loop control system as in Eq. (3), the roots of the relevant

characteristic polynomial, i.e. the poles of the control system, can be placed according to the specified performance requirements and thus the corresponding controller gains can be determined. One of the methods available for pole placement is to locate the poles by means of certain polynomials such as Butterworth and Chebyshev polynomials. This way, it becomes possible to decide on the poles such that the control system attains the desired bandwidth7,8,9. Here, the Butterworth polynomials leading to mimimum overshoot values in the system response are considered and the following third-order Butterworth polynomial can be used to equate the characteristic polynomial, i.e. the denominator polynomial, of the transfer function in Eq. (3)10:

( ) 1s2s2ssBc

2c

2

3c

3

3 +++=ωωω

(4)

where cω shows the desired bandwidth value of the control system in rad/s. Matching the mentioned characteristic polynomial in Eq. (3) to Eq. (4) and making the intermediate calculations,

the following expressions are obtained for pK , iK , and dK :

I

iJ1

s1

s1

tiB

mT sθ&& sθ& sθ+

-tKviK

tiK

-

( )sGc

+

-

sdθ VE

Figure 3. Single-loop control system with the PID controller.

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( ) ( )tviti2cip KKKJ2K /−= ω (5)

( )tvi3cii KKJK /ω= (6)

( ) ( )tviticid KKBJ2K /−= ω (7)

B. Single-Loop Gimbal Control System with the PIV Type Controller PIV type controller which is often implemented in the control of electric motors is another kind of the classical

controllers formed by modifying the PID structure. In the PIV controller, the position feedback is combined with the velocity feedback11. Unlike the PID controller, the position error (E) is turned into the velocity command by multiplying it with the position gain ( pK ) and the integral gain ( iK ) operates on the velocity error rather than the

position error in this algorithm. Moreover, the velocity gain ( vK ) is introduced instead of the derivative gain in the PID law ( dK )12,13. Here, the necessary velocity information is provided either by means of a speed sensor or using an estimator. In this work, the velocity measurements are assumed to be taken by means of a gyro.

The transfer function of the closed-loop control system with the PIV controller can be obtained from the block

diagram in Fig. 4 as follows:

( )( ) 1sdsdsd

1ss

12

23

3sd

s

+++=

θθ

(8)

where for pitvi KKKKK =δ , ( ) δKKKKKd itviti1 /+= , ( ) δKKKKBd vtviti2 /+= , and δKJd i3 /= . Equating the characteristic polynomial of the transfer function in Eq. (8) to the third-order Butterwoth

polynomial in Eq. (4), the related controller gains can be determined in the following manner as ( )2citi JK ωσ /= :

( )σω −= 2K cp / (9)

( ) ( )tviti2cii KKKJ2K /−= ω (10)

( ) ( )tviticiv KKBJ2K /−= ω (11)

Here, it should be noted that the iK expression in Eq. (10) is the same as the pK expression found for the PID

controller as in Eq. (5). Similarly, the vK and dK terms happen to be equal for both type of the controllers.

I

iJ1

s1

tiB

mT sθ&& sθ&+

-tKviK

tiK

-

pK+

-

sdθ

sKi

sKi

vK

Estimator

+

-

+

-

sθ̂&

sθVE

s1

Figure 4. Single-loop control system with the PIV controller.

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IV. Two-Loop Gimbal Control Systems The two-loop control system structure whose

schematic representation is shown in Fig. 5 consists of two control systems one of which operates inside the other. In this algorithm, the outer control loop attempts the inner gimbal to bring to the desired position while the inner loop which is at least four times faster than the outer one in order not to affect its dynamics is designated to make the angular speed of the gimbal zero. Here, “s” representing the Laplace variable, the outer loop controller symbolized with ( )sGc is constructed according to the classical PI control law whereas the PIV and robust controllers according to the ∞H norm are employed in the inner loop, or speed control system, shown by ( )sGv in order to minimize the diverting effects of the disturbing inputs.

Thus, as pK and iK stand for the proportional and integral gains, the position controller of the outer loop can be modeled in the following fashion:

( ) sKKsG ipc /+= (12)

From here, the closed-loop transfer function of the outer loop is obtained where 0K indicates the steady-state gain of the inner loop in the following fashion:

( )( ) 1sdsd

1sns

s

12

2

1

d ++

+=

θθ (13)

where ip11 KKdn /== and ( )i02 KK1d /= . Also, the second-order Butterworth polynomial can be formulated as follows:

( ) 1s2ssBc

2c

2

2 ++=ωω

(14)

Hence, equating the characteristic polynomial of the transfer function in Eq. (13) to the polynomial in Eq. (14), the expressions for pK and iK are obtained as given below10:

0cp K2K /ω= (15)

02ci KK /ω= (16)

A. Two-Loop Gimbal Control System with the PIV Type Speed Controller The block diagram of the speed control system shown by ( )sGv in Fig. 5 can be built with respect to the PIV

control law as given in Fig. 6. In this scheme, it is assumed that the necessary angular acceleration information is obtained by taking the time derivative of the angular velocity measurement. In fact, this is not applicable in real-time implementation due to the noise effects on the acquired data. Hence, the use of a conveniently designed estimator is more suitable in such cases11.

From Fig. 6, the transfer function of the closed-loop speed control system is obtained as follows:

1sdsd

n

12

2

0

sd

s

++=

θθ&

& (17)

( )sGc

+

-

sdθ( )sGv

sdθ&

s1sθ& sθE

Figure 5. Two-loop control system structure.

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where, as ( )iptviti0 KKKKK /=µ , ( )11n 00 += µ/ , ( ) ( )iptvitiitviti1 KKKKKKKKBd ++= / , and

( ) ( )iptvitivtvii2 KKKKKKKKJd ++= / .

As seen, the characteristic polynomial of the transfer function given in Eq. (17) possesses two roots. In the case

of finding the controller gains using a second-order Butterworth polynomial, two equations will arise for three parameters. Here, the required parameters, i.e. controller gains, can be calculated by means of certain formulas or some amprical approaches6,14,15,16,17. On the other hand, the sufficient number of equations to solve the parameters can be established by increasing the order of the control system with some small changes. Namely, as sT1 /− is an extraneous root sufficiently small compared to the original roots of the control system, the parameter vK can be modified as ( )1sTK sv +/ . Using this low-pass filter with the corner frequency at sT1 / , the frequency range within which vK is effective is also restricted and hence the effects of the high-frequency noise on the derivative action can be minimized5. Making this modification, Eq. (17) takes the following form:

1sdsdsd

nsn

12

23

3

01

sd

s

++++

=θθ&

& (18)

where, for ( )iptviti0 KKKKK /=µ and iptviti0 KKKKK +=γ , ( )11n 00 += µ/ , ( )1Tn 0s1 += µ/ ,

( ) 00sitviti1 TKKKBd γγ /++= , ( )[ ] 0isvtvitisi2 KTKKKBTJd γ/+++= , and 0si3 TJd γ/= . As can be noticed, the control system with the modified PIV controller has a zero at sT1z /−= whereas the

system with the original PIV does not have a zero dynamics. Conversely, putting sT1 /− at least 100 times far away from the system root at the farthest location with respect to the origin such that it does not affect the overall system dynamics, the existence of this zero will not cause any undesired result.

Eventually, equating the characteristic polynomial of the transfer function given in Eq. (18) to the third-order Butterworth polynomial in Eq. (4), as sf denotes the desired bandwidth of the control system (in Hz) and

( )2ssiti TJK ωκ /= with ss f2πω = , pK , iK , and vK are determined as given below:

( ) ( )sssp T2K ωκω −−= / (19)

( ) tviss2ssii KKT2TJK /ωω −= (20)

( )( )[ ] tvitisss2s

2sssiv KKBT1TT1TJK /−−−−= ωωω (21)

I

iJ1

s1

tiB

mT sθ&& sθ&+

-tKviK

tiK

-

pK+

-

sdθ&

sKi

sKi

vK

Estimator

+

-

+

-

s1

sθ̂&&

sθ

VE

Figure 6. Speed control system with the PIV controller.

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B. Two-Loop Gimbal Control System with the Robust Speed Controller Although the classical control laws are often used in the position control of the electromechanical systems, the

parameter uncertainties ignored in the modeling and disturbing inputs acting on the system under consideration cause these methods not to perform the control accurately. In this sense, the robust control methods come into the picture as one of the remedies6.

The robust controller design philosophy is based on the minimization of the effects of the factors such as noise, external load, and uncertainty on the output errors. In this optimization process, the norms of the output error vectors are used. The resulting controller is then called an ∞H controller when the infinity norm is used while the 2-norm leads an 2H controller. In designing the controller, each factor should be normalized in accordance with the decided weightings. If the effective frequency ranges are known, the frequency-dependent weighting functions will yield more satisfactory results. For instance, if the accuracy need is higher at lower frequencies, a low-pass filter can be used as weighting. Thus, it becomes possible to prevent the performance degradation of the controller.

In this study, a robust controller is designed according to the block diagram sketched in Fig. 7 using the ∞H control toolbox of MATLAB© software. The inputs and outputs of the controller are also given in Fig. 8. Here, the aim is to attain a controller which weighs down the effects of the noises on the command signal and gyro, and uncertainty on the input torque ( 1d , 2d , and 3d ) on the inner gimbal. In other words, the controller (K) is designed to minimize 1e and 2e which denote the penalties of the control signal and deviation from the ideal system. Here, y and u denote the input and output of the controller.

In Fig. 7, cmdW , distW , snoiseW , actW , and perfW stand for the weightings

of the command signal (input signal), gimbal control torque, gyro, torque motor, and deviation from the ideal system, respectively. idealW is used for the closed-loop transfer function of the ideal control system. The plant (inner gimbal) is indicated by the abbreviation “sys”. Here, cmdW and distW are designated as low pass filters with suitable magnitude and frequency values. Also, snoiseW is assumed to be a constant weighting and actW is defined as shown in Fig. 9.

KcmdW

snoiseW

actW

perfW

sys

idealW

distW

+ +

-

++

+

1d

2d

1d

y

2e

1e 3d

Figure 7. Speed control system with the robust controller.

sys

K

1d

2d

3du

1e

2e

1dy

Figure 8. Robust control

system model.

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The ideal system desired to be reached with the designed robust control system is described by the following

transfer function:

2nn

2

2n

ideals2s

wωωζ

ω++

= (22)

where nω and ζ represent the natural frequency and damping ratio specified for the ideal control system, and it is taken that nω =2⋅π⋅60 rad/s (=60 Hz) and ζ =1 (critical damping). From here, allowing the deviation of the designed control system from the ideal system to be 1 °/s, perfW is formed as a low pass filter whose corner frequency is at 60 Hz.

V. Computer Simulations In order to evaluate the performances of the proposed control systems, the relevant computer simulations are

conducted in the MATLAB© Simulink© environment. The numerical values of the parameters are given in Table 1. The simulation models include the variations in the stiffness of the connection cables and noise levels on the sensors. Moreover, the admissible steady-state error of the angular position of the gimbal is taken to be 1 mrad and the maximum angular shifting is considered as 163 µrad such that no blur exists for the selected case study. Also, the constructed control system models are converted into their discretized forms using the Tustin method18.

Mag

nitu

de, d

B

-20

-10

0

10

20

30

100

101

102

103

104

0

45

90

135

180

225

Phas

e, °

Frequency, Hz Figure 9. Selection of the actW weighting.

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A. Computer Simulations of the Single-Loop Control Systems In this part of the study, the single-loop control systems operating based on the PID and PIV control actions are

simulated with the bandwidth ( cf ) and sampling frequency values presented in Table 1. The angular motion coming from the base is also added to the models with zero mean and the standard deviation of 0.0057 N⋅m. Furthermore, the current command applied to the torque motor is limited at ±10 A and the resolver output is discretized regarding the noise at certain amount. The Bode diagrams (magnitude and phase) of both types of the control systems are shown in Fig. 10 and Fig. 11.

Mag

nitu

de, d

B

-40

-30

-20

-10

0

10

101

102

103

104

-90

-45

0

45

Phas

e, °

Frequency, rad/s Figure 10. Bode diagram of the single-loop control system with the PID controller.

Table 1. Numerical values used in the simulations.

Parameter Numerical Value tiB (N⋅m⋅s/rad) 4.270×10-2

cf (Hz) 15

sf (Hz) 60

iJ (kg⋅m2) 3.493×10-3

viK (A/V) 1

tK (N⋅m/A) 0.159

tiK (N⋅m/rad) 1.189

aT (s) 1/4000

sT (s) 1/400

vT (s) 1/4000 Simulation Sampling Frequency (Hz) 4000 Resolver Resolution (bit) 16

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The unit step responses of the single-loop control systems are given in Fig. 12 and Fig. 13 in addition to the

current requirement of the control system with the PID controller in Fig. 14. Moreover, the maximum current requirement, maximum overshoot (as percentage), settling time (according to the 5% criterion), steady-state error, and amount of the maximum oscillation values are tabulated in Table 2.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

0.5

1

1.5

Ti ( )

CommandActual

Ang

le, °

Time, s Figure 12. Unit step response of the single-loop control system with the PID controller.

Mag

nitu

de, d

B

-80

-60

-40

-20

0

101

102

103

-270

-180

-90

0

Phas

e, °

Frequency, rad/s Figure 11. Bode diagram of the single-loop control system with the PIV controller.

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0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-50

0

50

100

150

200

Cur

rent

, A

Time, s Figure 14. Current requirement of the single-loop control system with the PID controller.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

0.2

0.4

0.6

0.8

1

CommandActual

Ang

le, °

Time, s Figure 13. Unit step response of the single-loop control system with the PIV controller.

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B. Computer Simulations of the Two-Loop Control Systems Similar to the single-part control systems, the computer simulations are carried out for the two-loop control

systems using the data in the preceding section. Here, the angular velocity of the inner gimbal is calculated from the difference between the measurements of the gyro on the inner gimbal and the data coming from the inertial measurement unit. In the simulations, the speed data are restricted within the range of ±200 °/s and the noise on the speed measurement is also taken into account.

Mag

nitu

de, d

B

-40

-30

-20

-10

0

10

101

102

103

104

-90

-45

0

Phas

e, °

Frequency, rad/s Figure 15. Bode diagram of the angular position control system of the two-loop control systems with the PI controller.

Table 2. Simulation results of the single-loop control systems.

Controller Type

Maximum Current

Requirement (A)

Maximum Overshoot

(%)

Settling Time (ms)

Steady-State Error (mrad)

Maximum Amplitude of Oscillations

(µrad) PID 9.862 39.8 68.75 0 104.720 PIV 10.030 7.0 94.50 0 104.720

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Mag

nitu

de, d

B

-400

-300

-200

-100

0

100

10-2

100

102

104

-90

-45

0

45

90

ContinuousDiscretized (Sampling Frequency: 4 kHz)

Phas

e, °

Frequency, rad/s Figure 17. Bode diagram of the speed control system of the two-loop control system with the robust controller.

Mag

nitu

de, d

B

-60

-40

-20

0

20

101

102

103

104

-180

-135

-90

-45

0

Phas

e, °

Frequency, rad/s Figure 16. Bode diagram of the speed control system of the two-loop control system with the PIV controller.

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The Bode diagrams of the common outer loop, i.e. angular position control system, and the speed control systems with the PIV and robust controllers are given in Fig. 15, Fig. 16, and Fig. 17. Apart from these, the unit step responses of the two-loop control systems are presented in Fig. 18 and Fig. 19. The current requirement of the control system with the robust controller occurs as shown in Fig. 20. The maximum current requirement, maximum overshoot (as percentage), settling time (according to the 5% criterion), steady-state error, and amount of the maximum oscillation values are tabulated as presented in Table 3. Also, the responses of the speed control systems in the inner loop are shown in Fig. 21 and Fig. 22.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

0.2

0.4

0.6

0.8

1

1.2

1.4

CommandActual

Ang

le, °

Time, s Figure 19. Unit step response of the two-loop control system with the robust speed controller.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

CommandActual

Ang

le, °

Time, s Figure 18. Unit step response of the two-loop control system with the PIV type speed controller.

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0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-100

-50

0

50

100

150

200

CommandActual

Ang

ular

Vel

ocity

, °/s

Time, s Figure 21. Response of the speed control system with the PIV controller.

Table 3. Simulation results of the two-loop control systems.

Controller Type

Maximum Current

Requirement (A)

Maximum Overshoot

(%)

Settling Time (ms)

Steady-State Error (mrad)

Maximum Amplitude of Oscillations

(µrad) PIV 12.850 53.1 57.50 0 80.285

Robust 2.386 32.1 77.00 0 50.615

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0.5

1

1.5

2

2.5

Cur

rent

, A

Time, s Figure 20. Current requirement of the robust control system.

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VI. Conclusion In this study, the proposed single- and two-part control systems are compared for the precise control of the

gimbals of a cardanic structure used to support and enhance the FOV of a camera used in the certain air platforms to detect and track specified targets.

Referring to the Bode diagrams of the single-loop control systems, it can be observed that the PIV controller leads to a flat magnitude graph whereas the PID type controller causes a hump in the vicinity of the corner frequency. This is because the closed-loop transfer function of the former control system does not have a zero dynamics unlike the latter one. On the other hand, the phase behavior of the control system with the PID controller is much better than the other. As the phase angle between the input and output of the control system is initially zero and about 45° at the 3 dB decay of the magnitude in the system with the PID controller, the phase behavior caused by the PIV controller is different from zero even at the beginning and greater than 90° at the 3 dB decay. When graphs and collected data demonstrating the unit step response characteristics of the single-loop control systems are examined, the PID type controller seems to be more advantageous than the PIV controller in terms of the current expenditure and settling time. However, the maximum overshoot value of the control system with the PIV controller is smaller as expected from its Bode diagram. The maximum amplitude of the oscillations at steady-state seems to be the same for both type of the control systems and this value is below the allowable maximum value for the inexistence of blur.

In the two-loop control systems, the unit step response of the control system with the robust speed controller is more satisfactory than the system with the PIV type speed controller. In fact, the outer loops of both types of the control system are designed according to the PI control law. Yet, since the robust controller is capable of compensating the negative effects of the sensor noises at a higher level than the PIV type speed controller, its performance becomes superior. Namely, the current consumption, maximum overshoot, and maximum oscillation amplitude of the robust control system are quite low compared to the PIV type speed control system whereas the latter one settles down to the steady-state condition sooner. Beyond this difference, both types of the speed controllers are able to nullify the angular velocity of the gimbal. In a global evaluation, it is obvious that the two-loop control systems have better performance characteristics than their single-loop counterparts.

Eventually, it can be seen that the two-loop control system with the robust speed controller gives the best solution for the precise control of the considered gimbal among the control systems analyzed. Improving the electrical grounding of the sensors, more satisfactory results can be attained. On the other hand, an extra sensor, i.e. a gyro, would be required in order to close the inner stabilization loop of the entire control system with higher accuracy. In the final evaluation, the mounting and cost issues should also be taken into account.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-40

-20

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60

80

100

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CommandActual

Ang

ular

Vel

ocity

, °/s

Time, s Figure 22. Response of the speed control system with the robust controller.

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Acknowledgments The authors of this paper thank the Scientific and Technological Research Council of Turkey, Defence Industries Research and Development Institute (TÜBİTAK-SAGE) for the financial support to attend the Guidance, Navigation, and Control Conference organized by AIAA.

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