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Research Journal of Applied Sciences, Engineering and Technology 4(19): 3843-3851, 2012

ISSN: 2040-7467

Maxwell Scientific Organization, 2012

Submitted: May 08, 2012 Accepted: May 29, 2012 Published: October 01, 2012

Corresponding Author: Leghmizi Said, College of Automation, Harbin Engineering University, Harbin, Heilongjiang

150001, China

3843

Modeling, Design and Control of a Ship Carried 3 DOF Stabilized Platform

Leghmizi Said, Liu Sheng, Naeim Farouk and Boumediene LatifaCollege of Automation, Harbin Engineering University, Harbin, Heilongjiang 150001, China

Abstract: The system for stabilizing platform of a ship carried antenna a nd its core component arediscussed in this study. Relevant mathematics model of these components are established. Thus, thedynamic model of the system is deduced including the effects of friction, inertia and torque motors. UsingSolid Works, we built the mechanical structure, including the servo machine of each part of the system.The system under consideration is a system with strong interactions between three channels. By using theconcept of decentralized control, a control structure is developed that is composed of three control loops,each of which is associated with a single-variable controller. First, PID controller was applied; then,Takagi-Sugeno (TS) fuzzy controller was used for controlling the platform. Simulation tests wereestablished using Simulink of Matlab. The obtained results have demonstrated the feasibility andeffectiveness of the proposed fuzzy approach comparing to the PID controller. Simulation results are

represented in this study.

Keywords: Decentralized control, dynamic model, fuzzy controller, PID contoller, simulink, solidworks,Takagi-Sugeno (TS)

INTRODUCTION

The stabilized platform is the object which canisolate motion of the vehicle and can measure thechange of platforms motion and position incessantly. Itcan make the equipment which is fixed on the platformaim at and track object fastly and exactly. In thestabilized platform systems, the basic requirements areto maintain stable operation even when there arechanges in the system dynamics and to have very gooddisturbance rejection capability.

Since they began to be utilized about 100 yearsago, stabilized platforms have been used on every typeof moving vehicle, from satellites to submarines and areeven used on some handheld and ground-mounteddevices (Hilkert, 2008; Debruin, 2008). Its applicationis quite abroad and it becomes investigative hotspot inmost countries all the time.

The considered platform is a class of multivariableservomechanisms with multiple axes. The control ofsuch multivariable servomechanisms is, in general, nota simple problem, as there exist cross-couplings, orinteractions, between the different channels. Inaddition, this system is required to maintain stableoperation even when there are changes in the systemdynamics. In the stabilized platform systems, the basicrequirement is to have very good disturbance rejectioncapability. Presence of inherent nonlinearities such asstriction, friction, saturation of actuators, etc., also must

be taken into account.Many approaches have been proposed to control

such a complex interconnected system for example the

decomposition-coordination approach, the aggregation

approach, the multitime-scale approach and the

decentralized control approach (Linkens and Nyongesa,1998; Lee et al., 1995) Since the decentralized control

approach is reliable and practical in view of the

implementation, it is the most popular method that

attempts to design control schemes, where eachsubsystem is controlled independently based on local

information. However, the decentralized approaches arerestricted to stabilization and the dynamics of eachsubsystem and the interconnection terms are assumed to

be known (Nie, 1997; Shi and Singh, 1992). In practice,

the model of the considered platform contains vast

unknown uncertainties. Since fuzzy logic control hasbeen considered as an alternative to traditional control

schemes to deal with system dynamics uncertainty and

obtain the best performance of the system. Fuzzy

control is adopted as the subject of this study (Yeh,1999).

The objective of this study is to develop thedynamics model and the 3D design of the ship carriedstabilized platform. Then, apply the PID and Fuzzy

controllers for stabilizing the platform. By using thedecentralized control concept, we developed a controlstructure composed of three separate control channels,each of which is associated with a single variablecontroller. The simulation results in applying the two

proposed controller to a 3-DOF stabilization system arepresented which demonstrates the effectiveness of theproposed fuzzy controller comparing to the PIDcontroller.

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Res. J. Appl. Sci. Eng. Technol., 4(19): 3843-3851, 2012

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(Pitch)

(Roll)

(Yaw)

Fig. 1: The 3-DOF platform structure

SYSTEM DYNAMICS

System description: The considered system in this

study is composed of the platform, inner gimbal, outergimbal and the case (Fig. 1); each member is assumed

to be rigid and has one degree of freedom (Leghmizi

and Liu, 2010).

According to the Euler definition of the rotation

angles, we define the angles and rates relating the four

members of the gimbaled system as following (Barnes,

1971):

= Relative angle between the inner gimbal and the

platform, measured about the platform Y axis (Yp)

= Relative angular rate between the inner gimbal and

the platform, measured about the platform Y axis

(Yp) = Relative angle between the outer and inner

gimbals, measured about the inner gimbal Z axis

(ZI)

= Relative angular rate between the outer and inner

gimbals, measured about the inner gimbal Z axis

(ZI)

= Relative angle between the case and the outer

gimbals, measured about the outer gimbal X axis

(Xo)

= Relative angular rate between the case and theouter gimbal, measured about the outer gimbal Xaxis (Xo)

At each member of the gimbaled system weassociate an orthogonal coordinate system (Fig. 2)

platform (Xp, Yp, Zp), inner gimbal (XI, YI, ZI), outergimbal (XO, YO, ZO) and case (XC, YC, ZC).

The considered system platform is fixed on theship. Generally the satellite dish antenna is based on the

back part of the ship presented in Fig. 3.

Dynamics model: The mathematical modeling wasestablished using Euler theory. The Eulers momentequations are:

HiM (1)

The net torque M consists of driving torque appliedby the adjacent outer member and reaction torqueapplied by the adjacent inner member:

HHmdt

dHHi m

(2)

Hi : Inertial derivative of the vectorH

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Fig. 2: The system topology

Fig. 3: The case coordinates in the body-fixed frames

Hm : Derivative of H calculated in a rotating frame ofreference

m : Absolute rotational rate of the moving reference

frameH : Inertial angular momentum

M : External torque applied to the bodyBy applying Eq. (2) on the different parts of the

platform system, the system may be expressed as a set

of second-order differential equations in the statevariables. Solving this system of equations we obtain:

iooi

iooi

BABA

BCBC

(3)

iooi

oiio

BABA

ACAC

(4)

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iooi

iooi

p

p

p

p

BABA

BCBC

B

A

B

C

* (5)

where,

sinpA

1pB

py

Ipy

pI

MPYMC

*

iz

pzpx

iI

IIA sincoscos

iz

px

iz

pxi

II

IIB 22 cossin1

iz

oiz

iI

MIZMC

*

ox

iy

ox

pzpxix

oI

I

I

IIIA

2

22

2sin

sincoscos1

ox

pzpx

oI

IIB cossincos

ox

coxo

I

MCXMC

*

Detailed equations computation is presented in the

study (Leghmizi et al., 2011).

ESTABLISHING THREE DIMENSIONAL

MODEL OF THE STABILIZED PLATFORM

The design of a three-axis platform requires a total

of four bodies. These bodies include the base (case), the

inner, outer and platform gimbals.

The base, shown in Fig. 4 is designed to provide a

solid foundation to the three gimbals that will be

rotating around their respected axis. A rigid base is

responsible for preventing vibrations that will causeinaccurate movement and give unpredictable dynamic

responses. In the right section of the base is attached a

servo machine boxe, shown in Fig. 8a, responsible of

the rotation of the outer gimbal.

The outer gimbal, shown in Fig. 5, controls the

system platform roll. The outer gimbal will be directly

attached to the actuator mounted to the base. When the

actuator is activated it will allow the outer gimbal to

Fig. 4: The base unit of the platform

Fig. 5: The outer gimbal

Fig. 6: The inner gimbal

rotate 180. The second actuator boxe, shown in Fig.

8b, is contained inside the outer gimbal. The actuator is

firmly attached inside and is enclosed by a cap.

The inner gimbal, shown in Fig. 6, controls the 3-

DOF platform yaw. The middle gimbal is rotated by the

actuator housed in the outer gimbal. The middle gimbal

allows the platform to rotate 90. The third and finalactuator, shown in Fig. 8c, is attached the left side of

the inner gimbal.

The platform gimbal showed in Fig. 7 is

responsible for the platforms pitch. The platform

gimbal does not include housing for an actuator as there

are no additional gimbals to rotate.

The platform system assembly is represented in

Fig. 9.

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Fig. 7: The platform gimbal

Fig. 8: The machine boxes used in the platform

Fig. 9: Final assembly of the platform

Table 1: Platform parameters

Platform Inner gimbal Outer gimbal

Ipx 0.119 Iix 0.406 Iox 1.05

Ipy 0.119 Iiy 0.845 Ioy 1.05

Ipz 0.237 Iiz 1.020 Ioz 1.10

Dip 0.110 Doi 0.260 Dco 0.32

Using this software we can also calculate theprincipal moments of inertia taken at the center of mass

of each part of the platform system. These moments of

inertia will be used in the following simulation section.

The values found for these parameters are given inTable 1.

SIMULATION RESULTS AND DISCUSSION

The complete nonlinear dynamics for the stabilized

platform system was developed in the previous section.

Here, it suffices to note that designing a simulation for

the system based on these complete nonlinear dynamics

is extremely difficult. It is thus necessary to reduce the

complexity of the problem by considering the linearized

dynamics (Lee et al., 1996). This can be done by notingthat the gimbal angles variation are effectively

negligible and that the ship velocities effect is

insignificant.Applying the above assumptions to the nonlinear

dynamics, the following equations are obtained:

oo

oxixpx

pxpypz

co

oxixpxoxixpx

co

TIII

IIIF

IIIIII

D

)(sgn

1

(6)

mm

izpz

pzpxpy

oi

izpzizpz

oi

TII

IIIF

IIII

D

)(sgn

1

(7)

II

py

pypzpx

ip

pypy

ipT

I

IIIF

II

D

)(sgn

1 (8)

PID controller simulation: In the 3-D of platform we

will apply a decentralized PID which consiste of three

PID controllers applied to each part of the platformseparately as shown in Fig. 10 the PID parameters are

calculated for each part using the Ziegler-Nichols

method (Ziegler and Nichols, 1942). The obtained

parameters are listed in Table 2.

In order to see the outcome of the designed

controller, we performed a simulation in closed-loop

mode. This simulation was particularly useful for the

recognition of the effect of each PID coefficient to the

response of the system.

Simulation results will be presented to illustrate the

gimbals behavior to different PID parameters. They are

presented in Fig. 11, which contain the step response of

the platform system using the PID controller and in Fig.

12, which contain the impulsion response of the

platform response using the PID controller.

As shown in Fig. 11 and 12, the responses are

significantly acceptable but the response characteristics

still not well improved.

Figure 13 illustrates the position tracking responses

using PID controller. It can be seen that this controller

present bad tracking performance with big rising time.

This is due to the nonlinearities of the system that the

controller cant handle. For this an introduction of a non

linear controller is necessary.

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Fig. 10: PID control for the 3-DOF platform

Table 2: PID parameters

Kp Ki Kd

8.8 1.8 11.3

Fig. 11: Step response of the platform using PID controller

Fig. 12: Impulse response of the platform using PID controller

Fig. 13: Position tracking response using PID controller

Fig. 14: Disturbance rejection of the 3DOF platform using

PID controller

0

0.5

1.0

1.5

Gimbalsposition(rad)

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Time (s)

Platform

Inner gimbal

Outer gimbal

0

0.5

1.0

1.5

Gi

balsposition(rad)

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Time (s)

-0.5

Platform

Inner gimbal

Outer gimbal

0Gimbalsposition(rad)

0 1 2 3 5

Time (s)

-1

Platform

Inner gimbal

Outer gimbal

4 6 7 98

1

2

3

4

5

Reference

0

0.5

1.0

1.5

Gimbalspositio

n(rad)

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Time (s)

Platform

Inner gimbal

Outer gimbal

4.5 5.0

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Fig. 15: TS fuzzy controller for the 3-DOF platform

Also, in order to see the disturbance rejection

aptitude of the PID controller, small disturbance was introduced. The injected disturbance was a pulse of

0.1rad amplitude and adds to the system input at

time instant 3s.

The disturbance rejection capability of each part of

the stabilized platform using PID controller is plotted in

Fig. 14 They show that the controller is also unable of

dealing with this situation.

Fuzzy controller simulation: In the 3-D of platform

we will apply a decentralized Fuzzy controller which

consiste of three TS-Fuzzy controllers applied to each

part of the platform separately as shown in Fig. 15.

The structure of a complete fuzzy control system is

composed from the following blocs: Fuzzification,

Knowledge base, Inference engine, Defuzzification asshown in Fig. 3 (Chuen, 1990).

The general TS fuzzy systems in this study use 2

input variables. e, e, eand , , are selected as

input variables of each subsystem respectively and

defined as two variables representing the situation. cji is

selected as output of the jth subsystem and defined as a

variable representing the action. Notice that variables

for, , , , and assume linguistic terms as their

values such as positive-big, negative-small and zero,

etc.

Table 3: Rule base of the fuzzy logic controller

e\ NB NM NS ZR PS PM PB

PB ZR PS PM PB PB PB PB

PM NS ZR PS PM PB PB PB

PS NM NS ZR PS PM PB PB

ZR NB NM NS ZR PS PM PB

NS NB NB NM NS ZR PS PM

NM NB NB NB NM NS ZR PS

NB NB NB NB NB NM NS ZR

Using the Takagi-Sugeno model (Takagi and

Sugeno, 1985), the fuzzy system is characterized by a

set of p If-Then rules stored in a rule-base and

expressed as Ri: IF e is Ai and is Bi then:

210 peppcj

i

where, Ai and Bi are linguistic terms which in thisstudy can be NL, NM, NS, ZR, PS, PL and PB.

The rule base of this controller is summarized in

Table 3 for simplicity; the same universe of discourse

and the same fuzzy set are adopted for fuzzy input

variables. The membership functions of isosceles

triangles are used as the fuzzification function.

The Sugeno type fuzzy controller employ linear

functions of input variables as rule consequent, so the

steps of aggregation and defuzzification of fuzzy rules

are simultaneously and the final output of the system

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(a) (b)

(c)

Fig. 16: Step response of the platform system using PID and TS Fuzzy controller, (a) platform, (b) inner gimbal, (c) outer gimbal

is the weighted average of all rule outputs, computed

as:

N

i

i

N

i

i

j

i

l

c

T

1

1

(9)

The zero-order Sugeno model is applied, the output

level z is a constant (p1 = p2 = 0). The value of p0

depends on the linguistic term of the output. For

example if the output is NB (according to the rule base)

so p0 = -1.To observe the performance of the designed fuzzy

controller a comparison between the step response of

the platform using PID controller and the step response

of the platform using the fuzzy controller was done.

The results of the simulation investigating

positioning performance comparison of platform

system are shown in Fig. 16.

Figure 16 (Solid lines) shows step responses of the

stabilized platform system when controlled by three

separated order-0 TS fuzzy controllers. Figure 16

Fig. 17: Position tracking response of the platform

(dashed lines) shows step responses of the stabilizedplatform system when controlled by three separatedPID controllers. As shown in Fig. 16 the responses(solid lines) were significantly improved with smallerovershoot, shorter rising time.

Figure 17 illustrates the position tracking responsesusing TS fuzzy PD controller. It can be seen that thiscontroller present good tracking performance withminor rise time.

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Time (s)

PID

TS Fuzzy

Platformp

osition(rad)

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Time (s)

PID

TS Fuzzy

Innergimbalposition(rad)

0

0.5

1.0

1.5

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Time (s)

PID

Outergi

balposition(rad)

TS Fuzzy

-0.2

0.6

1.0

1.2

Platform

position(rad)

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Time (s)

Platform response

Desired trajectory

4.5 5.0

0.8

0.0

0.4

0.2

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CONCLUSION

Our research focused on the common coordinate,kinematics, dynamics, control system and softwaredesign for ship carried stabilized platform. For that inthis study we developed a dynamics modeling of the

platform and a 3D model of the platform usingSimulink and SolidWorks. Then, we considered the

problem of controlling this multivariableservomechanism where there exist cross-couplings

between the channels. A fuzzy PD control strategyusing a Takagi-Sugeno fuzzy model has been proposedand by comparing it with PID controller, it has beenshown in the study that uniformly stable operation isachieved together with asymptotic tracking of thereference command signals.

In the study, simulation results in applying theproposed TS fuzzy PD controller to a 3-Dofstabilization system have been presented whichdemonstrates the effectiveness of the fuzzy controller.Future study is directed to the optimization of thescaling factors of the fuzzy system and the intelligentmethod to generate an effective rule base.

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Debruin, J., 2008. Control systems for mobile satcomantennas. IEEE Contr. Syst. Mag., 28: 86-101.

Hilkert, J.M., 2008. Inertially stabilized platformtechnology concepts and principles. IEEE Contr.Syst. Mag., 28: 26-46.

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