untitled A publication of CCHHEEMMIICCAALL EENNGGIINNEEEERRIINNGG TTRRAANNSSAACCTTIIOONNSS VOL. 33, 2013 The Italian Association of Chemical Engineering Online at: www.aidic.it/cet Guest Editors: Enrico Zio, Piero Baraldi Copyright © 2013, AIDIC Servizi S.r.l., ISBN 978-88-95608-24-2; ISSN 1974-9791 Research on Heading Sensitive Drift Behavior of Inertial Platform System under the Influence of Magnetic Field Xiaokai Huang*, Yunxia Chen, Rui Kang School of Reliability and Systems Engineering, Room 536, Weimin Building, Beihang University, Haidian District, Beijing, China, 100191 huangxiaokai1986@126.com The heading sensitive drift of inertial platform system changes along with the degradation of components’ performance and the coupling characteristics under long-term storage conditions. Such heading sensitive drift is different from the drift during operation. It is also difficult to analyze its drift behavior for the model- based PHM system designing of inertial platform systems in engineering application. While the heading sensitive drift is influenced by various factors, this paper aims at dealing with part of this problem from one of the factors, i.e. magnetic field influence. This paper at the beginning derived the principle and the expression of the heading sensitive drift caused by magnetic field. And then, various drift parameters in such expressions were discussed, and the behavioral model of the heading sensitive drift influenced by the magnetic feature of components (such as the sensor, the torquer and the gyrorotor) was obtained. Finally, the long-term drift feature, the acceleration feature and the storage stability of the heading sensitive drift behavior were analyzed with the actual storage profile. The results of this paper indicate that although the heading sensitive drift caused by magnetic field has acceleration feature, the stability is able to meet the accuracy requirement of the inertial platform system under the current storage conditions. The drift value is so small that it can be ignored under the storage conditions. This study has great significance to the model-based PHM system design of inertial platform systems, which aims at improving the inertial platform systems parameters stability. 1. Introduction Heading sensitive drift mainly refers to the phenomenon of the gyro’s drift along with the heading attitude’s change in the inertial platform system. The drift value is over a dozen or dozens of times of the gyro precision level. Besides, the stability level of the heading sensitive drift is also hardly predictable. For such reasons, it has become a difficult issues in the research on precision of inertial platform system both at home and abroad ( Hu Pinghua/2000, Fredric Nadeau/1995, Zhang Dong-rong&Ye Bin/2010). Researches show that, based on its action principles, there are four factors that influence the heading sensitive drift, including 1) servo loop zero and structure disturbing torque, 2) vibration, 3) temperature and 4) magnetic field. During actual operation, measures such as Kalman filtering technique and GPS/INS integrated navigation technology are often employed to ensure the accuracy of the performance parameters of the inertial platform system (Hu Pinghua/2000, L.R.Sahawneh/2011, Arunasish&Acharya/2011). Since the heading sensitive drift is a major performance parameter of the system, to improve the accuracy of the heading sensitive drift will largely help to improve that of the whole system. However, for the missile inertial platform system which is subject to long-term storage and use for only once, the magnetic components inside the system, such as the sensor and the permanent magnet torque, will get degraded. Under long-term storage, the magnetism of such components is influenced by the geomagnetic field and the disturbance torque of external magnetic field. This will severely impacts the storage behavior of the heading sensitive drift of the inertial platform system. The influencing mechanism of those factors is complex and is quite different from the drift under operating conditions. This paper will first discuss the influence principle of the magnetic field on the heading sensitive drift and its expression. And then, the drifting characteristics of the parameters in the expression will be analyzed through both theoretical and experimental research. The behavioral model of the heading sensitive drift under the influence of magnetic field will be obtained. Ultimately, the long-time drift characteristic, acceleration performance and stability of heading sensitive drift are to be analyzed by employing an actual storage condition profile. The results indicate that although the heading sensitive drift caused by magnetic field has the acceleration effect, the stability can meet the accuracy requirement of the inertial platform system under the current storage conditions. The drift value is so small that it can be ignored under the storage 289 DOI: 10.3303/CET1333049 Please cite this article as: Huang X., Chen Y., Kang R., 2013, Research on heading sensitive drift behavior of inertial platform system under the influence of magnetic field, Chemical Engineering Transactions, 33, 289-294 DOI: 10.3303/CET1333049 conditions. The research is critical for reasonable resource allocation in respect of the calibration and maintenance in inertial platform system. 2. Principle of heading sensitive drift of the inertial platform system caused by the magnetic field 2.1 Research object Figure 1 is the frame structure of the inertial platform system, i.e., the research object of this paper. The system is mainly composed of the azimuth ring, the pitch ring, the rolling ring and other connecting structures. It provides measured value of the pitch angle, the roll angle and the azimuth angle for the device's missile attitude control through attitude angle sensor on the gimbal axis of the platform (Chen Yongbing&Zhong Bin/2007). Figure 1 Frame structure of inertial platform system Under the long-term storage influence of magnetic disturbance torque, the performance parameters of the magnetic sensor and those structures that are easily magnetized will get degraded. As a result, the gyro will output additional drift related to the long-term storage action of the magnetic disturbance, specifically, change in the storage behavior of the heading sensitive drift. 2.2 Principle of heading sensitive drift of the inertial platform system caused by the magnetic field The influence of magnetic field on the heading sensitive drift mainly refers to the influence of external magnetic field on magnetic components such as the inductive sensor, the permanent magnetic torque, and the hysteresis synchronous motor, as well as soft magnetic materials like the gyrorotor, the base and the end cap. Engineering application shows that the drift is mainly influenced by uniform magnetic field. It can be deduced from the literature (Hu Pinghua/2000) that the total disturbance torque influenced by the uniform magnetic field can be expressed as follows: DX PE TE RE DY PE TE RE M K K K M K K K ( 1 ) where, MDX and MDY stand for the total disturbance torque on the X axis and Y axis of the gyro caused by the uniform magnetic field respectively, KPE is the sensor’s electromagnetic torque, KTE is the disturbance torque coefficient at the zero position of the torquer, KRE is the leakage magnetic torque coefficient In line with the principle by which the disturbance torque of the inertial platform system causes the heading sensitive drift (Hu Pinghua/2000), we can obtain the expression of the heading sensitive drift caused by the magnetic disturbance torque of the inertial platform system as follows: 0 0 0 0 1 cos sin sin cos 1 sin cos cos sin PX DX DY DX DY PY DX DY DX DY kM M M M S HS kM M M M S HS ( 2 ) where, PX and PY are the additional drift output from the gyro’s X axis and Y axis, that is, the heading sensitive drift; MDX and MDY are the magnetic field disturbance torque on the gyro’s X axis and Y axis respectively, g·cm; is the time constant of the vertical gyro and the azimuth gyro, s; S0 is the servo loop rigidity, g·cm/rad; H is the moment of inertial of the gyro, kg·m2/s; and k is the residual elasticity coefficient of the gyro, g·cm/rad. 3. Storage behavioral model of the heading sensitive drift of the inertial platform system caused by the magnetic field In the passages below, this paper is going to make a thorough analysis of the storage features of the magnetic effect of the sensor’s electromagnetic torque coefficient KPE, the disturbance torque coefficient at the zero position of the torquer KTE, and the leakage magnetic torque coefficient surrounding the rotor KRE. 3.1 Storage behavioral model of parameters with magnetic characteristic Under the long-term storage conditions, the uniform magnetic field mainly impacts the electromagnetic damping coefficient of the gyrorotor, which then lead to changes of relevant coefficients such as the 290 sensor's electromagnetic torque coefficient, the disturbance coefficient at the torquer's zero position and the leakage magnetic torque coefficient surrounding the rotor. It is assumed in this paper that the magnetism degradation effect of all components is the same, and such characteristic can be reflected by the surface magnetic density of the gyro's soft magnetic materials. Therefore, based on theoretical analysis (Zhu Zhongping/2003), we can get the storage characteristics of the gyro shell 1J79 soft magnetic material of the inertial platform system through experimental measurements and Arrhenius model deduction: 23570.07 exp ln 8.314r EB t T ( 3 ) where r is the surface magnetic density; E is the external magnetic field intensity, whose unit is Gs; the unit of T is K; and the unit of t is hour. The Sensor’s electromagnetic torque The initial design value of the sensor’s electromagnetic torque of a certain platform system is KPE=0.97734×10-5 N·m/rad. Multiply this value with Equation (3), i.e., the magnetism degradation effect coefficient, and we can get the storage behavioral model of the sensor's electromagnetic torque coefficient under the influence of uniform magnetic field as follows: 7 23576.8414 10 exp ln 8.314PE EK t T (4) Disturbance torque coefficient at the zero position of the torquer The initial design value of the disturbance torque coefficient at the torquer's zero position of a certain platform system is KRE=3.2171kg·m/A. Multiply the above value with Equation (3), i.e., the magnetism degradation effect coefficient, and we can get the storage behavioral model of the sensor's electromagnetic torque coefficient under the influence of uniform magnetic field as follows: 23570.225197 exp ln 8.314RE EK t T (5) Leakage magnetic torque coefficient surrounding the rotor The initial design value of the leakage magnetic torque coefficient surrounding the rotor of a certain inertial platform system is KRE=1.568167N·m·h/r. Multiply the above value with Equation (3), i.e., the magnetism degradation effect coefficient, and we can get the storage behavioral model of the sensor's electromagnetic torque coefficient under the influence of uniform magnetic field as follows: 23570.109772 exp ln 8.314RE EK t T ( 6 ) 3.2 Storage behavioral models of other parameters It can be seen from Equation (2) that, apart from the electromagnetic torque coefficient, the disturbance torque coefficient at the torquer's zero position and the leakage magnetic torque coefficient surrounding the rotor, there are also other causes of the heading sensitive drift of the inertial platform system. Such causes include but are not limited to the rotor's deviation angles and servo loop rigidity S0, the residual elasticity coefficient and the gyro's angular momentum H. These parameters are mainly influenced by the temperature stress which inevitably exists under storage condition, and will show certain drifting characteristics under the long-term temperature stress. Here below is a detailed study of all these parameters in the storage behavioral model. Rotor’s deviation angle (sensor’s zero position) The output information of the gyro's X axis and Y axis acts on the inertial platform system through the feedback of the servo loop. Hence, we can take the temperature characteristic of the servo loop as that of the rotor's initial drift angle. By analyzing the temperature characteristic of the servo loop's temperature characteristic, we can get the storage behavioral model of the rotor's initial deviation angle (the sensor's zero's position) as follows (Pan Ronglin/1990, Hu Pinghua/2000): 3 4 9 2 8 2 9 3 4 9 2 8 2 9 61.2 / 10 (17.4132 1.04775 10 t 0.00139899 2.31568 10 2.35779 10 2.9888 10 ) 270 / 10 (17.4132 1.04775 10 t 0.00139899 2.31568 10 2.35779 10 2.9888 10 ) T t T t T T t T t T (7) Gyro’s time constant The calculation of the gyro’s time constant is as follows (Pan Ronglin/1990): / /zH J (8) 291 where, JZ is the moment of inertia of rotor's polar axis, is the rotor's gas damping coefficient, is the internal friction damping coefficient of the flexible joint, and is the orthogonal damping elasticity coefficient. It can be known from the above parameters that the gyro’s constant is mainly influenced by the damping feature of the materials. Therefore, the temperature feature of the damping coefficient of the materials can be used to reflect the temperature feature of the gyro’s time constant. By introducing the concept of equivalent viscous damping, this paper converts the gyro's damping into equivalent viscous damping (the conversion method is to deem that viscous damping consumes the same energy with other viscous damping in a vibration cycle), and take it as the temperature coefficient of the gyro time constant. Ultimately, the behavioral model of the gyro's time constant in a certain inertial platform system with an initial value of 60s is as follows: 8 19.35 18.51/ 1 54.2821 (0.421652122 10 ) lnTe t (9) Servo loop rigidity The expression of the servo loop rigidity is (Pan Ronglin/1990): 2 ' 0 1 /D g a m M s S s Js K K K F s R s s (10) where, Kg=H/C and C is the viscous damping coefficient, Km is the torque coefficient of the electric motor, R is the total resistance of the torque motor, ' aK F s is the transfer function of the servo amplifier, ' aK is the total magnification of the servo amplifier, F(s) is the network transfer function and J is Total moment of inertial of the torque motor rotating around the output shaft. It can be seen that the change of the servo loop rigidity depends on the temperature effect of the servo loop. Hence, the storage behavioral model of the servo loop rigidity can be obtained from Equation (7): 4 0 9 2 8 2 9 50 /18 (17.4132 1.04775 10 t 0.00139899 2.31568 10 2.35779 10 2.9888 10 ) S T t T t T (11) Residual elasticity coefficient The residual elasticity coefficient is defined as follows (Pan Ronglin/1990): 2 0 / 2k K a b c N (12) Generally, once the parameters of the flexible supporting structure have been determined, the adjustable parameters mainly include the moment of inertia a, b and c, and the rotating speed N. Therefore, the storage characteristic of the residual elasticity is mainly related to the rigidity of the gyro's material. Through experiment of the temperature characteristic of the gyro material rigidity, and taking it as that of the residual elasticity coefficient, we can get the storage behavioral model of the residual elasticity as follows: 8 16 5 11 13 10 2.3275 10 exp 26.6 / 8.31 10 360 1.75 10 t T k (13) Gyro’s angular momentum The expression of the gyro’s angular momentum is (Pan Ronglin/1990): zH J (14) It can be known from the above expression that the gyro’s angular momentum mainly depends on the design parameters and will not change with time or temperature. Therefore, the initial design value is set at 274.088 /H kg m s . 3.3 Storage behavioral model of heading sensitive drift of inertial platform system caused by the magnetic field Insert equations from Equation (3) to Equation (14) into Equation (2) and unify the units of all parameters, and we can obtain the storage behavioral model of the heading sensitive drift of the inertial platform system under the influence of the magnetic field. In order to analyze the model effectively, this paper uses the response surface identification method [9] to get a brief storage behavioral identification model as shown in Equation (15) below: 4 6 6 16 9 18 10 2 9 2 5 0.341219315687886 10 0.1263633001923 10 0.8376157718625 10 0.742 10 0.1330962847 10 0.2 10 0.155333485 10 0.7768987387 10 0.773430681067779 10 0.286422524 PX PY E T t E T T t E T 7 6 16 10 19 11 2 9 2 1321 10 0.18985955985011 10 0.3351 10 3016842984 10 0.4 10 0.353465779 10 0.17609702236 10 E T t E T T t E T ( 15 ) 292 293 It can be found from Table 2 and Figure 2 that the heading sensitive drift on the gyro’s X axis and Y axis diverges greatly, but the drift value stays stable at about 10-13. Such drift value can be ignored since the stability requirement for one year in current engineering is set at 0.2 (which means the maximum drift difference ). Therefore, the influence of the magnetic field can be disregarded in the resources allocation for the calibration and maintenance in inertial platform system. 5. Conclusion This paper has derived the heading sensitive drift behavioral model of the inertial platform system under the influence of uniform magnetic field. Through comprehensive analysis of the storage characteristics in the behavioral model, this paper has pointed out that the influence of magnetic field on the heading sensitive drift of the inertial platform system can be ignored. The research approach and conclusion are meaningful not only to theoretical research but also engineering application. The major contribution and innovative points are as follows: 1) This paper analyzed the heading sensitive drift mechanism caused by the magnetic field under the storage conditions .Its storage behavioral model has laid down a theoretic basis for future research on heading sensitive drift in the missile inertial platform system featuring long-term storage and one-time use. 2) The Matlab simulation indicates that the heading sensitive drift caused by magnetic field has an acceleration effect, but the drift value is so small that it can be ignored for navigation accuracy. The conclusions and findings hereof are of great significance for resources allocation of the calibration and maintenance in inertial platform system, and support the model-based PHM design of the inertial platform systems in theory. References Arunasish Acharya, Smita Sadhu, T.K. Ghoshal, 2011. Improved self-alignment scheme for SINS using augmented measurement. Aerospace Science and Technology. (15):125–128. 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