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Micro-machined Pendulum and Non-driven Micro-machined Gyroscope
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Physics Procedia
Physics Procedia 00 (2011)22000–000 Physics Procedia (2011) 517 – 523 www.elsevier.com/locate/procedia
2011 International Conference on Physics Science and Technology (ICPST 2011)
Micro-machined Pendulum and Non-driven Micro-machined Gyroscope Fu-xue Zhang a, Sheng-jie Qina,Lin-xia Tana,Hui Zhaob,a* a
Sensing Technique Research Center, Beijing Information Science and Technology University, Beijing 100101, China b
Beijing University of Posts and Telecommunications, Beijing 100101,China
Abstract The paper reported a new type of micro-machined pendulum which had gyroscopic effect when installed in rotating carrier. It was demonstrated that a micro-machined pendulum installed in rotating carrier, using the spinning of rotating carrier instead of traditional gyroscope’s driving force produced by its structure form a non-driven micromachined gyroscope. The new micro-machined gyroscope can output pitching, yawing and rolling angular velocity of the rotating carrier, which is equivalent to three traditional gyroscopes.
© 2011 Published by Elsevier B.V. Selection and/or peer-review under responsibility of Garry Lee. © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [name organizer] Keywords: micro-machined pendulum, angular velocity, rotating carrier, gyroscope, attitude;
1. Introduction The rapid development of rotating carrier makes its attitude sensitive technology in focus, however, there is no international and domestic report on gyroscopes which can meet the requirements of rotating carrier. The paper developed a new type of micro-machined pendulum and its working principle of the detection of pitching, yawing and rolling angular velocity when installed in rotating carrier[1-2]. The micro-machined pendulum that installed in rotating carrier had the functions of three traditional gyroscopes[3-8]. 2. Micro-machined pendulum A front view of impact resistant micro-machined pendulum chip as shown in Fig.1(a), Fig.1(b) was its
* Corresponding author. Tel.: 13910559351; fax:010-64879486. E-mail address: [email protected].
1875-3892 © 2011 Published by Elsevier B.V. Selection and/or peer-review under responsibility of Garry Lee. doi:10.1016/j.phpro.2011.11.080
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Fu-xueZhang/ ZhangPhysics et al. / Physics Procedia 22 000–000 (2011) 517 – 523 Fuxue Procedia 00 (2011)
signal detection circuit and Fig.2 showed the sectional drawing of the micro-machined pendulum chip structure. Pendulous reed suspended on the frame by cantilever beam, set a pair of end bushing symmetrically on the up and bottom of silicon pendulous reed. When rotating carrier was in pitch or yaw motion, the pendulous reed swung with the twist of beam which caused the capacitance change in signal detection circuit, and the unbalance bridge output attitude signal. Discomposing the output signal, the pitching, yawing and rolling angular velocity can be obtained.
Fig. 1. (a) Micro-machined pendulum chip
Fig.1.(b) Signal detection circuit
Fig. 2. The sectional drawing of the MEMS chip
3. Principle of micro-machined pendulum in the application of rotating carrier attitude detection The principle of the detection of pitching, yawing and rolling angular velocity when micro-machined pendulum was installed in rotating carrier was shown in Fig.3. The micro-machined pendulum that installed in rotating carrier constituted a closed loop circuit system, and its principle was shown in Fig.4.
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Fu-xue Zhang et al.Physics / Physics Procedia0022(2011) (2011)000–000 517 – 523 Fuxue Zhang/ Procedia
Fig. 3. The principle of micro-machined pendulum
Fig. 4. The principle of micro-machined pendulum installed on rotating carrier for angular velocity detect
A micro-machined pendulum can output rolling and transverse angular velocity (in polar coordinates), line with geographical coordinates, output pitching, yawing and rolling angular velocity. Micro-machined pendulum installed on rotating carrier, its kinematic equation was expressed as
J yα + Dα + [( J z − J x )ϕ 2 + KT ]α = ( J z + J y − J x )ϕΩ sin ϕt
(1)
Stationary solution of equation (1) is
α=
( J z + J y − J x )ϕΩ [( J z − J y − J x )ϕ 2 + KT ]2 + ( Dϕ ) 2
sin ϕt
From (2), we can see that the output swing angle α of micro-machined pendulum had relation with the rolling velocity ϕ and transverse angular velocityΩ, the output waveform as shown in Fig.5 and Fig.6.
(2)
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Fig. 5. The output wave form of micro-machined pendulum
Fig. 6. (a)carrier signal;
Fig.6.(b)envelop signal
In Fig.5, the vertical axis represented the output voltage signal, the horizontal axis represented time, rolling velocity can be available by carrier signal (as in Fig.6(a)), envelop signal is the transverse angular velocity (as in Fig.6(b)), if the transverse angular velocity is constant, envelop signal is a horizontal line, combined with geographical coordinates, output pitching, yawing and rolling angular velocity. Form characteristics stated above, micro-machined pendulum simply in structure, can output pitching, yawing and rolling angular velocity, has the functions of three traditional gyroscopes and low in cost. 4. Application of micro-machined pendulum in rotating carrier single-channel attitude stable system Micro-machined pendulum shown in Fig.7 was in application of micro-machined pendulum in rotating carrier single-channel attitude stable system, the accuracy of output signal is 0.5° in 15 second measurement.
Fig. 7. Structure sketch of CJS-DR-W1 micro-machined pendulum
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Fu-xue Zhang et al.Physics / Physics Procedia0022(2011) (2011)000–000 517 – 523 Fuxue Zhang/ Procedia
Rotating carrier attitude stabilization adopts “bang-bang control” which is a simple and reliable control mode and often used in rotating carrier currently. Single-channel control or “bang-bang control” briefly described as follows: The output of micro-machined pendulum is in a carrier - envelope form equivalent to an amplitude modulation signal (as in Fig.5). The frequency of carrier signal multiplies 360° was the inner angular velocity ( ϕ ), the envelope signal was the voltage variation due to transverse angular velocity. By introducing linear signal, established a linear relationship of pulse width modulation signal and transverse angular velocity and design a circuit to produce the pulse width modulation signal. Output signal of micro-machined pendulum can be expressed as Ut=Ahsin(ωt+ϕ)
(3)
Where, Ut is the output signal of micro-machined pendulum; Ah is the envelope signal, which is in direct proportion to the magnitude of input signal transverse angular velocity; ω is the rolling angular velocity; ϕ is the initial phase angle. From ϕ to 180°+ϕ is the positive-going square wave signal, solenoids I of servos is powered, rudder angle is +δ and the force is +F; from180°+ϕ to 360°+ϕ is the negative-going square wave signal, solenoids II of servos is powered, rudder angle is -δ and the force is –F. Carrier spins a round, the direction of average control force is 90°+ϕ, its magnitude is 2F. The voltage output control of micromachined pendulum is shown in Fig.8, Udk only depends on the zero-crossing point of Ut. The zerocrossing point of Ut is only relevant to carrier signal and is not relevant to the envelope signal, so Udk is not relevant to the magnitude of transverse angular velocity. That is, the average control force generated by Udk can’t be used to control by different magnitude of transverse angular velocity.
Fig. 8. Voltage output control of micro-machined pendulum
In order to establish a relationship between average control force and transverse angular velocity, linear signal should be brought in. The frequency of linear signal is set to a fixed value f(Hz) and its amplitude is Us, then the synthesized signal is Uk=Ahsin(ωt+ϕ)+Us sin(2πft),
(4)
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Fu-xueZhang/ ZhangPhysics et al. / Physics Procedia 22 000–000 (2011) 517 – 523 Fuxue Procedia 00 (2011)
According to the zero-crossing point of output signal, transfer the output signal of micro-machined pendulum to control square wave signal. Combined with equation (4), Udk can be expressed as Udk=sgn[Ahsin(ωt+ϕ)+Us sin(2πft)],
(5)
So, when Ahsin(ωt+ϕ)+Us sin(2πft)>0, Udk is the positive-going square wave signal; when Ahsin(ωt+ϕ)+Us sin(2πft)<0, Udk is the negative-going square wave signal. At this point, because the zero-crossing point of is linear with Ah and Ah is proportional to transverse angular velocity, Udk is proportional to the input signal transverse angular velocity. A pulse width modulation control signal with equal amplitude and unequal width was generated by different transverse angular velocity. The width of pulse signal is linear with magnitude of transverse angular velocity. Carrier spins a round, the phase of rudder changes four times, using a pair of control surface to fulfill the control of the rotating carrier’s attitude at the same time is achieved, which is singlechannel attitude stabilization control of rotating carrier.
Fig. 9. Pulse width modulation control signal
Single-channel attitude stability control system is mainly using transverse and rolling angular velocity of micro-machined pendulum to control the carrier in steady fight. 5. Conclusion Micro-machined pendulum installed on rotating carrier, using the spinning of rotating carrier instead of traditional gyroscope’s driving force produced by its structure to form a non-driven micro-machined gyroscope. The new micro-machined gyroscope can detect pitching, yawing and rolling angular velocity at the same time, which has the functions of three traditional gyroscopes. Micro-machined pendulum was applied in rotating carrier single-channel attitude stable system, the accuracy of output signal is 0.5° in 15 second measurement, is an ideal inertial device to sensing transverse angular velocity. Acknowledgements The research work of this paper was supported by National Natural Science Foundation of China (60971024), Beijing Municipal Natural Science Foundation (4112020) and Key Laboratory of Modern Measurement & Control Technology (Beijing Information Science &Technology University), Ministry of
Fu-xueFuxue ZhangZhang/ et al. /Physics PhysicsProcedia Procedia 00 22 (2011) (2011) 000–000 517 – 523
Education. The authors acknowledge them and the staff at the Sensing Technique Research Center, Beijing Information Science and Technology University. References [1] Fuxue Zhang, Wei Zhang, Silicon Micromechantcal Gyroscope, US 7,805,994 B2. [2] Zhang Fuxue, Zhang Wei, Silicon micromechanlcal gyroscope without driving structure, GB 2449955A. [3] Zhang Fuxue, Wang Hongwei, Zhang Wei, Liu Yu, Carrier-driven Silicon Micro-machined Gyroscope, ZL 200410028228.X. [4] Zhang Fuxue, Zhang Nan, Mao Xu, Impact Resistant Silicon Micro-machined Gyroscope, ZL 200510134857.3. [5] Zhang Fuxue, Zhang Nan, Mao Xu, Two-dimensional Silicon Micro-machined Gyroscope, ZL 200510134858.8. [6] Zhang Fu-xue, Wang Hongwei, Zhang Wei, Mao Xu, Silicon Micro-machined Gyroscope, ZL 200410029089.0. [7] Zhang Fuxue, Zhang Wei, A New Type of Silicon Micro-machined Gyroscope, ZL 200710105849.5. [8] Yan Qingwen, Zhang Fuxue, Zhang Wei, Attitude Algorithm Software for Silicon Micro-machined Gyroscope, Registration Number of Computer Software Copyright Certificate: 0157869.
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Physics Procedia
Physics Procedia 00 (2011)22000–000 Physics Procedia (2011) 517 – 523 www.elsevier.com/locate/procedia
2011 International Conference on Physics Science and Technology (ICPST 2011)
Micro-machined Pendulum and Non-driven Micro-machined Gyroscope Fu-xue Zhang a, Sheng-jie Qina,Lin-xia Tana,Hui Zhaob,a* a
Sensing Technique Research Center, Beijing Information Science and Technology University, Beijing 100101, China b
Beijing University of Posts and Telecommunications, Beijing 100101,China
Abstract The paper reported a new type of micro-machined pendulum which had gyroscopic effect when installed in rotating carrier. It was demonstrated that a micro-machined pendulum installed in rotating carrier, using the spinning of rotating carrier instead of traditional gyroscope’s driving force produced by its structure form a non-driven micromachined gyroscope. The new micro-machined gyroscope can output pitching, yawing and rolling angular velocity of the rotating carrier, which is equivalent to three traditional gyroscopes.
© 2011 Published by Elsevier B.V. Selection and/or peer-review under responsibility of Garry Lee. © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [name organizer] Keywords: micro-machined pendulum, angular velocity, rotating carrier, gyroscope, attitude;
1. Introduction The rapid development of rotating carrier makes its attitude sensitive technology in focus, however, there is no international and domestic report on gyroscopes which can meet the requirements of rotating carrier. The paper developed a new type of micro-machined pendulum and its working principle of the detection of pitching, yawing and rolling angular velocity when installed in rotating carrier[1-2]. The micro-machined pendulum that installed in rotating carrier had the functions of three traditional gyroscopes[3-8]. 2. Micro-machined pendulum A front view of impact resistant micro-machined pendulum chip as shown in Fig.1(a), Fig.1(b) was its
* Corresponding author. Tel.: 13910559351; fax:010-64879486. E-mail address: [email protected].
1875-3892 © 2011 Published by Elsevier B.V. Selection and/or peer-review under responsibility of Garry Lee. doi:10.1016/j.phpro.2011.11.080
518 2
Fu-xueZhang/ ZhangPhysics et al. / Physics Procedia 22 000–000 (2011) 517 – 523 Fuxue Procedia 00 (2011)
signal detection circuit and Fig.2 showed the sectional drawing of the micro-machined pendulum chip structure. Pendulous reed suspended on the frame by cantilever beam, set a pair of end bushing symmetrically on the up and bottom of silicon pendulous reed. When rotating carrier was in pitch or yaw motion, the pendulous reed swung with the twist of beam which caused the capacitance change in signal detection circuit, and the unbalance bridge output attitude signal. Discomposing the output signal, the pitching, yawing and rolling angular velocity can be obtained.
Fig. 1. (a) Micro-machined pendulum chip
Fig.1.(b) Signal detection circuit
Fig. 2. The sectional drawing of the MEMS chip
3. Principle of micro-machined pendulum in the application of rotating carrier attitude detection The principle of the detection of pitching, yawing and rolling angular velocity when micro-machined pendulum was installed in rotating carrier was shown in Fig.3. The micro-machined pendulum that installed in rotating carrier constituted a closed loop circuit system, and its principle was shown in Fig.4.
519 3
Fu-xue Zhang et al.Physics / Physics Procedia0022(2011) (2011)000–000 517 – 523 Fuxue Zhang/ Procedia
Fig. 3. The principle of micro-machined pendulum
Fig. 4. The principle of micro-machined pendulum installed on rotating carrier for angular velocity detect
A micro-machined pendulum can output rolling and transverse angular velocity (in polar coordinates), line with geographical coordinates, output pitching, yawing and rolling angular velocity. Micro-machined pendulum installed on rotating carrier, its kinematic equation was expressed as
J yα + Dα + [( J z − J x )ϕ 2 + KT ]α = ( J z + J y − J x )ϕΩ sin ϕt
(1)
Stationary solution of equation (1) is
α=
( J z + J y − J x )ϕΩ [( J z − J y − J x )ϕ 2 + KT ]2 + ( Dϕ ) 2
sin ϕt
From (2), we can see that the output swing angle α of micro-machined pendulum had relation with the rolling velocity ϕ and transverse angular velocityΩ, the output waveform as shown in Fig.5 and Fig.6.
(2)
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Fu-xue Zhang et al. / Physics Procedia 22 (2011) 517 – 523 Fuxue Zhang/ Physics Procedia 00 (2011) 000–000
Fig. 5. The output wave form of micro-machined pendulum
Fig. 6. (a)carrier signal;
Fig.6.(b)envelop signal
In Fig.5, the vertical axis represented the output voltage signal, the horizontal axis represented time, rolling velocity can be available by carrier signal (as in Fig.6(a)), envelop signal is the transverse angular velocity (as in Fig.6(b)), if the transverse angular velocity is constant, envelop signal is a horizontal line, combined with geographical coordinates, output pitching, yawing and rolling angular velocity. Form characteristics stated above, micro-machined pendulum simply in structure, can output pitching, yawing and rolling angular velocity, has the functions of three traditional gyroscopes and low in cost. 4. Application of micro-machined pendulum in rotating carrier single-channel attitude stable system Micro-machined pendulum shown in Fig.7 was in application of micro-machined pendulum in rotating carrier single-channel attitude stable system, the accuracy of output signal is 0.5° in 15 second measurement.
Fig. 7. Structure sketch of CJS-DR-W1 micro-machined pendulum
521 5
Fu-xue Zhang et al.Physics / Physics Procedia0022(2011) (2011)000–000 517 – 523 Fuxue Zhang/ Procedia
Rotating carrier attitude stabilization adopts “bang-bang control” which is a simple and reliable control mode and often used in rotating carrier currently. Single-channel control or “bang-bang control” briefly described as follows: The output of micro-machined pendulum is in a carrier - envelope form equivalent to an amplitude modulation signal (as in Fig.5). The frequency of carrier signal multiplies 360° was the inner angular velocity ( ϕ ), the envelope signal was the voltage variation due to transverse angular velocity. By introducing linear signal, established a linear relationship of pulse width modulation signal and transverse angular velocity and design a circuit to produce the pulse width modulation signal. Output signal of micro-machined pendulum can be expressed as Ut=Ahsin(ωt+ϕ)
(3)
Where, Ut is the output signal of micro-machined pendulum; Ah is the envelope signal, which is in direct proportion to the magnitude of input signal transverse angular velocity; ω is the rolling angular velocity; ϕ is the initial phase angle. From ϕ to 180°+ϕ is the positive-going square wave signal, solenoids I of servos is powered, rudder angle is +δ and the force is +F; from180°+ϕ to 360°+ϕ is the negative-going square wave signal, solenoids II of servos is powered, rudder angle is -δ and the force is –F. Carrier spins a round, the direction of average control force is 90°+ϕ, its magnitude is 2F. The voltage output control of micromachined pendulum is shown in Fig.8, Udk only depends on the zero-crossing point of Ut. The zerocrossing point of Ut is only relevant to carrier signal and is not relevant to the envelope signal, so Udk is not relevant to the magnitude of transverse angular velocity. That is, the average control force generated by Udk can’t be used to control by different magnitude of transverse angular velocity.
Fig. 8. Voltage output control of micro-machined pendulum
In order to establish a relationship between average control force and transverse angular velocity, linear signal should be brought in. The frequency of linear signal is set to a fixed value f(Hz) and its amplitude is Us, then the synthesized signal is Uk=Ahsin(ωt+ϕ)+Us sin(2πft),
(4)
522 6
Fu-xueZhang/ ZhangPhysics et al. / Physics Procedia 22 000–000 (2011) 517 – 523 Fuxue Procedia 00 (2011)
According to the zero-crossing point of output signal, transfer the output signal of micro-machined pendulum to control square wave signal. Combined with equation (4), Udk can be expressed as Udk=sgn[Ahsin(ωt+ϕ)+Us sin(2πft)],
(5)
So, when Ahsin(ωt+ϕ)+Us sin(2πft)>0, Udk is the positive-going square wave signal; when Ahsin(ωt+ϕ)+Us sin(2πft)<0, Udk is the negative-going square wave signal. At this point, because the zero-crossing point of is linear with Ah and Ah is proportional to transverse angular velocity, Udk is proportional to the input signal transverse angular velocity. A pulse width modulation control signal with equal amplitude and unequal width was generated by different transverse angular velocity. The width of pulse signal is linear with magnitude of transverse angular velocity. Carrier spins a round, the phase of rudder changes four times, using a pair of control surface to fulfill the control of the rotating carrier’s attitude at the same time is achieved, which is singlechannel attitude stabilization control of rotating carrier.
Fig. 9. Pulse width modulation control signal
Single-channel attitude stability control system is mainly using transverse and rolling angular velocity of micro-machined pendulum to control the carrier in steady fight. 5. Conclusion Micro-machined pendulum installed on rotating carrier, using the spinning of rotating carrier instead of traditional gyroscope’s driving force produced by its structure to form a non-driven micro-machined gyroscope. The new micro-machined gyroscope can detect pitching, yawing and rolling angular velocity at the same time, which has the functions of three traditional gyroscopes. Micro-machined pendulum was applied in rotating carrier single-channel attitude stable system, the accuracy of output signal is 0.5° in 15 second measurement, is an ideal inertial device to sensing transverse angular velocity. Acknowledgements The research work of this paper was supported by National Natural Science Foundation of China (60971024), Beijing Municipal Natural Science Foundation (4112020) and Key Laboratory of Modern Measurement & Control Technology (Beijing Information Science &Technology University), Ministry of
Fu-xueFuxue ZhangZhang/ et al. /Physics PhysicsProcedia Procedia 00 22 (2011) (2011) 000–000 517 – 523
Education. The authors acknowledge them and the staff at the Sensing Technique Research Center, Beijing Information Science and Technology University. References [1] Fuxue Zhang, Wei Zhang, Silicon Micromechantcal Gyroscope, US 7,805,994 B2. [2] Zhang Fuxue, Zhang Wei, Silicon micromechanlcal gyroscope without driving structure, GB 2449955A. [3] Zhang Fuxue, Wang Hongwei, Zhang Wei, Liu Yu, Carrier-driven Silicon Micro-machined Gyroscope, ZL 200410028228.X. [4] Zhang Fuxue, Zhang Nan, Mao Xu, Impact Resistant Silicon Micro-machined Gyroscope, ZL 200510134857.3. [5] Zhang Fuxue, Zhang Nan, Mao Xu, Two-dimensional Silicon Micro-machined Gyroscope, ZL 200510134858.8. [6] Zhang Fu-xue, Wang Hongwei, Zhang Wei, Mao Xu, Silicon Micro-machined Gyroscope, ZL 200410029089.0. [7] Zhang Fuxue, Zhang Wei, A New Type of Silicon Micro-machined Gyroscope, ZL 200710105849.5. [8] Yan Qingwen, Zhang Fuxue, Zhang Wei, Attitude Algorithm Software for Silicon Micro-machined Gyroscope, Registration Number of Computer Software Copyright Certificate: 0157869.
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