A Missile-Borne Angular Velocity Sensor Based on ... - Semantic Scholar

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A Missile-Borne Angular Velocity Sensor Based on Triaxial Electromagnetic Induction Coils Jian Li *, Dan Wu and Yan Han Institute of Signal Capturing & Processing Technology, Key Laboratory of Shanxi Province, North University of China, Taiyuan 030051, China; [email protected] (D.W.); [email protected] (Y.H.) * Correspondence: [email protected]; Tel.: +86-139-9424-2766 Academic Editors: Subhas Mukhopadhyay and Chinthaka Pasan Gooneratne Received: 22 July 2016; Accepted: 26 September 2016; Published: 30 September 2016

Abstract: Aiming to solve the problem of the limited measuring range for angular motion parameters of high-speed rotating projectiles in the field of guidance and control, a self-adaptive measurement method for angular motion parameters based on the electromagnetic induction principle is proposed. First, a framework with type bent “I-shape” is used to design triaxial coils in a mutually orthogonal way. Under the condition of high rotational speed of a projectile, the induction signal of the projectile moving across a geomagnetic field is acquired by using coils. Second, the frequency of the pulse signal is adjusted self-adaptively. Angular velocity and angular displacement are calculated in the form of periodic pulse counting and pulse accumulation, respectively. Finally, on the basis of that principle prototype of the sensor is researched and developed, performance of measuring angular motion parameters are tested on the sensor by semi-physical and physical simulation experiments, respectively. Experimental results demonstrate that the sensor has a wide measuring range of angular velocity from 1 rps to 100 rps with a measurement error of less than 0.3%, and the angular displacement measurement error is lower than 0.2◦ . The proposed method satisfies measurement requirements for high-speed rotating projectiles with an extremely high dynamic range of rotational speed and high precision, and has definite value to engineering applications in the fields of attitude determination and geomagnetic navigation. Keywords: angular velocity; angular displacement; self-adaptive frequency tracking measurement; FPGA

1. Introduction High-speed rotating projectiles, with rotational speeds generally in a range from 2 rps to 50 rps, have become one of the most important kinds of ammunition among conventional ammunition. On the one hand, a high-speed rotating projectile ensures flight stability by way of rotation; on the other hand, this kind of projectile changes flight attitude and corrects its flight trajectory through adjusting its rotational speed, so as to accurately attack targets. In the course of structure improvement and performance testing of high-speed rotating projectiles, the accurate measurement of angular motion parameters, such as angular velocity and angular displacement, is key for optimizing the structure and improve the attacking accuracy. The precision guidance of high-speed rotating projectiles is a research hotspot in the field of international arms and ammunition at present. Scientific researchers mainly use gyroscopes to obtain the angular velocity information of projectiles nowadays [1–12]. For example, the angular velocity sensor based on a magnetically suspended control moment gyroscope (MSCMG) [13], the capacitive angular velocity sensor and the angular velocity sensor based on magnetohydrodynamics at low frequency [14,15], etc. Although these sensors have certain advantages of small volume and high damage impact resistance, they still have problems of small measuring ranges, zero drift and high cumulative errors when measuring rotational Sensors 2016, 16, 1625; doi:10.3390/s16101625

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problems of small measuring ranges, zero drift and high cumulative errors when measuring rotational speed. Though some of the errors can be corrected by some algorithms like Kalman prediction, the requirements of large range and precision for measuring speed of speed. Though some dynamic of the errors can be high corrected by some algorithms the likerotational Kalman prediction, high-speed rotating still cannot be satisfied under for actual combat the conditions. Aiming the requirements of projectiles large dynamic range and high precision measuring rotational speed at of addressing the problems described above, this paper presents a method for measuring angular motion high-speed rotating projectiles still cannot be satisfied under actual combat conditions. Aiming at parameters on the electromagnetic induction principle. specificfor working of this method is as addressing based the problems described above, this paper presentsThe a method measuring angular motion follows: under different speeds, an induction coil of aThe bent “I-shape” typeof is this used to acquire parameters based on therotation electromagnetic induction principle. specific working method is as signals of a high-speed rotating projectile moving across a geomagnetic field. A self-adaptive frequency follows: under different rotation speeds, an induction coil of a bent “I-shape” type is used to acquire tracking measurement is proposed to obtain angular velocity angular displacement signals of a high-speedalgorithm rotating projectile moving acrossthe a geomagnetic field.and A self-adaptive frequency information of the projectile rotation. The cumulative error during the measurement is eliminated by tracking measurement algorithm is proposed to obtain the angular velocity and angular displacement using the periodically pulse clear method, thereby realizing the measurement of the angular motion information of the projectile rotation. The cumulative error during the measurement is eliminated by parameters of the high-speed rotating projectile, satisfying its measurement of using the periodically pulse clear method, therebyand realizing the measurement of therequirements angular motion wide range of rotational speed and high precision. The proposed method has definite value to parameters of the high-speed rotating projectile, and satisfying its measurement requirements of wide engineering applications thehigh fields of attitude and geomagnetic navigation [16]. range of rotational speedin and precision. Thedetermination proposed method has definite value to engineering applications in the fields of attitude determination and geomagnetic navigation [16]. 2. Measurement Principle of the Sensor 2. Measurement Principle of the Sensor 2.1. Basic Principle of Measuring Angular Velocity 2.1. Basic Principle of Measuring Angular Velocity The measurement method of angular velocity proposed in this paper draws from the theory of measurement of angular proposed in1.this paper draws from the theory of digitalThe frequency meters.method The basic principlevelocity is shown in Figure digital frequency meters. The basic principle is shown in Figure 1.

x (t )

T

xs (t ) T0

Figure 1. Schematic diagram of frequency measurement based on period method. Figure 1. Schematic diagram of frequency measurement based on period method.

A measured measured signal signal x(t) x(t) is is converted converted into into aa gate gate signal signal through a shaping circuit. Under Under the the A circumstancesthat thatthe the standard standard frequency frequencysignal signalxxs(t) withhigher higherfrequency frequencyisistaken takenas as aa periodic periodic circumstances s (t)with pulsesignal, signal,the themeasured measured signal signal is iscalculated calculated by bypulse pulsecounting countingwithin withinaagate gatetime timeT. T.Assuming Assumingthat that pulse the count value is N, the cycle of measured signal and standard signal are T and T , respectively. the count value is N, the cycle of measured signal and standard signal are Txx and T00, respectively. Then, the the cycle cycle of of the the measured measured signal signal is: is: Then,

T Txx  =N N ∗TT00

(1)(1)

f f x  f00 fx = N N

(2) (2)

and the frequency of the measured signal is: and the frequency of the measured signal is:

ItIt isis known known by by observation observation of of Equations Equations(1) (1) and and (2) (2) that that when when counting counting aa standard standard frequency frequency signal with periodic pulse counting, the frequency of the measured signal can be accordingly. calculated signal with periodic pulse counting, the frequency of the measured signal can be calculated accordingly. However, rotational angular motion of parameters of the projectileinmeasured this paper However, rotational angular motion parameters the projectile measured this paperininclude not include not only the angular velocity information of the projectile rotation, but also real-time angular only the angular velocity information of the projectile rotation, but also real-time angular displacement displacement thethe rotation. the angular displacement information, rotation information ofinformation the rotation.ofFor angularFor displacement information, the rotation anglethe of projectile angle of projectile that one cycle Tx of the measured signal corresponds to 360°. The angular

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displacement is output in a cumulative way by using standard frequency signal xs(t). The period of that one cycle Tx of the measured signal corresponds to 360◦ . The angular displacement is output in each pulse represents a fixed step-progressive accumulation angle , where  = 360/N. In this way, a cumulative way by using standard frequency signal xs (t). The period of each pulse represents a fixed  accumulates to 360° with N cycles. Because the angular displacement that each pulse represents is step-progressive accumulation angle θ, where θ = 360◦ /N. In this way, θ accumulates to 360◦ with N fixed, therefore, the count value N is a stable constant. Variable N stands for the resolution of the cycles. Because the angular displacement that each pulse represents is fixed, therefore, the count value angular displacement. However, in the process of frequency measurement, the frequency of a N is a stable constant. Variable N stands for the resolution of the angular displacement. However, standard signal is changeless, while the count value N varies with the difference of the measured in the process of frequency measurement, the frequency of a standard signal is changeless, while the signal. Consequently, angular displacement information cannot be output effectively. Aiming at the count value N varies with the difference of the measured signal. Consequently, angular displacement problems mentioned above, this paper presents a self-adaptive frequency tracking measurement information cannot be output effectively. Aiming at the problems mentioned above, this paper presents algorithm. On the premise that the value of pulse counting is N, the algorithm realizes measurement a self-adaptive frequency tracking measurement algorithm. On the premise that the value of pulse of angular displacement and angular velocity by changing the frequency of the standard signal selfcounting is N, the algorithm realizes measurement of angular displacement and angular velocity by adaptively. changing the frequency of the standard signal self-adaptively. 2.2. Principle of Self-Adaptive Self-Adaptive Frequency Frequency Tracking Tracking Measurement Measurement 2.2. Principle of The principle principleofofthethe self-adaptive frequency tracking measurement is inshown The self-adaptive frequency tracking measurement methodmethod is shown Figurein 2. Figure 2. Supposing that measured signal is x(t), the standard signal is x s(t). When the pulse counting Supposing that measured signal is x(t), the standard signal is xs (t). When the pulse counting value value is fixed the cumulatively output angular displacement is 180°. Thefrequencies frequenciesof of the the first first ◦ . The is fixed at N, at theN,cumulatively output angular displacement is 180 three cycles cycles of of the the measured measuredsignal signalare aref f1,, ff2 and f3, respectively. The corresponding frequencies of the three 1 2 and f 3 , respectively. The corresponding frequencies of the first three cycles of the standard signal are fs 0, fs1 and fs2, respectively. The half period of the measured first three cycles of the standard signal are fs0 , fs1 and fs2 , respectively. The half period of the measured signal x(t) x(t) is is taken taken as as gate gate time time after after processing processing the the signal signal with with shaping shaping circuit circuit modulation. modulation. signal

x (t ) T1

T2

T3

x s (t )

fs0

fS1 

f1 

fs0 2M1

1800

 00

1800

N  fs0 M1

f2 

3600

00

fS2 

f s1 2M 2

f3 

3600

1800

1800

00

N  fs1 M2

fs2 2M 3

1800

3600

1800

x s (t )

Figure 2. Schematic frequency tracking tracking measurement measurement method. method. Figure 2. Schematic diagram diagram of of the the self-adaptive self-adaptive frequency

Presupposing that that the the initial initial frequency frequencyof ofstandard standardsignal signalisisfsfs0,, the the count count value value is is M M1 during during the the Presupposing 0 1 gate time of the first cycle of the measured signal. Then, the current angular velocity can be calculated gate time of the first cycle of the measured signal. Then, the current angular velocity can be calculated by using using Equation Equation (3): (3): by

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1

f  1  fs0 f 1 1= 2  M ∗ f s0 2 ∗ M11

(3) (3)

In In order order that that the the angular angular displacement displacement can can be be output output effectively effectively after after calculating calculating the the angular angular velocity, requiring that that the thevalue valueofofpulse pulsecounting counting within same period, velocity, when requiring bebe NN within thethe same timetime period, the the frequency of the standard signal (t) should be updated by using Equation frequency of the standard signal xs(t)xsshould be updated by using Equation (4): (4): f s1f s1=

N N ∗ ffs0 s0 M M11

(4) (4)

Since Since the the count count value value of of standard standard signal signal is is M M11 under the current cycle, the angular displacement displacement information From the second cycle on, the detailed process information cannot be be effectively effectively output output yet. yet. From process is is as as follows: follows:

, outputting angular displacement information (1) Updating the the frequency frequencyof ofstandard standardsignal signalasasfs1fs, 1outputting (1) angular displacement information of thethe first cycle in ain cumulative way.way. TwoTwo sawtooth waves (STWs) are output in onein cycle. The value of first cycle a cumulative sawtooth waves (STWs) are output one cycle. The of pulse that each to is N. to The STW corresponds to an angular value of counting pulse counting thatSTW eachcorresponds STW corresponds is first N. The first STW corresponds to an displacement from 0◦ to from 180◦ , and the180°, second STW to ancorresponds angular displacement from angular displacement 0° to and thecorresponds second STW to an angular ◦ to 360◦ . 180 displacement from 180° to 360°. (2) ofthe the first first cycle. cycle. (2) Outputting angular velocity f 11 of (3) (3) Measuring angular velocity of the current cycle by utilizing standard signal Js11 and Equation (3), and updating the frequency of standard signal by using using Equation Equation (4). (4). In this thisway wayofof combining step (2) with (3),frequency the frequency of the standard signal can be In combining step (1), (1), (2) with (3), the of the standard signal can be updated updated self-adaptively, and the angular velocity angular displacement can be self-adaptively, and the angular velocity and angularand displacement information information can be output with a mode which lagsbehind one cycle the measured signal. Simultaneously, the designed aoutput modewith which lags one cycle thebehind measured signal. Simultaneously, the designed system system the outputs the refresh pulse, which the represents thephase initial ofthe every cycle signal. of the outputs refresh pulse, which represents initial zero of zero everyphase cycle of measured measured Theprovide refresh pulse can provide input attitude parameters to a subsequent inertial The refreshsignal. pulse can input attitude parameters to a subsequent inertial navigation system navigation system (INS) cooperating with angular displacement information. (INS) by cooperating withbyangular displacement information. 3. Designof ofAngular Angular Velocity Velocity Sensor 3. Design System System architecture and a specific specific design design scheme scheme of the prototype prototype of the the sensor sensor are are given given in in Figure 3. The sensor consists of five parts, including a data acquisition module, standard signal Figure 3. five parts, including a data acquisition module, standard signal frequency frequency update update module, self-adaptive frequency tracking measurement module and output module.

f ( i 1) 

1  f s (i ) 2  Mi

Mi

f s ( i 1) 

N  f s (i ) Mi

Figure 3. Schematic diagram of the general design scheme of the sensor. Figure 3. Schematic diagram of the general design scheme of the sensor.

3.1. Data Acquisition Module 3.1. Data Acquisition Module Under the conditions of different rotational speeds of a high-speed rotating projectile, an Under the conditions of different rotational speeds of a high-speed rotating projectile, electromagnetic induction coil is employed to obtain the real-time information about the projectile an electromagnetic induction coil is employed to obtain the real-time information about the projectile movement across a geomagnetic field. According to Faraday’s Law of Electromagnetic Induction, a movement across a geomagnetic field. According to Faraday’s Law of Electromagnetic Induction, framework of a bent “I-shape” type is used to wind an uniaxial coil, whose wire diameter is 0.09 mm,

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a framework of a bent “I-shape” type is used to wind an uniaxial coil, whose wire diameter is 0.09 mm, number number of of turns turns is is 9500, 9500, and and resistance resistance is is about about 665 665 Ω. Ω. Simultaneously, Simultaneously, triaxial triaxial coils coils are are installed installed in in number of turns is 9500, and resistance is about 665 Ω. Simultaneously, triaxial coils are installed in aa mutually orthogonal way to realize the measurement of triaxial geomagnetic signals, as shown in mutually orthogonal orthogonal way way to to realize realize the the measurement of triaxial triaxial geomagnetic geomagnetic signals, signals, as as shown shown in in a mutually measurement of Figure 4. Figure 4. Figure 4.

Figure 4. Schematic Schematic diagram diagram of installation method of triaxial coils. Figure 4. Schematic diagram of installation method of triaxial coils.

The relationshipsbetween between thetest test frequency and output voltage of wound the wound coil are The relationships frequency and output voltage of the field field coil are listed relationships betweenthe the test frequency and output voltage of the wound field coil are listed in 1. Table 1. in Table listed in Table 1. Table 1. 1. Relationship of Hz; Relationship between between frequency frequency and and voltage voltage of of output output signals Hz; Table 1. Relationship between frequency and voltage of output signals of coil coil (Frequency: (Frequency: Hz; Output voltage: mV). Output voltage: mV). Frequency Output Voltage Frequency Frequency Output Output Voltage Frequency Frequency Frequency Voltage 4 8.30 45 4 8.30 45 4 15 8.30 45 20.50 50 15 20.50 50 15 25 20.50 50 31.00 55 31.00 55 25 25 31.00 55 35 41.60 65 41.60 65 35 35 41.60 65

Output Voltage Frequency Output Voltage Output Voltage OutputVoltage Voltage Frequency Frequency Output Output Voltage 52.10 75 83.70 52.10 75 83.70 52.10 83.70 57.40 8575 94.30 57.40 8585 94.30 57.40 94.30 62.70 95 104.80 62.70 95 104.80 62.70 104.80 73.20 10095 110.00 73.20 100 110.00 73.20 100 110.00

The linearity of the induction coil is calibrated by linear fitting. The characteristic output curve and The linearity of the induction coil is calibrated by linear fitting. The characteristic output curve and The linearity of thein induction fitting curve are shown Figure 5.coil is calibrated by linear fitting. The characteristic output curve fitting curve are shown in Figure 5. and fitting curve are shown in Figure 5.

Output Outputvoltage voltage(mV) (mV)

120 120 100 100

Output Output characteristic characteristic curve curve of of coil coil Output characteristic curve Output characteristic curve Fitting curve Fitting curve

X: 100 X: 100 Y: 110.1 Y: 110.1

80 80 60 60 40 40 20 20 0 00 0

X: 4 X: 4 Y: 8.802 Y: 8.802

20 20

40 40

60 60

Rotational test frequency of coil (Hz) Rotational test frequency of coil (Hz)

80 80

100 100

Figure 5. Output characteristic curve of coil. Figure 5. Output characteristic curve of coil.

Figure 5 reveals that when employing an induction coil to cut a fixed magnetic field, the Figure 5 reveals that when employing an induction coil to cut a fixed magnetic field, the frequency of the induced magnetic signal is in a range from 4 Hz to 100 Hz. The cutting frequency frequency of the induced magnetic signal is in a range from 4 Hz to 100 Hz. The cutting frequency and induced voltage generated show a good linear relationship with linearity of 0.5% F.S., thereby and induced voltage generated show a good linear relationship with linearity of 0.5% F.S., thereby satisfying the measurement requirements of a large range of rotational speeds for a high-speed satisfying the measurement requirements of a large range of rotational speeds for a high-speed

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Figure 5 reveals that when employing an induction coil to cut a fixed magnetic field, the frequency of the induced magnetic signal is in a range from 4 Hz to 100 Hz. The cutting frequency and induced voltage generated show a good linear relationship with linearity of 0.5% F.S., thereby satisfying the measurement requirements of a large range of rotational speeds for a high-speed rotating projectile. Weak signals induced by the coils are amplified self-adaptively within an appropriate range by using a signal conditioning circuit, so as to output gate signals after half-wave shaping. 3.2. Self-Adaptive Frequency Tracking Measurement Module and Frequency Update Module A digital to analog converter (DAC) is utilized to control voltage-frequency converter (VFC) and make it output a standard signal xs (t). The frequency of the standard signal is used to update Equation (4). The standard signal is updated under the control of the VFC at the initial time of every cycle of the measured signal. The relationship between DAC and VFC is as follows. Assuming that output voltage of DAC is Vi in the i-th cycle, the corresponding output frequency of VFC is fsi . According to the transmission characteristics of the VFC, the connection between these two parameters above is: f si = a ∗ Vi + b

(5)

where a and b are linear constants of the VFC obtained through a multi-point fitting method. Combined with Equation (4), the corresponding output voltage of DAC of the next cycle is: Vi+1 =

N b ( N − Mi ) ∗ Vi + ∗ Mi a Mi

(6)

Based on the approach that an angular velocity measurement model based on Equation (6) is built by taking advantage of FPGA, the value of DAC can be updated. Simultaneously, the count value Mi is latched up, and then the angular velocity can be calculated by using Equation (3). 3.3. Output Module The angular velocity and angular displacement information are both output in the form of voltage by utilizing the DAC. The angular displacement is output in the form of STW. Two STW are output in one cycle. When the pulse counting value reaches N, the DAC outputs a STW signal with presupposed amplitude. The full voltage of each STW corresponds to angular displacements of 180◦ and 360◦ , respectively. The corresponding angular displacement can be calculated by using the output voltage. 4. Experimental Verification 4.1. Linearity Calibration of the VFC The sensitivity of the VFC determines the corresponding relation between the regulating voltage of the DAC and VFC. In order to realize a self-adaptive frequency tracking measurement algorithm, the sensitivity of the VFC is calibrated before experiments. An AD654 of Analog Device Instrument (ADI Company, Norwood, MA, USA) is chosen as VFC, whose relationships between input voltage and output frequency are listed in Table 2. Table 2. Calibration table of VFC (Voltage: V; Frequency: kHz). Voltage

Frequency

Voltage

Frequency

Voltage

Frequency

Voltage

Frequency

Voltage

Frequency

0.1 0.3 0.5 0.7 0.9

4.48 14.20 23.65 33.57 43.17

1.1 1.3 1.5 1.7 1.9

52.72 62.30 71.97 81.50 91.26

2.1 2.3 2.5 2.7 2.9

100.97 110.42 120.25 129.70 139.50

3.1 3.3 3.5 3.7 3.9

149.20 158.70 168.75 178.21 187.91

4.1 4.3 4.5 4.7 4.9

197.66 207.26 216.94 226.78 236.21

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7 of 12 The calibration curve of the VFC’s linearity is obtained according to Table 2, as shown in Figure 6.

Calibration curve of linearity of VFC

Output frequency Output frequency (kHz)(kHz)

250

Measurement points of output Calibration curve of linearity of Fitting curve Measurement points of output Fitting curve

250 200 200 150

VFC

150 100 100 50 50 0 0

0 0

1 1

2

3

Input voltage (V) 2

3

4

5

4

5

Input voltage (V) Figure 6. Calibration curve of linearity of VFC.

Figure 6. 6. Calibration Calibration curve curve of of linearity linearity of of VFC. VFC. Figure

Based on the linear fitting approach, the corresponding output characteristic equation of the VFC,Based whichonalso implies the relationship between regulating voltage of the DAC and VFC is thelinear linearfitting fitting approach, corresponding output characteristic equation the on the approach, thethe corresponding output characteristic equation of theofVFC, expressed as: VFC, which also implies the relationship between regulating voltage theVFC DAC and VFCas: is which also implies the relationship between regulating voltage of the DACof and is expressed expressed as: f  48.2499  V  0.3473 (7) f = 48.2499 ∗ V − 0.3473 (7) f  48.2499  V  0.3473 It can be concluded that the linearity of the selected VFC is 0.052% F.S. This good linearity (7) can It can concluded that the linearity linearity of the the selected selected VFC is 0.052% 0.052% F.S. of This good can satisfy the be high precision demands for measuring the VFC angular velocity high-speed rotating It can be concluded that the of is F.S. This good linearity linearity can satisfy the high precision demands for measuring the angular velocity of high-speed rotating projectiles. projectiles. satisfy the high precision demands for measuring the angular velocity of high-speed rotating projectiles. 4.2. Semi-Physical Semi-Physical Simulation Simulation Experiment—Alternating Experiment—Alternating Magnetic Magnetic Field 4.2. Field In order order to angular accuracy of of the 4.2. Semi-Physical Simulation Experiment—Alternating Magnetic Field In to calibrate calibrate the the angular velocity velocity measurement measurement accuracy the sensor, sensor, simulation simulation experiments are carried out on the basis of using a magnetic shielding device and simulative alternating experiments out on basis ofvelocity using a magnetic shielding deviceof and simulative alternating In orderaretocarried calibrate thethe angular measurement accuracy the sensor, simulation magnetic field generator of Helmholtz coils. The novel sensor researched and developed based on the magnetic field Helmholtz The novel sensor researched andsimulative developedalternating based on experiments aregenerator carried outofon the basis ofcoils. using a magnetic shielding device and designed system is gently put in a simulative alternating magnetic field offield Helmholtz coils ascoils shown the designed system is gently put in a simulative alternating magnetic of Helmholtz as magnetic field generator of Helmholtz coils. The novel sensor researched and developed based on ◦ to ensure in Figure 7. The inclination angle of the fixed table-board is set as 30 that under the action shown in Figure 7. The of the fixedalternating table-boardmagnetic is set as 30° to of ensure that under the designed system is inclination gently putangle in a simulative field Helmholtz coilsthe as of the alternating magnetic field, the triaxial electromagnetic induction coils can all output cutting action of the alternating magnetic field, the triaxial electromagnetic induction coils can all output shown in Figure 7. The inclination angle of the fixed table-board is set as 30° to ensure that under the magnetic inductioninduction signals. Furthermore, the frequency of the signalofgenerator, which represents the cutting signals. Furthermore, frequency the signal generator, which action ofmagnetic the alternating magnetic field, the triaxial the electromagnetic induction coils can all output rotational speed frequency of a projectile under actual working conditions, is set at a range from 5 Hz represents the rotational speed frequency of a projectile actual conditions, is set at a cutting magnetic induction signals. Furthermore, the under frequency ofworking the signal generator, which to 100 from Hz. The intensity of The the applied magnetic field ismagnetic ±1 Gauss. The count pulse value ispulse 1024 range 5 Hz to 100 Hz. intensity of the applied field is ±1 Gauss. The count represents the rotational speed frequency of a projectile under actual working conditions, is set at a per half cycle,per which means that N means = 1024.that N = 1024. value 1024 half cycle, range is from 5 Hz to 100 Hz. which The intensity of the applied magnetic field is ±1 Gauss. The count pulse value is 1024 per half cycle, which means that N = 1024.

(a)

(b)

(a) test platform of the simulative alternating magnetic (b) field: (a) Simulative Figure 7. Experimental Figure 7. Experimental test platform of the simulative alternating magnetic field: (a) Simulative magnetic generator; (b) Experimental test platform. alternating magnetic field: (a) Simulative Figure 7. field Experimental platform of the magnetic field generator;test (b) Experimental testsimulative platform. magnetic field generator; (b) Experimental test platform.

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Under the condition that the frequency of the alternating magnetic field is 100 Hz, the oscillogram Under thesignal condition that the frequency of the of the output of the sensor is shown in Figure 8. alternating magnetic field is 100 Hz, the oscillogram of the output signal of the sensor is shown in Figure 8.

Figure Oscillogramofofthe the sensor output signal with a simulative rotational 100(a)rps: Figure 8. Oscillogram sensor output signal with a simulative rotational speedspeed of 100ofrps: (a) Angular Angulardisplacement displacementinformation; information;(b) (b)The Therefresh refreshpulse; pulse;(c) (c)Angular Angularvelocity velocityinformation. information.

As seen from fromFigure Figure8, 8, there three types of signal output the sensor: Ascan can be be seen there areare three types of signal output by theby sensor: angularangular velocity velocity signal, angular displacement signal and the refresh pulse signal. When the presupposed signal, angular displacement signal and the refresh pulse signal. When the presupposed frequency of frequency of themagnetic alternating magnetic field 100 Hz,velocity the angular velocity signal stable with small the alternating field is 100 Hz, theisangular signal is stable withissmall ripples of less ripples of less than 40 mV. The corresponding frequency of the refresh pulse stabilizes at 100 Hz, than 40 mV. The corresponding frequency of the refresh pulse stabilizes at 100 Hz, which illustrates which illustrates that the designed sensor can accurately detect the initial zero during every cycle and that the designed sensor can accurately detect the initial zero during every cycle and achieve the achieve theoffunction of automatic zeroduring clearing theofprocess of measurement. Simultaneously, function automatic zero clearing theduring process measurement. Simultaneously, two STW two STW representing angular displacement information from 0° to 360° are output between two ◦ ◦ representing angular displacement information from 0 to 360 are output between two refresh pulses. refresh pulses. Experiments are conducted with the preset values listed in Table 3 one after another. Experiments are conducted with the preset values listed in Table 3 one after another. Under different Under different frequencies, the corresponding angular information velocity parameter information and frequencies, the corresponding angular velocity parameter and measurement errors are measurement errors are acquired as follows. acquired as follows. Table Table3.3.Measurement Measurementresults resultsofofangular angularvelocity velocityparameter. parameter. Serial Presupposed Voltage Corresponding Serial Frequency/Hz Presupposed to Angular Voltage Corresponding Number Velocity/V Number Frequency/Hz to Angular Velocity/V 1 5 0.219 0.219 21 10 5 0.430 0.430 32 2010 0.854 3 20 0.854 4 30 1.277 4 30 1.277 55 5050 2.124 2.124 66 7070 2.971 2.971 3.818 77 9090 3.818 4.219 88 100100 4.219

Angular Angular Velocity/rps Velocity/rps 4.9851 4.9851 9.9709 9.9709 19.9430 19.9430 29.9159 29.9159 49.8708 49.8708 69.8258 69.8258 89.7807 89.7807 99.7699 99.7699

Measurement Measurement Error/% Error/% 0.298 0.298 0.291 0.291 0.285 0.285 0.280 0.280 0.258 0.258 0.249 0.249 0.244 0.244 0.230 0.230

RMS RMS Noise/mV Noise/mV 36 36 35 35 32 32 35 35 30 30 32 32 34 34 30 30

RMS noise: root-mean-square value RMS noise: thethe root-mean-square valueofofnoise. noise.

As Table 3 shows, along with the change of alternating frequency of the magnetic field, the As Table 3 shows, along with the change of alternating frequency of the magnetic field, the sensor sensor can realize angular velocity measurements within an extremely high dynamic range from 5 can realize angular velocity measurements within an extremely high dynamic range from 5 Hz to Hz to 100 Hz, with a maximum measurement error of less than 0.3%. 100 Hz, with a maximum measurement error of less than 0.3%.

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4.3.Physical PhysicalSimulation SimulationExperiment—Three-Axis Experiment—Three-AxisFlight Flight Turntable Turntable 4.3. 4.3. Physical Simulation Experiment—Three-Axis Flight Turntable In order order to to calibrate calibrate the the angular angular displacement displacement measurement measurement accuracy accuracy of of the the sensor, sensor, test test In In orderwere to calibrate the angular displacement measurement accuracycontrol of theflight sensor, test experiments conducted using a three-axis position-rate-swing temperature turntable. experiments were conducted using a three-axis position-rate-swing temperature control flight experiments were conducted a three-axis temperature control flight ◦ . The angular The highest test frequency theusing turntable is turntable 1000◦ /s,position-rate-swing with a rate precision error of ±0.01 turntable. The highest test of frequency of the is 1000°/s, with a rate precision error of ±0.01°. turntable. The highest test frequency of the turntable is 1000°/s, with a rate precision error of ±0.01°. velocity sensor is fixed at theisheart asturntable, shown in as Figure 9. The turntable is controlled The angular velocity sensor fixed of at the the turntable, heart of the shown in Figure 9. The turntable The angular velocity sensor is fixed at the heart of the turntable, as shown in of Figure 9. The turntable ◦ . The and adjusted to skew 30 rotational test frequency of the inner frame the turntable is set at is controlled and adjusted to skew 30°. The rotational test frequency of the inner frame of the turntable isdifferent controlled and adjusted to skew 30°. The rotational test frequency of the inner frame of the turntable angularangular rotationrotation frequencies. is set at different frequencies. is set at different angular rotation frequencies.

(a) (a)

(b) (b)

Figure 9. Experimental three-axis flight turntable test platform: (a) Three-axis turntable; (b) Fixed Figure9. 9.Experimental Experimentalthree-axis three-axisflight flightturntable turntabletest testplatform: platform:(a) (a)Three-axis Three-axisturntable; turntable;(b) (b)Fixed Fixed Figure platform of the sensor. platform of the sensor. platform of the sensor.

Under the condition that the rotational test frequency of the inner frame of the turntable◦ is Under condition that thatthe therotational rotational frequency of inner the inner the turntable is Under the the condition testtest frequency of the frameframe of the of turntable is 1000 /s, 1000°/s, an oscillogram of the sensor output signal is shown in Figure 10. 1000°/s, an oscillogram of the output sensor signal outputissignal is in shown in10. Figure 10. an oscillogram of the sensor shown Figure

(a) (a) (b) (b) (c) (c)

Figure 10. Oscillogram of the sensor output signal with a simulative rotational speed of 1000°/s: (a) Figure Oscillogram ofof thethe sensor output signal with a simulative rotational speed of 1000°/s: Figure10. 10. Oscillogram sensor signal with simulative rotational speed of 1000◦(a) /s: Angular displacement information; (b) output The refresh pulse; (c)a Angular velocity information. Angular displacement information; (b) The refresh pulse; (c) Angular velocity information. (a) Angular displacement information; (b) The refresh pulse; (c) Angular velocity information.

It can be seen from Figure 10 that when rotational test frequency of the turntable is 1000°/s, the It can be seen from Figure 10 that when rotational test frequency of the turntable is 1000°/s, the ◦ /s, It can be seen from of Figure 10 thatpulse whenstabilizes rotational test frequency the turntable is 1000can corresponding frequency the refresh at 2.770 Hz, whichofshows that the sensor corresponding frequency of the refresh pulse stabilizes at 2.770 Hz, which shows that the sensor can the corresponding frequency of the refreshevery pulsecycle stabilizes at 2.770 Hz, shows that the sensor accurately detect the initial zero during and achieve the which function of automatic zero accurately detect the initial zero during every cycle and achieve the function of automatic zero clearing during the measurement. Simultaneously, the output STW of the sensor is stable, the initial clearing during the measurement. Simultaneously, the output STW of the sensor is stable, the initial zero of the STW and the refresh pulse have a one-to-one correspondence. The output DC voltage of zero of the STW and the refresh pulse have a one-to-one correspondence. The output DC voltage of

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can accurately detect the initial zero during every cycle and achieve the function of automatic zero Sensors 2016, 16, 1625 of 12 clearing during the measurement. Simultaneously, the output STW of the sensor is stable, the 10 initial zero of the STW and the refresh pulse have a one-to-one correspondence. The output DC voltage of the the regulation DAC is steady with small ripples, which illustrates that the sensor has stable regulation DAC is steady with small ripples, which illustrates that the sensor has stable performance, performance, and the obtained angular displacement is accurate. and the obtained angular displacement is accurate. The voltage information of the angular displacement signal, obtained through Figure 10, is The voltage information of the angular displacement signal, obtained through Figure 10, converted into angle information (as shown in Figure 11a) by integrating with a time horizon of 1 s is converted into angle information (as shown in Figure 11a) by integrating with a time horizon (as shown in Figure 11c). The rotational frequency of the turntable is 1000°/s, which means that the of 1 s (as shown in Figure 11c). The rotational frequency of the turntable is 1000◦ /s, which means that angular displacement accumulates 1000° in 1 s. When integrating the actual angular displacement the angular displacement accumulates 1000◦ in 1 s. When integrating the actual angular displacement signal, the error is 0.1°, thus satisfying the measurement requirements. signal, the error is 0.1◦ , thus satisfying the measurement requirements. Angular displacement

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Time (s) Angular displacement accumulation 1000 X: 1.069 Y: 999.9

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◦ /s. Figure Figure11. 11. Accumulative Accumulative calculation calculation graph graph of ofangular angulardisplacement displacementat at1000 1000°/s.

according to presupposed rotation frequencies. The Multi-group experiments experiments are arecarried carriedout out according to presupposed rotation frequencies. corresponding experimental test test results are given in Table 4. 4. The corresponding experimental results are given in Table Table 4. Experimental test results of three-axis flight turntable. Table 4. Experimental test results of three-axis flight turntable. Serial Serial Number Number 1 1 2 2 3 3

Rotational Frequency of Rotational Frequency of Three-Axis Turntable/°/s Three-Axis Turntable/◦ /s 600 600 900 900 1000 1000

Angular Angular Velocity/rps Velocity/rps 1.6667 1.6667 2.5020 2.5020 2.7770 2.7770

Angular Angular Displacement/°/s Displacement/◦ /s 599.8 599.8 900.2 900.2 999.9 999.9

Measurement Measurement Error/° ◦ Error/ 0.2 0.20.2 0.2 0.1 0.1

On the basis of the analysis of Table 4, it is concluded that when the inner frame of the turntable Onat the600, basis the analysis Table 4, it isthe concluded that when theofinner frame of displacement the turntable rotates 900ofand 1000°/s, of respectively, measurement errors the angular ◦ rotates at through 600, 900the andsensor 1000 are /s, all respectively, the thereby measurement errors the angular acquired less than 0.2°, satisfying theof actual angular displacement displacement ◦ , thereby satisfying the actual angular displacement acquired through the sensor are all less than 0.2 measurement requirements for a high-speed rotating projectile. measurement requirements for a high-speed rotating projectile. 5. Conclusions 5. Conclusions Aiming at meeting the demands for measuring angular motion parameters of high-speed Aiming at meeting demands measuring angular motion parameters high-speed rotating rotating projectiles, thisthe paper puts for forth a new method for measuring the of angular velocity and projectiles, this paper puts forth a new method for measuring the angular velocity and angular angular displacement parameters of the rotation of a projectile based on the electromagnetic displacement parameters of the rotation of a projectile based on the electromagnetic induction induction principle, and also designs the corresponding sensor. To begin with,principle, triaxial electromagnetic induction coils are used to acquire the cutting geomagnetic signals of the projectile. Next, a self-adaptive frequency tracking measurement algorithm, which combines pulse counting with a way of updating the frequency of a standard signal self-adaptively, is proposed by utilizing DAC and VFC to calculate the angular velocity and angular displacement information, and a principle

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and also designs the corresponding sensor. To begin with, triaxial electromagnetic induction coils are used to acquire the cutting geomagnetic signals of the projectile. Next, a self-adaptive frequency tracking measurement algorithm, which combines pulse counting with a way of updating the frequency of a standard signal self-adaptively, is proposed by utilizing DAC and VFC to calculate the angular velocity and angular displacement information, and a principle prototype of the sensor is designed based on FPGA. Third, angular velocity performance tests are carried out by using a simulative alternating magnetic field generator of Helmholtz coils, within the alternative frequency range from 5 rps to 100 rps. The measurement errors are all less than 0.3%. Finally, angular displacement performance tests are conducted by utilizing a three-axis position-rate-swing temperature control turntable, in a range from 1 rps to 3 rps. The angular displacement measurement errors are all lower than 0.2◦ . The experimental results both show that the sensor can measure angular motion information within a range from 1 rps to 100 rps, and can realize real-time measurements of the angular motion parameters of a high-speed rotating projectile with high precision. Two research topics are scheduled to be developed in the near future. On the one hand, the final purpose of the sensor is to provide motion parameters for attitude determination of high-speed rotating projectiles and geomagnetic navigation. How to construct a navigation model and match with the interface of the current navigation system would be a direction for further research. On the other hand, the stability and balance of the self-adaptive frequency tracking measurement model should be analyzed to apply the available sensor for whole trajectory measurement of high-speed rotating projectiles. Acknowledgments: This work is partly supported by grants from the National Science Foundation of China (No. 61227003). It is also supported by the 973 Program (No. 2013CB311804). Author Contributions: Jian Li designed and implemented the self-adaptive frequency tracking measurement algorithm based on FPGA, and conducted semi-physical angular velocity simulation experiments. Dan Wu designed the triaxial electromagnetic induction coils, researched and developed the angular velocity sensor as well. Yan Han designed the physical angular displacement simulation experiments. Conflicts of Interest: The authors declare no conflict of interest.

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