Modeling and error compensation of MEMS gyroscope dynamic output data within the whole temperature range

Yanshun Zhang, Shuwei Wang

School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing, 100191, China

E-mail: zhangyanshun@buaa.edu.cn,wsw_phenix@sina.com

Keywords:MEMS Gyroscope, Dynamic Modeling, RBF neural network, Error Compensation.

Abstract.In this paper, the output data of MEMS gyroscope ADRX150 under different input

angular velocity within the temperature range of −30~50is collected and analyzed. Taking the

nonlinear and random characteristics of the output data of MEMS gyroscope ADRX150 into

account, the dynamic output data model based on RBF neural network is established, which is

training and taking the performance testing with the experimental data collection. The results

indicate that, the model has high accuracy and good generalization ability.

Introduction

MEMS gyroscope is one of the leading-edge technology , combined withprecision machinery,

microelectronics, semiconductor integrated circuit technology and other new technologies . With

features of low cost, small size and easy-to- integrate, MEMS gyro has developed vigorously in

many countries, and widely applied in aviation, weapons and civil fields[1, 2]. However, MEMS

gyros’ main materials are polysilicon or crystal silicon. In size condition, silicon has a lot of

physical and mechanical properties different from macroeconomic conditions. The variations in the

ambient conditions such as the temperature also add errors in the gyros’ output. So, the MEMS gyro

is characterized by nonlinear and random behaviors of its output [3].

The document[4] analyzedthe error characteristics of MEMS gyroscopefrom the perspective of

signal analysis. And the document[5,6] talked about MEMS gyro scale factor error and the

modeling and compensation method of temperature error. While the document[7] made researches

on least squares method used for the modeling of MEMS gyro scale factor, bias and error

compensation at room temperature. These studies play a role in improving the precision of MEMS

gyro. However, under the action of ambient temperature and angular velocity, MEMS gyroscopes

show severe non-linear error, which changes in the whole measuring range. The non-linear error is

difficult to express by analytic functions, and the accuracy of the model established by polynomial

fitting method is not high as well. The intelligent learning through the study of experimental

samples achieves the approximation of complex nonlinear function, which can be used in the

modeling and compensation of the output data error of MEMS gyroscope. Based on the above

technical background, this paper used MEMS gyros ADRX150 as the research object for the

following research, considering the ambient temperature and angular velocity which are the prime

cause of the gyroscope output error. With ambient temperature and output voltage of gyro as a

model input, we established ADRX150nonlinear dynamic output angular velocity model based on

RBF neural network,and compensated for error, after studying the training samples consisted of

experimental data.

The output signal model of ADXRS150

The ADXRS150 operates on the principle of a resonator gyro, which uses analog devices’

surface-micromachining process to make a functionally completed and low cost angular rate sensor

integrated with all of the required electronics on one chip. Its working prinsiples are as shown in

Fig. 1.

Advanced Materials Research Vols. 311-313 (2011) pp 768-771

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Fig.1 The working prinsiples of ADXRS150

Under the action of the drive voltage + sin, the movement of the inspection quality driving

by the inner frame produced the angular vibration frequency of . Then if there is an angular

velocity input around framework of the plane normal, the role of Coriolis force generated the

rotating of the outer frame. The rotation caused the value of detecting changes in capacitance of the

capacitor (∆C). After processing, we can get the voltage signal ∆proportional to Ω.

∆ =

( !" )$Ω(1)

Where % is the gyro quality factor, & is the moment of inertia of the inner frame,

&' , &)'respectively is the y-axis moment of inertia of the inner and outer frame,*+is the swing angle

frame, ,- is the amplification factor of the detection circuit,,. is the transfer function of the

annunciator.

The change of temperature can cause changes of mechanical parameters and detection circuit

parameters, which lead to random errors in gyro output and the ,.became nonlinear under different

angular velocity input,contributing to the nonlinear scale factor of ∆ andΩ. The error factor

discussed above is interacted and mutual coupling, as a result, it is difficult to model and

compensation with analytical method.

Experimental proposal

In this paper, the mapping relationship between gyro output voltage, ambient temperature and the

output angular velocity of ADXRS150, is established in the principle of RBF neural network, and

the error compensation is according to the actual output angular velocity of ADXRS150. A single

speed turntable in the temperature control box is required in this test. The output voltage of gyro

under different ambient temperature and angular velocity is collected for the following purposes:

1.part of the data collected can be used as samples of RBF neural network training, for the

establishment of model. 2. Another part is used as the test data of the model, for validating the

model and taking the performance testing.

The collection and analysis of the dynamic output data of ADXRS150 within the whole

temperature range

The experimental setup mainly includes temperature control box, turntable and data acquisition and

processing system. The temperature control box is used to provide the required testing temperature,

and the reference angular velocity is provided by the turntable. The dynamic range of turntable is

±600°/3, the angular resolution is 0.001°/3, the range of the temperature control box is−70~150,

the accuracy of temperature control is±0.2. Data acquisition and processing system includes data

acquisition circuit and the data processing computer. ADXRS150 is selected as the A/D module for

signal acquisition. The 16-bit A/D convertor completes analog signal quantification, transmitting

the quantized digital data to the computer through the serial port. The computer storages the data,

and runs the MATLAB program for the gyro output modeling, error compensation and model

validation.

tUU ωsin10

+

ZΩ xθ

sk

C∆

Vk

u∆gf

v

Advanced Materials Research Vols. 311-313 769

°C °C °C

The outputs of the ADXRS150 are analog voltages that are proportional to the input angular rate.

The nominal scale factor of the ADXRS150is8 = 0.01259/°/:, and zero-bias voltage isb =

0.0317V (corresponding to angular velocity 2.536°/3 ).

Taking the practical applications of the gyroscope into account, the range of testing temperature

is chosen from −30 to50, the range of the angular velocity is chosen as±120°/3. The selected

testing points of temperature are−30,−20,−10, 0, 10, 20, 30, 40, 50 . The

output data of gyroscope are respectively collected under the different reference angular velocity at

each testing point of temperature. The reference angular velocities for RBF neural network

modeling are ±120°/3, ±100°/3, ±60°/3, ±30°/3, ±10°/3, ±0.1°/3 , and the reference angular

velocities for model validation are ±40°/3, ±20°/3, ±15°/3, ±5°/3. The data collected are shown

in Fig.2, Fig.3, Fig.4, Fig.5.

Fig.2 The angular velocity Fig.3The error of the angular Fig.4The angular velocity

at the model point velocity at the model pointat the testing point

Fig.5The error of the angular velocity Fig .6 The fitting error of the model Fig. 7The error of angular velocity at the testing pointof neural

networkat testing point

In the Fig.2 and Fig.3, the maximum angular velocity error of the data for modeling is −0.708°/3,

and the mean square error is 0.206°/3. As for the data for testing in Fig.4 and Fig.5, the maximum

angular velocity error is −0.794°/3, and the mean square error is 0.189°/3. It can be seen from the

figures above that under the action of the ambient temperature and the input angular velocity, the

bigger error of the angular velocity of ADXRS150, the more difficult to express the error

distribution by analytic functions.

The neural network modeling of the output signal of ADXRS150

The method of neural network can ignore specific processes or the physical parameters of the

system. The complex nonlinear mapping between the input and output data can be established by

learning from the training samples, which has good generalization ability and has been widely used

in the modeling of nonlinear system. RBF Neural Networks is a forward network of good

performance, with features of the best performance of global approximation, quick and easy

training method, and the absent of local optimization problem. In this paper, the method of RBF

neural network is applied in the establishment of the nonlinear mapping ( = @(, A)) of the output

voltage of gyro, the ambient temperature and the true value of the angular velocity , which help

to realize the compensation of error. Therefore, we choose B = (, A) as the input vector, while

C = Das the output vector. The training error of neural network is chosen as5 × 10FG, and the spread

constant of neural network is0.96. Finally, the fitting error of neural network after training is shown

in Fig. 6.

-50

0

50

-2

0

2-200

0

200

temperatureoutput voltage

angula

r velo

city

-500

50

-2

0

2-1

-0.5

0

0.5

err

or

of

an

gu

lar

ve

loc

ity

temperatureoutput voltage -50

0

50

-1

-0.5

0

0.5-50

0

50

output voltage temperature

err

or

of

angula

r velo

city

-50

0

50

-1

-0.5

0

0.5-0.8

-0.6

-0.4

-0.2

0

err

or

of

angula

r velo

city

temperatureoutput voltage

-50

0

50

-2

0

2-0.1

0

0.1

temperatureoutput voltage

fitt

ing e

rror

-40-20

020

4060

-1

-0.5

0

0.5

-0.1

-0.05

0

0.05

0.1

0.15error of angula

r velo

city

temperatureoutput voltage

770 Advanced Materials and Processes: ADME 2011

In Fig.6, the maximum fitting error of the model is 0.0737°/3, while the minimum fitting error is

−0.073°/3, and the Mean square deviation is 0.023°/3. This shows that the model using neural

network method well established the mapping between the output voltage of gyro, the ambient

temperature and the true value of the angular velocity, namely , we can estimateat high

accuracy according to the output voltage of gyro and the ambient temperature.

Validation of the model and accuracy test

We can get the error of the output at the testing point by putting the collected output voltage of gyro

and temperature at thetesting point into the model of RBF neural network.

In Fig.7, the maximum angular velocity error of gyro after compensation is 0.141°/3, and the

mean square deviation is 0.059°/3. Compensated maximum gyro error and mean square error are

respectively 17.6% and 31.2°/3 of the value before compensation. Data processing results show

that the RBF neural network model applied in this paper has good generalization ability, and can

achieve high-precision gyro error compensation within the whole measuring range of the

gyroscope.

Conclusion

This paper proposed the method based on RBF neural network for modeling and error

compensation of the dynamic angular velocity of ADXRS150 within the whole temperature range,

aiming at the characteristics of the output signal of ADXRS150. In the experiment, we trained the

RBF neural network, validated the model and had the generalization test with the collected data.

Data processing results show that, the RBF neural network model applied in this paper showing the

mapping between the output voltage of gyro, the ambient temperature and the true value of the

angular velocity, has high accuracy and good generalization ability. It can achieve high-precision

gyro dynamic error compensation within the whole measuring range of the gyroscope, which

improved the precision of gyroscope. The method proposed in this paper can also be used for other

sensor nonlinear error modeling and compensation.

Acknowledgment

This research has been supported by 863 projects of China (Grant No. 2006AA06Z223，Grant No.

2008AA121302) and the National Natural Science Foundation of China (Grant No.60736025).

References

[1] Hanse, J.G., “Honeywell MEMS Inertial Technology & Product Status”, Position Location and

Navigation Symposium, 2004, pp.43 – 48.

[2] Jacques Leclerc, “MEMs for Aerospace Navigation”, Aerospace and Electronic Systems

Magazine, IEEE, the 14th Saint Petersburg International Conference on Integrated Navigation

Systems, Saint Petersburg, Russia, 2007, 2007,22(10):31-36.

[3] R. Zhu, D. Sun, Z.Y. Zhou, D.Q. Wang: Measurement. Vol. 40(2007), p.322

[4] N. E. Sheimy, H. Y. Hou, X.J.Niu: IEEE Transactions on instrumentation and

measurement.Vol.57(2008),p.140

[5] J.L.Li, J.C.Fang, W.Sheng: Journal of Beijing University of Aeronautics

andAstronautics.Vol.33(2007),p.1064(In Chinese)

[6] J.C.Fang, J.L.Li :IEEE Transactions on instrumentation and measurement.Vol.58(2009), p.2923

[7] L. Sahawneh, M.A. Jarrah. Development and calibration of low cost MEMS IMV for UAV

applications[J]. Proceeding of the 5th International Symposium on Mechatronics and its

Applications (ISMA08), Amman, Jordan, May 27-29, 2008, 1-9.

Advanced Materials Research Vols. 311-313 771

Advanced Materials and Processes: ADME 2011 10.4028/www.scientific.net/AMR.311-313 Modeling and Error Compensation of MEMS Gyroscope Dynamic Output Data within the Whole

Temperature Range 10.4028/www.scientific.net/AMR.311-313.768

DOI References

[3] R. Zhu, D. Sun, Z.Y. Zhou, D.Q. Wang: Measurement. Vol. 40(2007), p.322.

http://dx.doi.org/10.1016/j.measurement.2006.05.020 [4] N. E. Sheimy, H. Y. Hou, X.J. Niu: IEEE Transactions on instrumentation and measurement. Vol.

57(2008), p.140.

http://dx.doi.org/10.1109/TIM.2007.908635 [6] J.C. Fang, J.L. Li : IEEE Transactions on instrumentation and measurement. Vol. 58(2009), p.2923.

http://dx.doi.org/10.1109/TIM.2009.2016780