An MEMS gyroscope detects input angular rate signals by using the Coriolis force [1
]. The precision of a MEMS gyroscope has improved a great deal over the past years, but poor temperature characteristics limit its application. This is due to three aspects: the silicon structure has a high temperature coefficient; the silicon-glass bonding style and package cause thermal residual stress; and the monitoring system sometimes drifts with temperature. So, it can be concluded that the methods of MEMS gyroscope temperature compensation should comprise four aspects, as follows.
Structure improvement: A temperature compensation fork was arranged in the MEMS gyroscope structure to compensate the influence of temperature in [3
], and in the temperature range of −20 to 80 °C, the maximum relative error of the resonant frequency was reduced from 16.3% to 3.1%. Reference [4
] described the MEMS gyroscope structure compensation with a disturbance estimator and indicated that the architecture’s imperfect fabrication and asymmetry can also decrease the temperature characteristics. A thermal stress structure was utilized in a cylindrical gyroscope to improve temperature performance in [5
], and the open-loop temperature drift rate was reduced by about 2 thirds after the structure was optimized. Two epoxy materials were filled between the structure substrate and package to decrease the quality factor temperature coefficient of the gyroscope in [6
], and the temperature coefficient of the drive and sense mode resonant frequencies were 124.1 ppm/°C and −106.9 ppm/°C. In [7
], a novel stress compensation method was proposed to assist conventional temperature compensation to improve the long-term drift of MEMS gyroscopes, and a long-term (around 3 hours) test showed that the angle random walk was 0.15°/√h, and bias instability was 1°/h. Reference [8
] presented an architecture which had a higher temperature stability and robustness; in this structure, the drive-mode operational frequency and the sense-mode bandwidth can be set independently, and the uncompensated temperature coefficients of bias and scale factor were 313 °/(h·°C) and 351 ppm/°C, respectively. Reference [9
] presented an example of temperature compensation in the silicon resonator’s architecture by using an I-shaped beam. The structure improvement requires design, fabrication, packaging and other processes, which requires a long-term research cycle.
Software temperature compensation: Multi-resolution analysis was employed to compensate temperature drift and de-noising. In [10
], the radial basis function (RBF) neural network method was used in an ASDXRS150 sensor with the −40 °C to 60 °C temperature range, and the compensation results showed that the method improved the maximum gyro error and mean square error value by 17.6% and 31.2%, respectively. A wavelet transform algorithm was reported in [11
] to reduce the temperature drift of an MEMS gyroscope. Reference [12
] employed lifting wavelet transform method to improve the noise performance of an MEMS gyroscope. Reference [13
] processed the output data with a linear compensation algorithm by using the relationship between the temperature inside the gyroscope’s shell and the output data; after the compensation, the temperature coefficients of bias stability improved from 229.1 °/(h·°C) to 35.7 °/(h·°C). Reference [14
] introduced an integrated electromechanical–thermal error model and employed a least-squares algorithm to compensate the bias drift caused by temperature and acceleration. Variational mode decomposition (VMD) and genetic-Elman neural network methods are used to compensate temperature drift and denoising in [15
] and [16
]. A radial basis function neural network based on the genetic algorithm with Kalman filter was reported in [17
], and the bias stability and angle random walk of the MEMS gyroscope was improved from 178 °/h to 1.6 °/h and 5.89°/√h to 0.71°/√h, respectively, within the −40 °C to 60 °C temperature range. Reference [18
] used a high-order polynomial to compensate the bias of a double H quartz tuning fork gyroscope on a digital signal processing platform; the variation of the bias in the range −40 °C to 80 °C reduced from 300 mV to 0.2 mV because of the compensation. The software compensation methods usually cannot deal with the output data online and lack real-time capability; thus, they are better used in the data analysis research area.
Hardware temperature compensation: A hardware temperature compensation method based on a circuit amplifier was proposed in [19
], and through the temperature variable resistor temperature compensation, the scale factor and temperature bias coefficient were optimized from 693 ppm/°C to 250 ppm/°C and from 103.89 °/(h·°C) to 9.70 °/(h·°C), respectively. Bandwidth temperature compensation methods were proposed in [20
] and [21
], and the bandwidth was improved from 13 Hz to more than 100 Hz. The hardware temperature compensation methods have better real-time characteristics and a short development cycle.
Temperature-control: Reference [22
] proposed a temperature-control system to steady the ambient temperature to improve the gyroscope’s temperature performance. On-chip temperature control technology was utilized to decrease the MEMS gyroscope’s temperature drift in [23
]; the micro thermal resister, heater and a thermal isolate package were employed to form the on-chip temperature control system. Those methods require a good deal of power consumption and are not fit for low-power application regions.
In this paper, a temperature compensation method based on drive mode vibration characteristics is proposed to improve gyro precision, and the results are analysed. This paper is organized as follows: the structure of the MEMS gyroscope and the monitoring system are introduced in Section 2
; the temperature compensation method is shown in Section 3
; Section 4
shows the temperature experiment; and finally, the conclusion is given in Section 5
4. Temperature Compensation Experiments
The MEMS gyroscope is fixed on the turntable in a temperature chamber, which is shown in Figure 9
. The turntable is employed to calibrate the scale factor of the gyroscope, and the temperature chamber is utilized to provide different temperature environments. The power supply is used to provide +10 V, −10 V and ground voltage, and the multimeter is used to pick up the output signal of the gyroscope. Temperature variable resistors RT
are employed in the “Scale Factor” and “Bias Com” modules to reduce the scale factor and temperature bias drift. Another temperature-variable resistor, Rtr
, is employed to measure the real-time temperature inside the gyroscope shell, and the temperature value is picked up with the Vout
value synchronously. The temperature range in this paper is set as −40 °C to 60 °C, and the scale factor is tested every 20 °C. Each temperature experiment is repeated three times to verify the repeatability of the method.
The temperature compensation process is divided into three steps:
Firstly, the temperature drift of the scale factor is tested based on which voltage module parameters are set (which has already been discussed in Section 3.3
Secondly, the scale factor temperature compensation method is tested, and the result curves are shown in Figure 10
; also, three repeatability experiments are finished, and the variation of the three experiments are 1.485%, 1.623% and 1.824%, respectively, with an average value of 1.577%.
Thirdly, the temperature bias drift is tested based on which voltage module parameters are set (which has already been discussed in Section 3.4
Fourthly, the temperature bias compensation method is applied, and the three repeatability results are shown in Figure 11
; the curves show that the repeatability of the compensation method is good. The results of bias before and after temperature compensation are shown in Figure 12
. The variation of the three bias temperature compensation experiments are 1.914%, 1.868% and 1.912%, respectively, and the average value is 1.913%. The Allan derivation curves before and after temperature variation are shown in Figure 13
, and the full-temperature bias stability (BS) and angular rate walking (ARW) parameters also improved from 29.52 °/h to 19.59 °/h and from 1.43 °/h/√Hz to 1.20 °/h/√Hz, respectively. Table 6
shows MEMS gyroscope temperature compensation test result.
In this study, the MEMS gyroscope temperature compensation method is investigated by using drive mode vibration characteristic compensation. The gyroscope working principle including drive mode and sense mode loops are analyzed, and the drive loop amplitude controlling voltage reference is set as the compensation point. Based on this, the scale factor temperature compensation circuit is designed and simulated. Then, the output level of the sense loop is investigated, and the temperature bias compensation circuit is designed and simulated. After that, temperature experiments are arranged, and the results show that, using the method proposed in this paper, the variation of the scale factor improves from 3.680% to 1.577% with a temperature range from −40 °C to 60 °C (enhanced by 57.14%). Furthermore, the bias variation improves from 3.880% to 1.930% (enhanced by 52.25%). The bias stability and angular rate walking parameter are also optimized (45.97% and 16.08%) in the benefit of the scale factor improvement. The experiment results verify the method proposed in this paper.