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This paper presents an approach for realizing a phase difference measurement of a new gyro. A silicon micromachined gyro was mounted on rotating aircraft for aircraft attitude control. Aircraft spin drives the silicon pendulum of a gyro rotating at a high speed so that it can sense the transverse angular velocity of the rotating aircraft based on the gyroscopic precession principle when the aircraft has transverse rotation. In applications of the rotating aircraft single channel control system, such as damping in the attitude stabilization loop, the gyro signal must be kept in sync with the control signal. Therefore, the phase difference between both signals needs to be measured accurately. Considering that phase difference is mainly produced by both the micromachined part and the signal conditioning circuit, a mathematical model has been established and analyzed to determine the gyro's phase frequency characteristics. On the basis of theoretical analysis, a dynamic simulation has been done for a case where the spin frequency is 15 Hz. Experimental results with the proposed measurement method applied to a silicon micromachined gyro driven by a rotating aircraft demonstrate that it is effective in practical applications. Measured curve and numerical analysis of phase frequency characteristic are in accordance, and the error between measurement and simulation is only 5.3%.

With the increasing development of MEMS and inertial guidance technology, all kinds of micromachined gyros have successfully developed and are gaining increasing popularity for shared use in military and civil applications [

This kind of gyro is difficult to design and manufacture and the cost is high. In order to avoid the difficulties brought about by the driving part, this paper puts forward a novel gyro that uses the rotation of the aircraft itself as a driving part. In this paper, the studied gyro, which has been fabricated on s monocrystalline silicon wafer by means of bulk micromachining manufacturability techniques, belongs to the gyro without driving structure class. Since there is no driving structure, the structure is simple and easy to process [

In the practical applications, dynamic characteristics of micromechanical gyroscope is the key [_{k}_{g}_{s}_{k}_{g}_{s}_{g}_{g}_{g}_{k}_{g}

Because the gyro signal is a negative feedback, the gyro signal and control signal need to be in phase. Therefore, it is a key that the phase difference be accurately measured so as to adjust and compensate the phase in practical applications.

The rotating aircraft-driven silicon micromachined gyro is installed on the rotating aircraft. In

Angular momentum is same in the direction as the

Waveforms in _{x}_{y}_{z}_{T}

_{1} is a integration constant, which value is determined by the initial conditions, _{n}

Then, the amplitude of the angular vibration can be written as:

The phase difference is:

In the chip process, we have four steps. The first step shapes a movable section, the second step etches the damping bars, the next is buffer layer etching on the beams and the last step forms the silicon pendulum. The masks of the four steps and chip are shown in

Using the above four step etching, the final chip is obtained. A picture of the chip is shown in

Considering that it is convenient to calculate the torsion stiffness of an elastic torsion beam, it is supposed that on processing the torsion angle is proportional to the length of the beam, warping of the cross sections of elastic torsion beam are same, and values are same, but in opposite direction, for the torsion moment of the two ends of an elastic torsion beam.

Under the condition of the above assumptions, using elastic mechanics, the torsion stiffness with rectangular cross section can be obtained by:

Practically the torsion angle _{T}

If

The displacement of the silicon pendulum edge node is far less than both the lateral size and gap relative to the electrodes in the torsion motion of

When a rectangular plate with length

Since the infinite series can quickly converge, the damping coefficient is approximately equal to the first term of

The chosen relevant dimensions are: ^{−}^{6}_{a}·s, thus, the damping factor of the silicon pendulum can be figured out:

Moment of inertia (_{x}_{y}_{z}

In order to analyze the phase-frequency characteristics of the Si micromachined gyro driven by a rotating aircraft, the vibration of the silicon pendulum can be represented as a SISO system, of which the excitation signal is given by

Using the Laplace transformation, the transfer function of

Then, the frequency characteristic is:

Finally, we can easily obtain the phase-frequency characteristic:

In actual applications, the working frequency (ω) is less than the natural frequency of _{n}

The phase-frequency characteristics are simulated and plotted for a Si micromachined gyro driven by a rotating aircraft. The plotted curve is shown in

In

The Si micromachined gyro principle block diagram is shown in

We chose an AD620 chip, which constitutes the differential amplifier circuit. We connect the gyro's sensed signal with its noninverting and inverting inputs. Its magnification times are adjusted by a resistor cross input. Meanwhile, we add a LPF at the noninverting and inverting inputs, respectively. The transfer function of the differential amplifier circuit is written as:

Because the gyro's working frequency ranges from 1 Hz to 50 Hz, the band width of the BPF is designed to be 81 Hz. The transfer function for BPF is:

In order to filter the noise, we design the second order LPF. Its cut-off frequency is 63.5 Hz and transfer function is:

For the gain circuit, its function is mainly amplifying the signal and large transmission bands. The peak gain is 17.3 dB, so the transfer function is designed to be:

Then, for the entire conditioning circuits, the transfer function is:

According to

According to the amplitude-frequency characteristics of

The model structure built according to the working principles of the gyro is shown in

In _{T}

The driving signal frequency is set to 15 Hz and simulates the aircraft spin frequency. Because the input drive signal simulates the aircraft rotation driving, when the aircraft has a transverse angular velocity, the silicon pendulum will generate an angular vibration. Because the silicon pendulum is of microscopic scale, the moment of inertia around the driving axis is very small, so the angle of vibration is also very small and the detected signal is a small signal. Therefore, the input driving signal amplitude is smaller in the modeling. In order to compare the phase difference between the input driving signal and the gyro output signal, a gain of _{u}

The gyro was installed on a MEMS three-axis precision turntable.

Given an input angular velocity of 180°/s, the turntable rolling axis is rotating at a high speed. At the same time, through the data acquisition card of the MEMS three-axis precision turntable, we will obtain data of the frame angular displacement and gyro output signal. After data acquisition is completed, the speed of the rolling axis is increased. In the same way, measurement is accomplished.

In order to compare to the simulation result as shown in

As shown in the

This paper introduces a new type of micromachined gyro, and its working principles were analyzed. For the MEMS micromachined gyro driven by a rotating aircraft, the movement equation is presented and the dynamic parameters are calculated. Based on the motion equation, we analyzed the phase frequency characteristics and plotted the characteristic phase frequency curve under different damping ratio scenarios. Combined with the dynamic parameters, a dynamic simulation model has been set up. When the spin frequency is 15 Hz, the obtained phase difference simulation is 43.2°. On the basis of this analysis, we designes a phase delay measurement method. Using this method, we have measured the characteristic phase frequency curve. Ranging from 5 Hz to 25 Hz, the measured curve was in accord with the simulation. When the spin frequency is chosen as 15 Hz, by measurements we obtained a phase difference of 40.9°. The relative error with respect to the simulation is only 5.3%. The measured results prove that the accuracy is good and the data of the measured phase difference can meet the requirements of adjusting the phase for the single channel control of a rotating aircraft.

This work was supported by the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2011MS0910), the Natural Science Foundation of Beijing, China (Grant No. 4112020), Beijing Key Laboratory for Sensor (Grant No. KF20131077204), Beijing Engineering Research Center of Optoelectronic Information and Instrument (Grant No. GD2013005), and State key Laboratory of Electronic Thin Films and Integrated Devices (UESTC) (Grant No. KFJJ201210).

The authors declare no conflict of interest.

A generic MEMS gyroscope with the driving part.

The block diagram of damping loop.

Gyro structure schematic diagram.

Detection capacitances.

Output voltage waveform with a constant input angular velocity.

Experimental platform.

Experimental waveform.

AM waveform.

Test control panel.

Silicon pendulum structure.

The masks of four steps.

Picture of the chip.

Phase frequency characteristic curves for different damping ratios.

Block diagram of gyro working principle.

Bode plot of

Modeling of the dynamic simulation.

Dynamic simulation waveform.

Measuring platform.

Control platform.

Working status.

Phase delay comparison chart.

The experimental phase-frequency characteristic curve.

Phase-frequency characteristic experimental records.

5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | |

0 | −13.3 | −20.1 | −28.8 | −36.3 | −40.9 | −50.3 | −53.6 | −61.2 | −67.3 | −72 |