Large-caliber telescope non-linear interference detecting and filtering method

Abstract

A large-caliber telescope non-linear interference detecting and filtering method is provided. The measure of the oil pad interference is accomplished with one of the following two methods, accelerometer and encoder, or using both of the said methods simultaneously. The filtering of the oil pad interference: set a NOTCH frequency as the main interfering frequency by using NOTCH filter to filter the interference and distinctly improve the telescope performance. The telescope and method is specific to a large-caliber telescope with an oil pad, by using an acceleration sensor and an encoder to precisely measure the non-linear interfering frequency of the telescope oil pad system, by using a NOTCH digital filter to accurately filter the interference due to the oil pad system, and through adjusting parameters of the digital filter to change the filter frequency band on the basis of the change of the oil pad interfering frequency.

Claims

1. A method to detect and filter large-caliber telescope non-linear interference, the method comprising the following steps: (1) determining if an oil pad interference is accomplished with one or both of an accelerometer method and an encoder method; wherein, the accelerometer sensor method includes: (1)-1. setting an accelerometer at a base of a telescope azimuth shaft; and setting an additional accelerometer at a gear oil diverter of an oil pad; (1)-2. inputting signals of the accelerometer and the additional accelerometer into an industrial personal computer via an AD adaptor card; (1)-3. wherein, when the oil pad is turned off and the telescope is static, measuring the signals of the accelerometer and the additional accelerometer and plotting an acceleration vs frequency curve; (1)-4. wherein, when the oil pad is turned on and the telescope is static, measuring the signals of the accelerometer and the additional accelerometer and plotting an acceleration vs frequency curve; (1)-5. obtaining the oil pad vibration interference frequency by comparing the acceleration vs. frequency curve of step (1)-3 and the acceleration vs. frequency curve of step (1)-4; wherein the encoder method includes: (2)-1. using a photoelectrical encoder as a position sensor on the telescope azimuth shaft; (2)-2. inputting a signal of the photoelectrical encoder into the industrial personal computer via a photoelectrical encoder acquisition card; (2)-3. measuring the signal from the photoelectrical encoder with the oil pad turned off and the telescope static, continuously sampling for a period of time, and plotting an encoder data curve and a FFT (fast Fourier transformation) curve; (2)-4. measuring the signal from the photoelectrical encoder with the oil pad turned on and the telescope static, continuously sampling for a period of time, and plotting an encoder data curve and a FFT curve; (2)-5. obtaining the oil pad vibration interference frequency by comparing the acceleration curve and the FFT (fast Fourier transformation) curve; (3) filtering the oil pad interference frequency: by using a NOTCH filter and setting a NOTCH frequency at the interference frequency obtained in step (1), the interference being filtered to improve performance of the telescope.

2. The method to detect and filter large-caliber telescope non-linear interference according to claim 1, wherein the specific method to obtain parameters is: setting a band eliminating filter, taking a natural frequency ω.sub.nz as the interference frequency to be filtered, T.sub.s being a closed loop sampling cycle of the telescope servo system, and a damping coefficient ζ.sub.z selected according to the simulation and experimental result.

3. The method to detect and filter large-caliber telescope non-linear interference according to claim 2, wherein light damping is selected for the telescope oil pad system interference.

4. The method to detect and filter large-caliber telescope non-linear interference according to claim 2, wherein, with the natural frequency ω.sub.np and the damping coefficient ζ.sub.z of a band-pass filter, heavy damping is selected for the telescope oil pad system interference.

5. The method to detect and filter large-caliber telescope non-linear interference according to claim 2, wherein a frequency response formula of the NOTCH filter is: $\begin{array}{cc}.Math.H\left(e^{\mathrm{j\omega }}\right).Math.=\{\begin{array}{c}1,\omega \ne {\omega }_0\\ 0,\omega ={\omega }_0\end{array}& \left(1\right)\end{array}$ The time domain transfer function of the NOTCH filter is: $\begin{array}{cc}G\left(s\right)=\frac{s^2+2{\zeta }_z{\omega }_{\mathrm{nz}}+{\omega }_{\mathrm{nz}}^2}{s^2+2{\zeta }_p{\omega }_{\mathrm{np}}+{\omega }_{\mathrm{np}}^2}& \left(2\right)\end{array}$ where, ω.sub.nz is the natural frequency at zero point, ζ.sub.z the damping coefficient at zero point, ω.sub.np the natural frequency at extreme point, and ζ.sub.p the damping coefficient at extreme point.

6. The method to detect and filter large-caliber telescope non-linear interference according to claim 5, wherein the NOTCH filter is expressed with the following constant coefficient linear differential equation: $\begin{array}{cc}y\left(n\right)=\underset{i=0}{\overset{M}{.Math.}}{a}_{i}x\left(n-i\right)-\underset{i=1}{\overset{N}{.Math.}}{b}_{i}y\left(n-i\right)& \left(3\right)\end{array}$ where x(n) and y(n) are respectively input and output signal series, and a.sub.i and b.sub.i the filter coefficients; performing Z conversion on both sides of formula (3), and by converting the S plane into the Z plane of the NOTCH filter, the transfer function of the digital filter is obtained: $\begin{array}{cc}H\left(z\right)=\frac{\underset{i=0}{\overset{M}{.Math.}}{a}_i{z}^{-i}}{\underset{i=0}{\overset{N}{.Math.}}{b}_i{z}^{-i}}=\frac{\underset{i=1}{\overset{M}{.Math.}}\left(z-z_i\right)}{\underset{i=1}{\overset{N}{.Math.}}\left(z-p_i\right)}& \left(4\right)\end{array}$ where, z.sub.i and p.sub.i are respectively the zero points and extreme points of the transfer function.

7. The method to detect and filter large-caliber telescope non-linear interference according to claim 6, wherein the expression of the NOTCH filter is written as: $\begin{array}{cc}\frac{N\left(z\right)}{D\left(z\right)}=\frac{1+n_1{z}^{-1}+n_2{z}^{-2}}{1+d_1{z}^{-1}+d_2{z}^{-2}}& \left(5\right)\end{array}$ where, N(z) is a band eliminating filter, D(z) is a band-pass filter, n.sub.1 and n.sub.2 are respectively the parameters of the band eliminating filter N(z), and d.sub.1 and d.sub.2 are respectively the parameters of the band-pass filter.

8. The method to detect and filter large-caliber telescope non-linear interference according to claim 6, wherein the parameters in the formula (5) are obtained using the formula below: $\begin{array}{cc}{\alpha }_z=1+2{\zeta }_z{\omega }_{\mathrm{nz}}{T}_s+{\omega }_{\mathrm{nz}}^2{T}_s^2& \left(6\right)\\ {\alpha }_p=1+2{\zeta }_p{\omega }_{\mathrm{np}}{T}_s+{\omega }_{\mathrm{np}}^2{T}_s^2& \left(7\right)\\ n_1=-\frac{2{\zeta }_z{\omega }_{\mathrm{nz}}{T}_s+2}{{\alpha }_z}& \left(8\right)\\ n_2=\frac{1}{{\alpha }_z}& \left(9\right)\\ d_1=-\frac{2{\zeta }_p{\omega }_{\mathrm{np}}{T}_s+2}{{\alpha }_p}& \left(10\right)\\ d_2=\frac{1}{{\alpha }_p}.& \left(11\right)\end{array}$

Description

BRIEF DESCRIPTION

(1) Some of the embodiments will be described in detail, with reference to the following figures, wherein like designations denote like members, wherein:

(2) FIG. 1 is acceleration and frequency correlation curve when the oil pad is turned off;

(3) FIG. 2 is acceleration and frequency correlation curve when the oil pad is turned on;

(4) FIG. 3 is encoder data curve when the oil pad is turned off;

(5) FIG. 4 is encoder data FFT curve when the oil pad is turned off;

(6) FIG. 5 is encoder data curve when the oil pad is turned on;

(7) FIG. 6 is encoder data FFT curve when the oil pad is turned on;

(8) FIG. 7 is block diagram of telescope control system;

(9) FIG. 8 is BODE diagram of NOTCH filter;

(10) FIG. 9 is Zero extreme point diagram of NOTCH filter;

(11) FIG. 10 is Block diagram of telescope control system with the NOTCH added;

(12) FIG. 11 is Encoder data curve after NOTCH filtering; and

(13) FIG. 12 is Encoder data FFT curve after NOTCH filtering.

DETAILED DESCRIPTION

(14) Embodiment 1, Large-Caliber Telescope Non-Linear Interference Detecting and Filtering Method

(15) In the following, embodiments of the invention are further described in conjunction with attached drawings and embodiment.

(16) Two acceleration sensors are respectively set at the base of the telescope azimuth shaft and the gear oil diverter of the oil pad of a telescope with a caliber of 2.5 m. The signal of the accelerometer is input into the UMAC movement controller via the AD control card ACC-28E+OPT-1, and fed into the industrial personal computer via the Ethernet bus. When the oil pad is turned off and the telescope is static, the signals of the two accelerometers are measured and the acceleration vs frequency curve is plotted, as shown in FIG. 1. When the oil pad is turned on and the telescope is static, the signals of the two accelerometers are measured and the speed vs frequency curve is plotted, as shown in FIG. 2. It can be found by comparing the curves in the two diagrams that, after the oil pad is turned on, vibration peak occurs at the frequencies of 24.75 Hz and 322 Hz on the telescope azimuth shaft platform vibration curve. This shows that the vibration at this frequency band has transferred to the base on the azimuth shaft turn table.

(17) Comparison and verification was done further with encoder method. A photoelectrical encoder is used as the position sensor at the telescope azimuth shaft, its signal is input into the UMAC movement controller via the ACC-51E card, and fed into the industrial personal computer via the Ethernet bus. Measure the signal from the photoelectrical encoder with the oil pad turned off and the telescope static, make continuous sampling for a period of time, and plot the encoder data curve (or the telescope position curve) as shown in FIG. 3 and the FFT fast Fourier transformation curve, as shown in FIG. 4. Collect encoder data for analysis with the oil pad turned on and the telescope static, as shown in FIG. 5, and use the FFT method to convert it from time domain signal into frequency domain signal for frequency spectrum analysis, as shown in FIG. 6. Compare the acceleration curve and FFT fast Fourier transformation curve, when the oil pad is turned on, the encoder data fluctuation increases, PV=5 cts, with strong fluctuating cycles, from which frequency response of 0.825 Hz and 24.75 Hz can be read, however, no frequency peak of 322 Hz occurs. This difference shows that the vibration of 322 Hz only reached the platform of azimuth shaft, but the measuring element is at a location not sensitive to this vibration, and the encoder reading is not affected, that is, the vibration does not enter the control circuit, therefore the control system does not produce a control signal of this frequency, and it will not make the actuator to produce the control force corresponding to 322 Hz.

(18) In the following, a NOTCH digital filter is used to filter off the most important interference in the oil pad system, its frequency being 0.825 Hz. The original block diagram of the control system is as shown in FIG. 7.

(19) The sampling cycle is T.sub.s=0.005 s, as the response frequency measured in this system under oil pad interference ω=0.825 Hz, i.e. the signal of 0.825 Hz hoped to be filtered is the filter center frequency. Set a light damping band eliminating filter, with natural frequency ω.sub.nz=0.825 Hz=2π*0.825=5.1836 rad/s, and closed loop sampling cycle for the servo system, with damping coefficient ζ.sub.z=0.04; and a heavy damping band pass filter, ω.sub.np=0.1425 Hz=0.1425*2π=8.9535 rad/s, with damping coefficient ζ.sub.z=0.8.

(20) $\begin{array}{cc}{\alpha }_z=1+2{\zeta }_z{\omega }_{\mathrm{nz}}{T}_s+{\omega }_{\mathrm{nz}}^2{T}_s^2=1.0027& \left(12\right)\\ {\alpha }_P=1+2{\zeta }_P{\omega }_{\mathrm{np}}{T}_s+{\omega }_{\mathrm{np}}^2{T}_s^2=1.0736& \left(13\right)\\ n_1=-\frac{2{\zeta }_z{\omega }_{\mathrm{nz}}{T}_s+2}{{\alpha }_z}=-1.9966& \left(14\right)\\ n_2=\frac{1}{{\alpha }_z}=0.9973& \left(15\right)\\ d_1=-\frac{2{\zeta }_p{\omega }_{\mathrm{np}}{T}_s+2}{{\alpha }_p}=-1.9296& \left(16\right)\\ d_2=\frac{1}{{\alpha }_p}=0.9314& \left(17\right)\end{array}$ Therefore we obtain

(21) $\begin{array}{cc}\frac{N\left(z\right)}{D\left(z\right)}=\frac{1+n_1{z}^{-1}+n_2{z}^{-2}}{1+d_1{z}^{-1}+d_2{z}^{-2}}=\frac{1-1.9966z^{-1}+0.9973z^{-2}}{1-1.9296z^{-1}+0.9314z^{-2}}& \left(18\right)\end{array}$

(22) The original proportional gain must be multiplied by the reciprocal of the DC gain of the NOTCH filter, to maintain the rigidity of the whole filter. The new proportional gain is equal to the gain of NOTCH filter divided by the original proportional gain.

(23) $\begin{array}{cc}{P}_{\mathrm{new}}=P\frac{{\omega }_{\mathrm{np}}^2}{{\omega }_{\mathrm{nz}}^2}\frac{{\alpha }_z}{{\alpha }_p}=\frac{{8.9535}^2}{{5.1836}^2}\frac{1.0027}{1.0736}P=2.786P& \left(19\right)\end{array}$

(24) The BODE diagram of this NOTCH filter is as shown in FIG. 8, and the zero point diagram of the NOTCH filter is as shown in FIG. 9, it can be seen that the zero point and extreme point of the digital NOTCH filter are in conjugate symmetric distribution, and all extreme points are within the unit circle, the zero point is 0.9983±0.0258i and the extreme point 0.9648±0.0250i, meeting the system stability requirements.

(25) Add the designed NOTCH filter, the block diagram of the telescope control system is as shown in FIG. 10. The effect of using this filter is as shown in FIGS. 11 and 12.

(26) It can be seen that the method used in embodiments of the invention is an ideal method to remove the oil pad vibration narrow band interference, and it eliminates the narrow band interference without producing attenuation to other frequencies.

(27) Although the present invention has been disclosed in the form of preferred embodiments and variations thereon, it will be understood that numerous additional modifications and variations could be made thereto without departing from the scope of the invention.

(28) For the sake of clarity, it is to be understood that the use of “a” or “an” throughout this application does not exclude a plurality, and “comprising” does not exclude other steps or elements. The mention of a “unit” or a “module” does not preclude the use of more than one unit or module.