RU2188392C1 - Method of determination of true heading of inclined object with the use of gyroscopic angular-rate sensor - Google Patents

Abstract

FIELD: precision instrumentation engineering; manufacture of gyrocompasses and analytical course-indicating units. SUBSTANCE: proposed method consists in preliminary fixing of measuring axes of gyroscope to body axes of object, alignment of signs of change of voltages of reference resistance of gyroscope with direction of azimuthal turn of its body around spinning axis, determination of coefficients of gyroscope drift model, latitude of object and angles of inclination of plane of gyroscope sensitive axes in pitching and rolling. In gyrocompassing at initial position of gyroscope, voltages of references of its channels are measured Then, gyroscope is turned around spinning axis in inclined plane of sensitive axes of gyroscope counter-clockwise to equidistant positions within 360 dwg.; angular distance between them is so selected that angle of 90 deg. Should be multiple of it. Angle of turn relative to initial position and voltages of reference resistances of two channels of gyroscope are measured at each angular position. Thus, true heading angle of object is determined analytically on basis of indications thus obtained. EFFECT: enhanced accuracy of determination of true heading. 3 dwg

Description

 The invention relates to the field of precision instrumentation, mainly gyroscopic and can be used to create gyrocompasses and heading devices of an analytical type.

 There is a method of determining the true course using a gyroscopic angular velocity sensor (see, for example, the book by B.I. Nazarov and G.A. Khlebnikov "Gyro-stabilizers of rockets". M., 1975, pp. 193-196), according to which the course direction the measuring axis of the gyroscope is determined analytically from the results of measurements of projections of the horizontal component of the angular velocity of the Earth.

 In order to improve the accuracy of determining the course, methods are used to reduce the influence of gyro drift. So, the gyroscopic angular velocity sensor, the measuring axis of which is located in the horizontal plane, is turned at different azimuthal angles and the output information from the gyroscope is taken at these angles in the form of an electrical voltage from the reference resistance in the feedback circuit.

 Based on the fact that a number of moments of the gyroscope, not connected with its body, change sign during its turns in azimuth, known methods have been developed that allow mutual compensation of harmful moments. However, these well-known methods of auto-compensation do not completely exclude the error in determining the course from the harmful moments of the gyroscope, as well as from other sources, for example, non-alignment of the sensitivity axes to the horizon.

 The prototype is a method for determining the true heading using a gyroscopic angular velocity sensor based on its analytical calculation (see the article VL Budkin, SP Redkin "Gyrocompassing on a Movable Object by Means of Angular Rate Sensor on the Basis of Dynamically Tuned Gyro". Second International Symposium on Inertial Technology in Beijing. Beijing, China, October, 1988, pp. 143-151).

где U₁₁, U₁₂ - напряжения с эталонных сопротивлений гироскопа соответственно по первому и второму каналам,
К_н11, К_н12 - крутизна гироскопа по напряжению по первому и второму каналам,
Ω - угловая скорость вращения Земли,
φ - широта местоположения объекта,
υ,γ - углы наклона плоскости осей чувствительности гироскопа соответственно по тангажу и крену,
ω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{ду}}$ , ω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{дх}}$ - дрейф гироскопа соответственно по первому и второму каналам.In this method, gyrocompassing is carried out using an angular velocity sensor based on a dynamically tuned gyroscope (DUS-DNG) with its strap-on installation on the object. Preliminarily, the gyroscope’s measuring axes are tied to the axes connected to the object, the signs of voltage changes from the gyroscope reference resistances are coordinated with the direction of the azimuthal rotation of its body around the axis of proper rotation, the gyro drift model coefficients, the object’s latitude, the gyroscope’s pitch axes along the pitch and roll, measure the voltage from the reference resistance of the gyroscope, operating in the mode of an angular velocity sensor. After that, the azimuthal angle of the stationary oblique object is determined using the expression

where U ₁₁ , U ₁₂ are the voltages from the reference resistances of the gyroscope, respectively, along the first and second channels,
K _n11, K _n12 - the slope of the gyroscope by voltage along the first and second channels,
Ω is the angular velocity of rotation of the Earth,
φ is the latitude of the location of the object,
υ, γ are the angles of inclination of the plane of the axes of sensitivity of the gyroscope in pitch and roll, respectively,
ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{do}}$ , ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dh}}$ - drift of the gyroscope, respectively, on the first and second channels.

 However, in the known method, the true course is determined with an error that is caused by errors in the task and measurement: the gyroscope slope in voltage, latitude, pitch and roll angles, gyroscope drift model, voltages from the reference gyroscope resistances.

K_н11,ΔK_н11,K_н12,ΔK_н12 - крутизна гироскопа по напряжению и погрешность ее задания по первому и второму каналу,
ω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{ду}}$ ,_Δω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{ду}}$ ,ω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{дх}}$ ,_Δω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{дх}}$ - скорость дрейфа гироскопа и погрешность ее задания по первому и второму каналу,
Ω - угловая скорость вращения Земли,
φ,Δφ - широта местоположения и погрешность ее задания,
υ,Δυ - угол наклона объекта по тангажу и погрешность его задания,
γ,Δγ - угол наклона объекта по крену и погрешность его задания,
ΔU₁₁,ΔU₁₂ - погрешность измерения напряжений на эталонных сопротивлениях гироскопа.The expression for the gyrocompassing error on a stationary oblique object using an angular velocity sensor based on a dynamically tuned gyroscope can be represented as

K _n11 , ΔK _n11 , K _n12 , ΔK _n12 - the slope of the gyroscope in voltage and the error of its task on the first and second channel,
ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{do}}$ , _Δ ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{do}}$ , ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dh}}$ , _Δ ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dh}}$ - the gyro drift velocity and the error of its task on the first and second channel,
Ω is the angular velocity of rotation of the Earth,
φ, Δφ - the latitude of the location and the error of its job,
υ, Δυ - pitch angle of the object and the error of its job,
γ, Δγ is the angle of inclination of the object along the roll and the error of its task,
ΔU ₁₁ , ΔU ₁₂ - measurement error of the voltages at the reference resistances of the gyroscope.

 In accordance with expression (2), the error in determining the course in the known method was calculated with the parameters given in table 1.

 In FIG. 1 shows the theoretical dependence of the error in determining the true rate in a known manner, obtained with these parameters.

 Thus, from the dependence 1 shown in FIG. 1, it follows that in the known method of determining the true course, there is a significant error due to the parameters of the gyroscope and errors in their assignment, the angles of inclination of the plane of the measuring axis of the gyroscope and errors in their assignment, the angular velocity of the Earth, latitude the location and the error of its assignment, the error in measuring voltages from the reference resistances of the gyroscope. In this case, the error in determining the course has an oscillatory character depending on the course angle.

 The estimated amplitude of the change in the systematic error of gyrocompassing in the known method was 0.5 deg.

 The aim of the present invention is to improve the accuracy of determining the true course using a gyroscopic angular velocity sensor.

где ψ_i = 2π-arctga_i, если b_li>0, b_2i>0;
ψ_i = π-arctga_i, если b_li>0, b_2i<0;
ψ_i = π-arctga_i, если b_li>0, b_2i<0;

если b_li>0, b_2i>0;
a_i = b_lib_2i ^-1,

ω $\genfrac{}{}{0ex}{}{\text{1x}}{\text{0}}$ , ω $\genfrac{}{}{0ex}{}{\text{1y}}{\text{0}}$ - коэффициенты модели дрейфа, не зависящие от ускорения,

коэффициенты модели дрейфа, пропорциональные ускорению во второй степени,
U_11i, U_12i - напряжения с эталонных сопротивлений гироскопа соответственно по первому и второму каналу,
К_н11, K_н12 - крутизна гироскопа по напряжению по первому и второму каналу,
υ,γ - углы наклона объекта по тангажу и крену,
δ_i - угол поворота корпуса гироскопа вокруг оси собственного вращения относительно исходного положения,
Ω - угловая скорость вращения Земли,
φ - широта местоположения объекта,
n - число угловых положений гироскопа при повороте вокруг оси собственного вращения в пределах 360 градусов,
i - текущий индекс, характеризующий угловое положение гироскопа при поворотах вокруг оси собственного вращения.This goal is achieved by the fact that in the known method for determining the true course of an inclined object, including preliminary binding of the measuring axes of the gyroscope to the axes associated with the object, matching signs of voltage changes from the reference resistances of the gyroscope with the direction of the azimuthal rotation of its body around the axis of proper rotation, determining model coefficients the gyro drift, the latitude of the object’s location, the tilt angles of the plane of the measuring axes of the gyroscope in pitch and roll during gyro operation Compassing in the initial position of the gyroscope measures voltages from the reference resistances of its two channels, then rotate the gyroscope around the axis of proper rotation in the inclined plane of the measuring axes of the gyroscope counterclockwise equally spaced from each other in a position angle of 360 degrees, the angular distance between which is chosen so so that for him the angle of 90 degrees is a multiple, while in each angular position the angle of rotation is measured relative to the initial position and the voltage from the reference two resistances gyroscope channels, and then calculate true heading angle value according to the following formula

where ψ _i = 2π-arctga _i if b _li > 0, b _2i >0;
ψ _i = π-arctga _i if b _li > 0, b _2i <0;
ψ _i = π-arctga _i if b _li > 0, b _2i <0;

if b _li > 0, b _2i >0;
a _i = b _li b _2i ^-1 ,

ω $\genfrac{}{}{0ex}{}{\text{1x}}{\text{0}}$ , ω $\genfrac{}{}{0ex}{}{\text{1y}}{\text{0}}$ - coefficients of the drift model, independent of acceleration,

drift model coefficients proportional to acceleration to the second degree,
U _11i , U _12i are the voltages from the reference resistances of the gyroscope, respectively, along the first and second channel,
K _n11 , K _n12 - the steepness of the gyroscope by voltage along the first and second channel,
υ, γ are the pitch angles of the object in pitch and roll,
δ _i - the angle of rotation of the gyroscope body about the axis of proper rotation relative to the initial position,
Ω is the angular velocity of rotation of the Earth,
φ is the latitude of the location of the object,
n is the number of angular positions of the gyroscope when rotated around the axis of proper rotation within 360 degrees,
i is the current index characterizing the angular position of the gyroscope during rotations around the axis of proper rotation.

В соответствии с выражением (4) была рассчитана погрешность определения истинного курса на каждом угле δ_i поворота корпуса гироскопа вокруг оси собственного вращения и среднее значение погрешности для этих углов при параметрах, приведенных в табл.2.The gyrocompassing error in the proposed method can be determined using the following expression

In accordance with expression (4), the error in determining the true course at each angle δ _{i of} rotation of the gyroscope body around the axis of proper rotation and the average error for these angles were calculated for the parameters given in Table 2.

In FIG. Figure 2 shows the theoretical dependence of the error in determining the true course at different angles δ _{i of} rotation of the gyroscope body about the axis of proper rotation and calculated dependence 2, which characterizes the average value of the error for these angles.

 From the dependence 1 shown in FIG. 2, it follows that the gyrocompassing error during rotation of the gyroscope body about the axis of proper rotation has an alternating, oscillatory character with a period of 360 degrees. In this case, dependence 1 is quasisymmetric with respect to the δ axis. In this regard, its average value, represented by dependence 2, has a value significantly less than the error of gyrocompassing in the initial state at δ = 0, which characterizes the known method. Figure 1 shows the average value of the error in the form of dependence 2 obtained at different azimuthal angles. The average value of the error is dependent on the azimuthal angle of the oscillatory nature. However, in this case, the amplitude amplitude of the average error is an order of magnitude smaller than the amplitude of the error oscillations obtained in the known method.

Thus, the proposed method for determining the true course of an inclined object using a gyroscopic angular velocity sensor has the following main differences from the known method:
- in the operation of taking readings from the gyroscope, the voltages from the reference resistances of the gyroscope are measured not only in the initial position, but also in the positions after rotation by the given angles of the gyroscope body around the axis of proper rotation in the plane of the measuring axes of the device, which characterizes the inclined plane of the object,
- the calculation of the angle of the true course of the object is carried out using the gyro readings at the given angles of rotation of the device body about the axis of proper rotation using the proposed new analytical relationships.

 In FIG. 1 shows the theoretical dependence of the error in determining the true course of the known and proposed methods.

 In FIG. 2 shows the theoretical dependence of the error in determining the true course at different angles of rotation of the gyroscope body about the axis of proper rotation and the average value of this error.

 Figure 3 shows the experimental dependence of determining the angle of the true course of the known and proposed methods.

 An experimental comparative assessment of the accuracy of determining the course was carried out using the known and proposed methods. Experimental studies were carried out using an angular velocity sensor based on a dynamically tuned gyroscope GVK-6. A dynamically tuned gyroscope was installed on the platform of an inclined-rotary stand, with the help of which the gyroscope was tilted along the roll and pitch and its body was rotated around its own rotation axis. The dynamically tuned gyroscope worked as an angular velocity sensor. From the reference resistances in the feedback loop of the gyroscope, readings were taken in the form of voltage. With the help of the stand, the gyroscope tilted 30 degrees along the roll and pitch. The readings were taken from the gyroscope in the initial position with a rotation angle around the axis of proper rotation δ = 0. Then, the gyroscope from its initial position was rotated counterclockwise around the axis of proper rotation by angles δ = 45, 90, 135, 180, 225, 270, 315, 360 degrees. At each of these angles, readings were taken from the gyroscope. Using these indications, the angles of the true course were determined using the known and proposed method.

 The measurement error was determined as the difference between the measured and known set course angles.

 In FIG. 3 shows the experimental dependence of the gyrocompassing errors on the azimuthal angle with the known method 1 and the proposed method 2.

 A comparison of these dependencies shows that the application of the proposed method can improve the accuracy of determining the true rate in comparison with the known method.

 So in the known method and the proposed method, the gyrocompassing error has an oscillatory dependence on the heading angle. However, the amplitude of the error of gyrocompassing in the proposed method is 2.3 times less than in the known method. Using the proposed method for determining the true course using a gyroscopic angular velocity sensor provides, in comparison with the known method, a significant increase in the accuracy of its finding in conditions of an inclined base, which makes it possible to expand the scope of gyrocompass devices based on an angular velocity sensor. So on the basis of the angular velocity sensor using the proposed method, it is possible to create dual-mode heading devices for ground moving objects, which determine the course when the object stops and save it when moving.

Claims (1)

A method for determining the true course of an oblique object using a gyroscopic angular velocity sensor, including preliminary linking the measuring axes of the gyroscope to the axes associated with the object, matching the signs of voltage changes with the reference resistances of the gyroscope with the direction of the azimuthal rotation of its body around its own rotation axis, determining the coefficients of the gyroscope drift model the latitude of the location of the object, the angles of inclination of the plane of the measuring axes of the gyroscope in pitch and roll, different The fact is that when gyrocompassing in the initial position of the gyroscope, the voltages from the reference resistances of its two channels are measured, then the gyroscope is rotated around the axis of proper rotation in the inclined plane of the measuring axes of the gyroscope counterclockwise equally apart from each other in an angle of position within 360 ^o , angular the distance between which is chosen so that for it an angle of 90 ^{o is} a multiple, while in each angular position measure the angle of rotation relative to the initial position and voltage with a standard resistance of the two channels of the gyroscope, and then calculate the value of the angle of the true course according to the following formula:

where ψ _i = 2π-arctan a _i if b _li > 0, b _2i >0;
ψ _i = π-arctan a _i if b _li > 0, b _2i <0;
ψ _i = π-arctan a _i if b _li <0, b _2i <0;
ψ _i = -arctg a _i if b _li <0, b _2i >0;
a _i = b _li b _2i ^-1 ;

ω $\genfrac{}{}{0ex}{}{\text{1x}}{\text{0}}$ , ω $\genfrac{}{}{0ex}{}{\text{1y}}{\text{0}}$ - coefficients of the drift model independent of acceleration;

drift model coefficients proportional to acceleration to the second degree;
U _lli , U _l2i are the voltages from the reference resistances of the gyroscope, respectively, along the first and second channel;
K _nll , K _n12 - the slope of the gyroscope by voltage along the first and second channel;
υ, γ are the pitch angles of the object in pitch and roll;
δ _i is the angle of rotation of the gyroscope body about the axis of proper rotation relative to the initial position;
Ω is the angular velocity of the Earth;
φ is the latitude of the location of the object;
n is the number of angular positions of the gyroscope when rotating around the axis of proper rotation within 360 ^o ;
i is the current index characterizing the angular position of the gyroscope during rotations around the axis of proper rotation.

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