RU2210740C1 - Method of gyrocompassing with use of gyroscopic transmitter of angular velocity mounted on platform controlled by azimuth and stabilized in plane of local horizon - Google Patents

Abstract

FIELD: development of gyrocompasses and course indicating device of semi-analytical type. SUBSTANCE: gyroscope is so mounted in advance on platform controlled by azimuth and stabilized in plane of local horizon that plane of measurement axes of gyroscope coincides with horizontal plane of platform. Platform is so placed on object that roll stabilization axis is directed perpendicular to symmetry plane of object, towards starboard. Platform is so set in horizon and azimuth that one horizontal axis of platform is directed to north and other to east, body of gyroscope is turned relative to platform around axis of own rotation. Gyrocompassing is conducted and gyrocompassing errors are determined after turn. Azimuthal angle of turn of body of gyroscope with reference to platform is found under which gyrocompassing error is minimal. Then azimuthal angle of turn of object with regard to platform is established during operational gyrocompassing. Angle of true course of object is computed by means of analytical expression with utilization of information on azimuthal position of object and gyroscope relative to platform. EFFECT: possibility of gyrocompassing when angular velocities of base are available, increased precision. 4 dwg

Description

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

 Known methods for determining the true course using a gyroscopic sensor of angular velocity (see, for example, the book by B.I. Nazarov and G.A. Khlebnikov "Gyro-stabilizers of rockets" M., 1975, pp. 193-196 and patent RU 2098766 C1 for cl G 01 C 21/14 of December 10, 1997), according to which the directional direction of the horizontal axis of the gyroscope on a fixed base is determined analytically using the results of readings from the gyroscope obtained at different azimuthal angles.

 The prototype is a method for determining the true course using a two-channel gyroscopic angular velocity sensor (see patent RU 2176708, class G 01 C 21/12 of December 10, 2001).

,
b₂ = U₁₁К_н11cosγ+ω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{ду}}$ cosγ-Ωsinφcosγsinυ,
ω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{дх}}$ ,ω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{дy}}$ - модель дрейфа гироскопа по осям X, Y,
U₁₁, U₁₂ - напряжения с эталонных сопротивлений датчика угловой скорости соответственно по первому и второму каналам,
K_н11, K_н12 - крутизна гироскопа по напряжению для первого и второго каналов,
υ,γ - углы наклона плоскости осей чувствительности гироскопа соответственно по тангажу и крену,
Ω - угловая скорость вращения Земли,
φ - широта местоположения объекта.In this method of determining the true course using a single gyroscope, the measuring axes of the gyroscope are pre-tied to the axes connected to the object, the gyroscope is used in the feedback mode of the current of the torque sensor, signals from the reference resistances of the angular velocity sensor are determined, then the system is phased during the preset operation measuring voltages from the reference resistances of the gyroscope, providing a negative increment of signals from the first and second channels of the gyroscope during azimuthal rotation e its housing counterclockwise by 90 ^o from the position at which the measuring Y first channel axis points to the north and the measurement axis X of the second channel to the east, determine the model coefficients of the drift of the gyroscope, while gyro in the desired kursovom object position determined by the angles of plane tilt the measuring axes of the gyroscope in pitch and roll, the angle of the latitude of the location of the object, the voltage from the reference resistances of the gyroscope in the first and second channels, and then determine the value of the true course of the measuring axis and the first channel of the gyroscope according to the following formula
K = 2π-arctan a if b ₁ > 0, b ₂ >0;
K = π-arctan a if b ₁ > 0, b ₂ <0;
K = π-arctan a if b ₁ <0, b ₂ <0;
K = -arctg a, if b ₁ <0, b ₂ > 0,
where a = b ₁ b ₂ ^-1 ;

,
b ₂ = U ₁₁ K _n11 cosγ + ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{do}}$ cosγ-Ωsinφcosγsinυ,
ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dh}}$ , ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dy}}$ - model of gyro drift along the X, Y axes,
U ₁₁ , U ₁₂ - voltage from the reference resistance of the angular velocity sensor, respectively, on the first and second channels,
K _n11 , K _n12 - the slope of the gyroscope in voltage for the first and second channels,
υ, γ are the angles of inclination of the plane of the axes of sensitivity of the gyroscope in pitch and roll, respectively,
Ω is the angular velocity of rotation of the Earth,
φ is the latitude of the location of the object.

где

ΔU₁₁, ΔU₁₂ - погрешность измерения напряжений с эталонных сопротивлений датчика угловой скорости соответственно по первому и второму каналам,
ΔK_н11, ΔK_н12 - погрешность задания крутизны гироскопа по напряжению для первого и второго каналов,
Δυ,Δγ - погрешность задания углов наклона плоскости осей чувствительности гироскопа соответственно по тангажу и крену,
Δφ - погрешность задания широты местоположения.Gyrocompassing using the known method is possible in a fixed base. Angular movements of the base cause very significant gyrocompassing errors. These errors can be estimated by calculation using the following expression for gyrocompassing error

Where

ΔU ₁₁ , ΔU ₁₂ - the error of voltage measurement from the reference resistances of the angular velocity sensor, respectively, on the first and second channels,
ΔK _n11 , ΔK _n12 - the error of setting the slope of the gyroscope in voltage for the first and second channels,
Δυ, Δγ - the error of setting the angles of inclination of the plane of the axes of sensitivity of the gyroscope, respectively, in pitch and roll,
Δφ is the error in setting the latitude of the location.

скоростей изменения углов тангажа

и крена

при наличии ошибок в задании рассматриваемых параметров. При расчете погрешностей гирокомпасирования с использованием выражения (2) брались следующие значения параметров и ошибок их задания:
ΔU₁₁=ΔU₁₂=0,15 мВ,
K_н11=K_н12=3,5•10^-7 1/c мВ,
ΔK_н11=ΔK_н12=3,5•10^-10 1/с мВ,
ω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{дх}}$ = ω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{ду}}$ = 1 град/ч,
Δω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{дх}}$ = Δω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{ду}}$ = 0,01 град/ч,
φ=55,5 град,
Δφ=0,05 град,
Δυ = Δγ=0,017 град,
υ = γ=30 град.Consider the influence in the known method on the error of gyrocompassing the yaw rate

pitch angles

and roll

in the presence of errors in the task of the considered parameters. When calculating the gyrocompassing errors using expression (2), the following parameter values and their job errors were taken:
ΔU ₁₁ = ΔU ₁₂ = 0.15 mV,
K _n11 = K _n12 = 3.5 • 10 ^-7 1 / s mV,
ΔK _n11 = ΔK _n12 = 3.5 • 10 ^-10 1 / s mV,
ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dh}}$ = ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{do}}$ = 1 deg / h,
Δω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dh}}$ = Δω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{do}}$ = 0.01 deg / h
φ = 55.5 degrees
Δφ = 0.05 deg
Δυ = Δγ = 0.017 degrees,
υ = γ = 30 deg.

скоростей изменения углов тангажа

и крена

Зависимостями 1, 2, 3, 4, 5, 6, 7, 8 представлены погрешности гирокомпасирования соответственно на азимутальных углах 0, 45, 90, 135, 180, 225, 270, 315^o. Эти зависимости показывают, что на разных азимутальных углах угловые скорости рыскания, изменения углов по тангажу и крену обуславливают существенные погрешности гирокомпасирования. Таким образом, известный способ имеет ограничение на применение, обусловленное угловыми скоростями основания.Figure 2 shows the errors of gyrocompassing using a two-channel gyroscopic angular velocity sensor depending on the yaw rate

pitch angles

and roll

Dependencies 1, 2, 3, 4, 5, 6, 7, 8 represent the errors of gyrocompassing, respectively, at azimuthal angles of 0, 45, 90, 135, 180, 225, 270, 315 ^o . These dependences show that at different azimuthal angles, the angular yaw rates, changes in pitch and roll angles cause significant gyrocompassing errors. Thus, the known method has a limitation on the application, due to the angular velocity of the base.

=0,01 град/ч,
ω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{дх}}$ = ω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{ду}}$ = 0,01 град/ч.
На фиг. 3 показана погрешность гирокомпасирования с помощью двухканального гироскопического датчика угловой скорости в зависимости от азимутальной ориентации гироскопа.We study using expression (2) the influence in the known method on the error of gyrocompassing the azimuthal orientation of the gyroscope, characterized by the angle ψ. When calculating this gyrocompassing error, the following parameter values and their error errors were taken:
ΔU ₁₁ = ΔU ₁₂ = 0.15 mV,
K _n11 = K _n12 = 3.5 • 10 ^-7 1 / s mV,
ΔK _n11 = ΔK _n12 = 3.5 • 10 ^-10 1 / s mV,
Δω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dh}}$ = Δω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{do}}$ = 0.01 deg / h;
φ = 55.5 degrees
Δφ = 0.05 deg
υ = γ = 0.017 degrees,

= 0.01 deg / h
ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dh}}$ = ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{do}}$ = 0.01 deg / h.
In FIG. Figure 3 shows the error of gyrocompassing using a two-channel gyroscopic angular velocity sensor depending on the azimuthal orientation of the gyroscope.

From the dependence presented in figure 3, it is seen that in the known method, the azimuthal orientation of the gyroscope affects the error of gyrocompassing. Moreover, the error has a sinusoidal character. Since the known method assumes the strapdown installation of the gyro on the object, then at different courses of the object in this case there will be different gyrocompassing errors, which can reach significant values at the heading angles of 90 and 270 ^o .

 The technical result that can be obtained by implementing the present invention is the possibility of gyrocompassing using gyroscopic angular velocity sensors in the presence of angular velocities of the base and increasing the accuracy of gyrocompassing by eliminating the dependence of the gyrocompass error on the heading angle.

The technical result is achieved by the fact that in the known method of determining the true course using a two-channel gyroscopic angular velocity sensor, including the use of a gyroscope in the current feedback mode of the torque sensors, preliminary coordination of the signs of voltage changes with the reference resistances of the gyroscope with the direction of rotation of the housing around the axis of proper rotation, determination of the gyroscope drift model, and with gyrocompassing, determination of voltages from the reference resistances of the gyroscope according to the first at the second channels, the gyroscope is additionally pre-installed on a platform controlled in azimuth and stabilized in the plane of the local horizon so that the plane of the gyroscope measuring axes coincides with the horizontal plane of the platform, the platform is mounted on the object so that the roll stabilization axis coincides with the longitudinal axis of the object, the axis of stabilization along the pitch was directed perpendicular to the plane of symmetry of the object to the starboard side, after which the platform is set horizontally and in azimuth e so that one horizontal axis of the platform is directed north, the other east, rotate the gyroscope body relative to the platform around the axis of proper rotation, gyrocompass and determine gyrocompass errors after rotation, determine the azimuthal angle of rotation of the gyroscope body relative to the platform, at which the gyrocompassing error is minimal and then, during working gyrocompassing, the azimuthal angle of rotation of the object relative to the platform is determined and the angle of Nogo course object by the following formula
K = 2π-arctg (b ₁ b $\genfrac{}{}{0ex}{}{\text{-1}}{\text{2}}$ ) -ψ _g + ψ _g1 if b ₁ > 0, b ₂ >0;
K = π-arctg (b ₁ b $\genfrac{}{}{0ex}{}{\text{-1}}{\text{2}}$ ) -ω _g + ψ _g1 if b ₁ > 0, b ₂ <0;
K = π-arctg (b ₁ b $\genfrac{}{}{0ex}{}{\text{-1}}{\text{2}}$ ) -ω _g + ψ _g1 if b ₁ <0, b ₂ <0;
K = -arctg (b ₁ b $\genfrac{}{}{0ex}{}{\text{-1}}{\text{2}}$ ) -ω _g + ψ _g1 if b ₁ <0, b ₂ >0;
where b ₁ = -U ₁₂ K _n12 + ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dh}}$ ;
b ₂ = U ₁₁ K _n11 + ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dy}}$ ;
ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dx}}$ , ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dy}}$ - model of the gyro drift along the axes X _g1 , Y _g1 ;
U ₁₁ , U ₁₂ - voltage from the reference resistance of the angular velocity sensor, respectively, on the first and second channels,
K _n11 , K _n12 - the slope of the gyroscope in voltage for the first and second channels,
ψ _g - azimuthal angle of rotation of the object relative to the platform,
ψ _g1 - azimuthal angle between the horizontal axes of the platform and the gyroscope.

 The scheme for gyrocompassing using a gyroscopic angular velocity sensor mounted on a platform controlled in azimuth and stabilized in the plane of the local horizon is shown in Fig. 1.

When analyzing this scheme, we consider the following coordinate systems. The coordinate system O _d X _d Y _d Z _d is the Darboux coordinate system: the O _d X _d axis is directed north, the O _d Y _d axis is vertically upward, and the O _d Z _d axis is east. We associate the coordinate system O _with X _with Y _with Z _c with the object: the origin of the coordinate system is placed in the center of mass of the object, the axes O _with X _c and O _with Y _s are located in the vertical plane of symmetry of the object, while the axis O _with X _{s is} directed along the object’s body, and the axis O _с Y _с - perpendicular to the axis О _с Х _с , lying in the vertical plane of symmetry of the object, the axis O _c Z _{c is} perpendicular to the plane of symmetry of the object and forms the right coordinate system. We connect the right orthogonal coordinate system O _p X _p Y _p Z _p to the platform: the O _p Y _p and O _p Z _p axes lie in the plane of the platform, while the O _p X _p axis coincides with the roll stabilization axis when the planes of the platform and the outer rings, the axis O _p Z _p directed along the axis of stabilization of the platform along the pitch, the axis O _p Y _p perpendicular to the plane of the platform and directed along the axis of the platform. We connect the coordinate system O ₁ X ₁ Y ₁ Z ₁ with the outer ring of the gimbal suspension of the platform: the axis O ₁ X _{1 is} directed along the axis of the outer ring, which is the axis of stabilization of the platform along the roll, the axis O ₁ Y _{1 is} directed perpendicular to the plane of the ring, the axis is O ₁ Z ₁ coincides with the axis of the inner ring and the axis of stabilization along the roll. We will connect the coordinate system O ₂ X ₂ Y ₂ Z ₂ with the inner ring: we will direct the O ₂ Z ₂ axis along the axis of the inner ring, the O ₂ Y ₂ axis along the platform axis, the O ₂ X ₂ axis perpendicular to the plane of the inner ring. We will associate with the gyroscope the coordinate system O _g1 X _g1 Y _g1 Z _g1 : the axes O _g1 X _g1 and O _g1 Y _g1 are located in the measuring plane of the gyroscope, while the axis O _g1 X _{g1 is} directed along the measuring axis of the second channel, and the axis O _g1 Y _g1 - along the measuring axis of the first channel of the gyroscope, the axis O _g1 Z _{g1 is} directed along the axis of proper rotation of the gyroscope.

оси, связанные с объектом O_cZ_c и О_сХ_с, и оси O₁Z₁ и O₁X₁, О₂Z₂ и О₂Х₂, связанные с кольцами подвеса, повернутся на азимутальный угол ψ._г. От угловых движений объекта по тангажу

и крену

система координат, связанная с объектом, наклонится соответственно на угол тангажа υ и угол крена γ. При этом внешнее кольцо подвеса наклонится на угол тангажа υ.
Гироскоп работает в режиме обратной связи по токам датчиков момента и является двухканальным датчиком угловой скорости. Первый канал гироскопа содержит датчик угла 1, измеряющий поворот корпуса гироскопа относительно измерительной оси Y_г1, усилитель 2, эталонное сопротивление 3, датчик момента 4, создающий момент вокруг оси X_г1. Второй канал содержит датчик угла 5, измеряющий поворот корпуса гироскопа относительно измерительной оси X_г1, усилитель 6, эталонное сопротивление 7, датчик момента 8, создающий момент вокруг оси Y_г1. Напряжения U₁₁ и U₁₂, снимаемые с эталонных сопротивлений по первому и второму каналам, подаются в вычислитель 9.Let the axes associated with the platform and the object at the initial time point coincide with the Darboux coordinate system. Due to the angular movement of the object in azimuth with yaw rate

the axes associated with the object O _c Z _c and O _c X _s , and the axes O ₁ Z ₁ and O ₁ X ₁ , O ₂ Z ₂ and O ₂ X ₂ associated with the suspension rings, will rotate by the azimuthal angle ψ. _g . From pitch angular movements of an object

and roll

the coordinate system associated with the object will tilt respectively at a pitch angle υ and a roll angle γ. In this case, the outer suspension ring will bend at a pitch angle υ.
The gyroscope operates in feedback mode on the currents of torque sensors and is a two-channel angular velocity sensor. The first channel of the gyroscope contains an angle sensor 1, which measures the rotation of the gyroscope housing relative to the measuring axis Y _g1 , amplifier 2, reference resistance 3, torque sensor 4, creating a moment around the X axis _g1 . The second channel contains an angle sensor 5, which measures the rotation of the gyroscope housing relative to the measuring axis X _g1 , amplifier 6, a reference resistance 7, a torque sensor 8, which creates a moment around the _y1 axis _g1 . Voltages U ₁₁ and U ₁₂ , removed from the reference resistances in the first and second channels, are supplied to the calculator 9.

The gyroscopic angular velocity sensor is mounted on a platform controlled in azimuth and stabilized in the plane of the local horizon, the kinematic diagram of which is shown in Fig. 1. The device has a triaxial suspension, consisting of outer and inner rings. A stabilized platform is installed in the inner ring. The axis of rotation of the outer ring is mounted in bearings rigidly connected to the object and is oriented parallel to the longitudinal axis of the object. The axis of rotation of the inner ring is fixed in bearings rigidly connected to the outer ring. The stabilized platform has freedom of rotation with respect to the inner ring around the axis of the platform. The axis of rotation of the platform is fixed in bearings associated with the inner ring. The platform has three degrees of freedom relative to the object, and therefore the angular velocity sensor installed on it is isolated from the angular movements of the object, that is, it has full triaxial stabilization. Using control actions, the angular velocity of the platform relative to the inertial coordinate system is provided. When coordinating the axes of the platform with the axes of the Darboux system and the absence of linear motion of the projection object, the absolute angular velocity of the platform on its axis can be represented as
ω $\genfrac{}{}{0ex}{}{\text{P}}{\text{x}}$ = Ωcosφ;
ω $\genfrac{}{}{0ex}{}{\text{P}}{\text{y}}$ = Ωsinφ;
ω $\genfrac{}{}{0ex}{}{\text{P}}{\text{z}}$ = 0. (4)
In the steady state, for isodromic feedback of voltage from the reference resistances of the gyroscopic angular velocity sensor, it can be represented as follows
U ₁₁ = (-ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dy}}$ + ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{y}}$ ) K $\genfrac{}{}{0ex}{}{\text{-1}}{\text{n11}}$ ;
U ₁₂ = (ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dx}}$ -ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{x}}$ ) K $\genfrac{}{}{0ex}{}{\text{-1}}{\text{n12}}$ , (5)
where ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{x}}$ , ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{y}}$ - projection of the absolute angular velocity of the gyroscope body, respectively, on the axis X _g1 , Y _g1 .

Угловые движения объекта парируются системой стабилизации и на датчики угловой скорости не действуют. Пусть датчик угловой скорости установлен на точную платформу, погрешности стабилизации и дрейф которой малы и ими можно пренебречь. Для этого случая, в соответствии с взаимным расположением выбранных систем координат, проекции абсолютной угловой скорости на оси гироскопа можно представить в следующем виде:
ω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{x}}$ = Ωcosφsinψ_г1;
ω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{y}}$ = Ωcosφcosψ_г1. (6)
Подставив выражение (6) в (5), можно получить выражения для определения sinψ_г1 и cosψ_г1 в следующем виде:
cosψ_г1 = (U₁₁K_н11+ω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{дy}}$ )(Ωcosφ)^-1;
sinψ_г1 = (-U₁₂K_н12+ω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{дx}}$ )(Ωcosφ)^-1. (7)
В практике определения курсового угла с помощью датчика угловой скорости его вычисление проводят через функцию арктангенс. Тогда аналитическое выражение для определения азимутального угла ψ_г1 можно представить в следующем виде:
ψ_г1 = arctg(b₁b $\genfrac{}{}{0ex}{}{\text{-1}}{\text{2}}$ ), (8)
где b₁ = -U₁₂K_н12+ω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{дх}}$ ;
b₂ = U₁₁K_н11+ω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{дy}}$ .
При использовании функции тангенса квадрант, в котором расположен азимутальный угол ψ_г1, может быть вычислен по соотношению знаков b₁ и b₂. Зная квадрант, формулу для вычисления угла истинного курса измерительной оси первого канала гироскопа, можно представить в виде
K_r1=2π-arctg(b₁b₂ ^-1), если b₁>0, b₂>0;
K_r1=π-arctg(b₁b₂ ¹), если b₁>0, b₂<0;
K_r1=π-arctg(b₁b₂ ^-1), если b₁<0, b₂<0;
K_r1=-arctg(b₁b₂ ^-1), если b₁<0, b₂>0. (9)
Учитывая, что угол истинного курса К объекта есть угол, отсчитываемый по часовой стрелке, между осью О_дХ_д, направленной на север, и проекцией продольной оси объекта О_сХ_с на горизонтальную плоскость, то есть между направлением оси О₂Х₂, этот угол можно представить в виде
K = 2π-arctg(b₁b $\genfrac{}{}{0ex}{}{\text{-1}}{\text{2}}$ )-ψ_г+ψ_г1, если b₁>0, b₂>0;
K = π-arctg(b₁b $\genfrac{}{}{0ex}{}{\text{-1}}{\text{2}}$ )-ψ_г+ψ_г1, если b₁>0, b₂<0;
K = π-arctg(b₁b $\genfrac{}{}{0ex}{}{\text{-1}}{\text{2}}$ )-ψ_г+ψ_г1, если b₁<0, b₂<0;
K = -arctg(b₁b $\genfrac{}{}{0ex}{}{\text{-1}}{\text{2}}$ )-ψ_г+ψ_г1, если b₁<0, b₂>0, (10)
где ψ_г - азимутальный угол поворота объекта относительно платформы,
ψ_г1 - азимутальный угол между горизонтальными осями платформы и гироскопа.Let the platform with gyroscopes be located on an object that does not have a linear velocity relative to the Earth’s surface, but performs angular motion with velocities

The angular movements of the object are countered by the stabilization system and do not act on the angular velocity sensors. Let the angular velocity sensor be mounted on an accurate platform, the stabilization errors and drift of which are small and can be neglected. For this case, in accordance with the relative position of the selected coordinate systems, the projections of the absolute angular velocity on the axis of the gyroscope can be represented as follows:
ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{x}}$ = Ωcosφsinψ _g1 ;
ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{y}}$ = Ωcosφcosψ _g1 . (6)
Substituting expression (6) into (5), we can obtain expressions for determining sinψ _g1 and cosψ _g1 in the following form:
cosψ _g1 = (U ₁₁ K _n11 + ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dy}}$ ) (Ωcosφ) ^-1 ;
sinψ _g1 = (-U ₁₂ K _n12 + ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dx}}$ ) (Ωcosφ) ^-1 . (7)
In practice, determining the heading angle using the angular velocity sensor, its calculation is carried out through the arctangent function. Then the analytical expression for determining the azimuthal angle ψ _g1 can be represented as follows:
ψ _g1 = arctan (b ₁ b $\genfrac{}{}{0ex}{}{\text{-1}}{\text{2}}$ ), (8)
where b ₁ = -U ₁₂ K _n12 + ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dh}}$ ;
b ₂ = U ₁₁ K _n11 + ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dy}}$ .
When using the tangent function, the quadrant in which the azimuthal angle ψ _g1 is located can be calculated by the ratio of the signs b ₁ and b ₂ . Knowing the quadrant, the formula for calculating the angle of the true course of the measuring axis of the first channel of the gyroscope can be represented as
K _r1 = 2π-arctg (b ₁ b ₂ ^-1 ), if b ₁ > 0, b ₂ >0;
K _r1 = π-arctg (b ₁ b ₂ ¹ ) if b ₁ > 0, b ₂ <0;
K _r1 = π-arctg (b ₁ b ₂ ^-1 ), if b ₁ <0, b ₂ <0;
K _r1 = -arctg (b ₁ b ₂ ^-1 ) if b ₁ <0, b ₂ > 0. (9)
Given that the angle of the true heading K of the object is the angle counted clockwise between the axis O _d X _d directed to the north and the projection of the longitudinal axis of the object O _with X _s on a horizontal plane, that is, between the direction of the axis O ₂ X ₂ , this angle can be represented as
K = 2π-arctg (b ₁ b $\genfrac{}{}{0ex}{}{\text{-1}}{\text{2}}$ ) -ψ _g + ψ _g1 if b ₁ > 0, b ₂ >0;
K = π-arctg (b ₁ b $\genfrac{}{}{0ex}{}{\text{-1}}{\text{2}}$ ) -ψ _g + ψ _g1 , if b ₁ > 0, b ₂ <0;
K = π-arctg (b ₁ b $\genfrac{}{}{0ex}{}{\text{-1}}{\text{2}}$ ) -ψ _g + ψ _g1 , if b ₁ <0, b ₂ <0;
K = -arctg (b ₁ b $\genfrac{}{}{0ex}{}{\text{-1}}{\text{2}}$ ) -ψ _g + ψ _g1 , if b ₁ <0, b ₂ > 0, (10)
where ψ _g is the azimuthal angle of rotation of the object relative to the platform,
ψ _g1 - azimuthal angle between the horizontal axes of the platform and the gyroscope.

The azimuthal angle of rotation of the object ψ _g relative to the platform can be determined using the angle sensor located on the azimuthal axis of the platform.

The azimuthal angle ψ _g1 between the horizontal axes of the gyroscope and the platform is pre-selected. To do this, gyrocompassing is performed at different known azimuthal angles and the gyrocompassing error ΔK _g1 is determined and the angle ψ _g1 is found at which the gyrocompassing error is minimal.

где

υ₁,γ₁ - угол наклона платформы по тангажу и крену,

- платформы по крену, тангажу и в азимуте.The gyro compaction error using an angular velocity sensor mounted on a stabilized platform can be represented as

Where

υ ₁ , γ ₁ - the angle of inclination of the platform in pitch and roll,

- roll, pitch and azimuth platforms.

=0,01 град/ч,
ω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{дx}}$ = ω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{дy}}$ =1 град/ч,
Δω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{дx}}$ = Δω $\genfrac{}{}{0ex}{}{\text{г1}}{\text{дy}}$ = 0,01 град/ч,
φ=55,5 град,
K_н11=K_н12=3,5•10^-7 1/с мВ,
ΔK_н11=ΔK_н12=3,5•10^-10 1/с мВ,
Δφ=0,05 град.Using expression (11), the influence of the azimuth angle ψ _g1 on the gyrocompassing error was studied. The studies were carried out by computer calculations using the following parameters and the errors of their task:
ΔU ₁₁ = ΔU ₁₂ = 0.15 mV,
υ ₁ = γ ₁ = 0.017 degrees,

= 0.01 deg / h
ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dx}}$ = ω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dy}}$ = 1 deg / h,
Δω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dx}}$ = Δω $\genfrac{}{}{0ex}{}{\text{g1}}{\text{dy}}$ = 0.01 deg / h
φ = 55.5 degrees
K _n11 = K _n12 = 3.5 • 10 ^-7 1 / s mV,
ΔK _n11 = ΔK _n12 = 3.5 • 10 ^-10 1 / s mV,
Δφ = 0.05 deg.

The calculated error of gyrocompassing ΔK _g1 depending on the azimuthal angle ψ _g1 between the horizontal axes of the platform and gyroscope controlled in azimuth and stabilized in the plane of the local horizon is shown in Fig. 4.

When considering the dependence shown in figure 4, it is clear that there are two azimuthal positions of the gyro at angles ψ _g1 = 13.5 ^o and ψ _g1 = 148.5 ^o , when there is no gyrocompass error. Therefore, choosing one of these angles, for example, ψ _g1 = 13.5 ^o , in this azimuthal position fix the gyroscope body relative to the platform and in the future, with working gyrocompassing, this angle is preserved.

 The drift of the gyroscope mounted on the platform is determined as a result of preliminary calibration tests, based on which a drift model is used that is used in gyrocompassing.

Thus, the proposed gyrocompassing method using a gyroscopic angular velocity sensor mounted on a platform controlled in azimuth and stabilized in the plane of the local horizon has the following differences from the known method:
- in the preset operation, a gyroscopic angular velocity sensor is installed on a platform controlled in azimuth and stabilized in the plane of the local horizon,
- in the preset operation, the azimuthal position of the gyroscope is found relative to the platform at which the gyrocompassing error is minimal,
- the gyrocompassing operation determines new information about the azimuthal angle of rotation of the object relative to the platform,
- determination of the angle of the true course of the object is made according to a new analytical dependence, which uses information about the angles characterizing the azimuthal positions of the gyroscope and the object relative to the platform.

 Figure 1 shows a diagram for gyrocompassing using a gyroscopic angular velocity sensor mounted on a platform controlled in azimuth and stabilized in the plane of the local horizon.

 Figure 2 shows the errors of gyrocompassing using a two-channel gyroscopic angular velocity sensor depending on the yaw rate, the rate of change of pitch and roll angles.

 Figure 3 shows the error of gyrocompassing using a two-channel gyroscopic angular velocity sensor depending on the azimuthal orientation of the gyroscope.

 From the dependences presented in figure 2, it is seen that in the known method, the angular velocities of the object on which the gyroscopic angular velocity sensor is mounted significantly reduce gyro accuracy, making it practically impossible at angular velocities of pitch, roll and azimuth of more than 1 deg / hours

 In the proposed method, the angular velocity of the object in azimuth, pitch and roll do not act on the angular velocity sensor, since it is located on a platform that provides triaxial stabilization.

 From a comparison of the dependencies presented in figure 3 and figure 4, it can be seen that in the known method there is a dependence of the gyrocompassing error on the azimuthal orientation of the object, since the gyroscope is rigidly connected to the object by a strapdown method. At the same time, there are heading angles of the object at which a significant increase in the gyrocompassing error occurs.

 In the proposed method, the azimuthal orientation of the gyroscope in space is determined, which provides the minimum gyrocompassing error that is maintained during the working gyrocompassing due to the use of a platform controlled in azimuth and stabilized in the plane of the local horizon.

 Therefore, the application of the proposed method allows gyrocompassing with increased accuracy using a gyroscopic sensor of angular velocity in the conditions of angular movements of the object, which is impossible when applying the known method.

 The application of the proposed method allows to expand the scope of use of gyrocompass devices based on a gyroscopic angular velocity sensor due to the ability to determine the true course of an object subject to the effects of soil vibrations, waves of the water surface, wind loads.

Claims (1)

A gyrocompassing method using a gyroscopic angular velocity sensor mounted on a platform controlled in azimuth and stabilized in the plane of the local horizon, including the use of a gyroscope in the current feedback mode of torque sensors, preliminary coordination of the signs of voltage changes with the reference resistance of the gyroscope with the direction of rotation of the housing about its own axis rotation, determination of the gyro drift model, and with gyrocompassing - determination of stresses from reference copro of the gyroscopes through the first and second channels, characterized in that the gyroscope is pre-installed on a platform controlled in azimuth and stabilized in the plane of the local horizon so that the plane of the gyroscope measuring axes coincides with the horizontal plane of the platform, the platform is mounted on the object so that the stabilization axis along the roll coincided with the longitudinal axis of the object, the axis of stabilization along the pitch was directed perpendicular to the plane of symmetry of the object to the starboard side, after which they select the platform in the horizon and in azimuth so that one horizontal axis of the platform is directed north and the other east, rotate the gyroscope body relative to the platform about its own rotation axis, gyrocompass and determine gyrocompass errors after rotation, determine the azimuthal angle of rotation of the gyroscope body relative to the platform at which the gyrocompassing error is minimal, and then the azimuthal angle of rotation of the relative object is determined during working gyrocompassing but the platform and calculating the true course of the angle of the object using the following formulas:
K = 2π-arctg (b ₁ b $\genfrac{}{}{0ex}{}{\text{-1}}{\text{2}}$ ) -ψ _r + ψ _r1 if b ₁ > 0, b ₂ >0;
K = π-arctg (b ₁ b $\genfrac{}{}{0ex}{}{\text{-1}}{\text{2}}$ ) -ψ _r + ψ _r1 if b ₁ > 0, b ₂ <0;
K = π-arctg (b ₁ b $\genfrac{}{}{0ex}{}{\text{-1}}{\text{2}}$ ) -ψ _r + ψ _r1 if b ₁ <0, b ₂ <0;
K = -arctg (b ₁ b $\genfrac{}{}{0ex}{}{\text{-1}}{\text{2}}$ ) -ψ _r + ψ _r1 if b ₁ <0, b ₂ >0;
where b ₁ = -U ₁₂ K _n12 + ω $\genfrac{}{}{0ex}{}{\text{r1}}{\text{dx}}$ ;
b ₂ = U ₁₁ K _n11 + ω $\genfrac{}{}{0ex}{}{\text{r1}}{\text{dy}}$ ;
ω $\genfrac{}{}{0ex}{}{\text{r1}}{\text{dx}}$ , ω $\genfrac{}{}{0ex}{}{\text{r1}}{\text{dy}}$ - a model of the gyro drift along the axes X _g1 , Y _g1 ;
U ₁₁ , U ₁₂ - voltage from the reference resistance of the angular velocity sensor, respectively, on the first and second channels;
K _n11 , K _n12 - the slope of the gyroscope in voltage for the first and second channel;
ψ _r is the azimuthal angle of rotation of the object relative to the platform;
ψ _r1 is the azimuthal angle between the horizontal axes of the platform and the gyroscope.

Images