DE1811736A1 - Method and device for damping a pendulum oscillator - Google Patents

Description

LEAH SIEGLER, INC., Incorporated under the laws of the State of Delaware, Santa Monica, State of California (V.St.λ.)

Method and device for damping a pendulum Schwingers

The invention relates to a method and a device for damping the movements of a person around his position of equilibrium oscillating oscillator.

Oscillators that oscillate or vibrate about a position of equilibrium are used in many devices, so e.g. in ordinary heavy pendulums, bifilar and trifilar heavy pendulums, torsional pendulums, spring-centered waves, or resiliently suspended hates. These vibrations are often undesirable, especially in the case of a meridian pointer for the direct display of a meridional plane. A pendulum-shaped fevridian-pointing top, whose Running axis · lies horizontal to the earth's surface, precesses under the influence of the earth's rotation, so that its running axis adjusts to astronomical north. In addition

909834/0971

the gyro must of course be freely rotatable about its vertical or azimuthal axis.

Meridian-pointing or meridian-pointing gyroscopes are of great use in instruments for orientation and accurate direction indication is used. However, their usefulness has its limit where it becomes impossible The running axis can be set easily and quickly in the meridian direction or astronomical north direction. If there is no additional cushioning it often takes two days or more, until the running axis comes to rest in its equilibrium position in the meridian plane after oscillations around this plane has come.

For calming the swinging movements around its equilibrium position eddy current damping or damping working with viscosity were used up to now. In some Meridianweisern a continuous, speed proportional damping is used and the damping torque is smaller than the critical damping torque of the System chosen. Such a damping moment brings the oscillator into its equilibrium position after a certain time. However, it turned out that in many cases this period of time is too long and thus the usefulness of the transducer is impaired.

In more modern Meridianweisem an azimuthal Damping moment worked either to the instantaneous Elevation angle of the running axis or the current angular velocity is proportional to the axis of travel in the azimuthal plane. In both cases, the size of the Damping moment chosen so that it ale somewhat less is the critical damping torque; it lies between the

9 0 9 8 3 4/0 b 7 1

for a sufficient stability of the gyro according to its Calming in the meridian plane and the size necessary for the oscillation of the running axis in the permissible Angular range, among other things, the meridian plane required within a given time interval after the gyro was released Greatness of the attenuation monent.

Such danish institutions usually cooperate a damping ratio that is less than 1 (usually between 0.7 and 0.9), so that the running axis has a damped oscillation around the meridian or equilibrium position executes before it adjusts itself to the permissible azimuthal angular range. The setting time a meridian pointer with such a damping device is two to two and a half times the period of oscillation of the undamped oscillation of the top and in detail depends of course on the attenuation ratio used and the size of the initial azimuthal Angle. However, since the damping ratio is changed by temperature and other influences, this method contains a certain uncertainty factor with regard to the time within which the amplitude the running axis vibrations around the meridian plane below the size of the permissible azimuthal angle error range has sunk.

The object is therefore to specify a method and a device for damping the oscillating movements, the? ie in an accurate, reliable and from external Influences largely independent manner within as short a period of time as possible or at least immediately Allow the equilibrium position to come to rest.

90983A / UÖ /

This object is achieved by the method according to the invention solved, after which the movement of the oscillator remains undamped in a first preselected time interval and supercritical during a second preselected time interval is dampened. The start of the first time interval can be set at a point in time at which the transducer is out of its equilibrium position. A preferred embodiment of this method provides that the first and the second time interval are lined up alternately in a preselected number. Furthermore, the movement can initially be dampened supercritically during a third preselected time interval will. Finally, the first time interval can be approximately equal to the fourth part of the undamped natural period reduced by a time interval that is divided by the undamped natural period divided by 4 * ΤΓ times the Damping ratio is determined to be selected. It also proves to be particularly advantageous to use the expression to express the second time interval to

t ₂ - »(in

where T is the undamped natural period, S is the damping ratio, ψ _{0 is} the initial deflection from the equilibrium position and γ is the deflection from the equilibrium position at the end of the second time interval. The ratio <S between the first and the second interval is preferably given by

T (In T ^ - InF)

<o

2T

It is also advisable to make the supercritical damping dependent on the speed of the transducer. This dependency can either be in a proportional

9 0 9 8 3 k I 0 a '/'!

Functionality to the square of the speed of the oscillator or in a direct proportionality to the speed of the transducer. The supercritical damping ratio is preferably between about 5 and about 20, a value of around 10 is particularly favorable.

The method according to the invention can preferably be applied to vibrators, the movement of which corresponds to the differential equation

m ^ U, f D ff ₊ f (x) «0

obeys, where m is the moving mass, D is the damping coefficient, f (x) the restoring force acting on the mass, χ the displacement of the mass from its equilibrium position and t mean the time. It turns out to be advantageous to choose the damping coefficient so that that it is a function of the speed of the mass and for all speeds greater than for the critical Damping the mass is necessary. This speed function of the damping coefficient is preferably designed in such a way that that the damping coefficient is proportional to the square of the speed of the moving mass. Furthermore, the damping is preferably chosen so that at speeds of the moving mass below a preselected size this damping is mainly proportional to the speed and at speeds above the selected value is mainly proportional to the square of the speed of the moving mass.

With a meridian-pointing top whose movement is in normalized azimuth elevation coordinates to the differential equations

909834/0971

ac «t r

and

obey the instantaneous azimuth angle of the centrifugal barrel axis, γ ■ ~ Q of motion of the spin axis ψ- the normalized current elevation angle of the circles! running axis (y is the actual elevation angle, T "^ ₀ t normalized time ο" the supercritical damping ratio with respect to the azimuth plane, C the speed-proportional damping coefficient around the azimuth axis, H the torque of the rotor around the axis of the gyroscope, Sl the local horizontal component of the angular velocity of the earth's rotation, U) ₀ »-J ^ Lo. the angular frequency of the undamped oscillation of the gyro axis in the local geographic latitude and M the pendulum moment around the elevation axis of the gyro axis, so that the locus curves in a phase plane representation of the movement have a first asymptote with the equation t «(& - ~ \ [b ^z - V) V, along which the equilibrium position is reached most slowly, and a second asymptote with the equation? »(& ₊ - \ | 5 ² _1) _f along which the equilibrium position is reached the fastest, provides the method according to the invention that the first and the second asymptote are used as switching lines in such a way that the supercritical damping is switched off at the first asymptote and the gyro axis can freely precess until its movement flows into the second asymptote in the phase plane representation and at this confluence into the second asymptote, the supercritical © damping for the movement of the gyro is switched on, a movement that is entl ang the second asymptote up to the stable singular

909834/09 7 1

lar point at the one located in the meridional plane Origin continues. In the case of an initial supercritical damping during the third Time interval, start the precision movement of the rotating axis of the top from a fixed point without starting speed *

The device according to the invention for carrying out the method provides a sensor for the instantaneous speed of the oscillator, a damper that responds to the feeler, the supercritical one to the instantaneous speed Proportional damping is generated, and a control prior to that at pre-selected repetition intervals during of a preselected time interval the generated supercritical Allow damping to act on the transducer. This device in a Meridianweiser, which has a pendelförmipjen Contains gyroscope with a horizontal axis, which tends to move due to a movement caused by the rotation of the earth Precision torque to adjust a vertical axis in a meridional direction, preferably has a tap that generates an electrical signal proportional to the movement of the barrel axis around the vertical axis, a signal generator which is electrically connected to the tap and converts the tap signal into one of the speed converts an electrical signal proportional to the movement of the running axis, a timer that is set with a selected Repetition speed during a preselected period of time on the speed of the movement of the running axis proportional electrical signal generated, and a torque generator connected to the gyro on, which responds to the timer and at times a torque counteracting the precision torque by the vertical axis developed. It is particularly cheap

9 0 9 8 3 Λ / U ^f J 7 t

the movements of the running axis of the top to the horizontal To restrict azimuth plane. Furthermore, the device according to the invention is preferably designed in such a way that that a part is provided that can be rotated concentrically about the vertical axis of the gyro, that further a tap that generates an electrical signal as a function of the relative rotation of the gyro with respect to the rotatable one Part generated, also an auxiliary device for rotating the rotatable part about the vertical axis to reduce the relative movement between the top and the rotatable part essentially to zero, ultimately one Voltage source, the voltage of which is proportional to the angular speed of the rotating part, then a torque generator, which responds to this voltage, a supercritical damping for the movement of the gyro generated around the vertical axis and connected to a second voltage source, and finally an adjustment device is provided for controlling the torque generator so that it can control the azimuthal movement of the gyro only temporarily disabled. Finally, the nature of the torque generator's dependence on voltage may be be a linear function. It is also advantageous if the torque generator is essentially linear from the Voltage depends, as long as the latter remains below a preselected voltage value, and essentially quadratic depends on the voltage if the latter is greater than the preselected value. The torque generator works here preferably electromagnetic. And moreover, it is quite advantageous if the size of the torque generator delivered torque to the geographical latitude of the gyro location with the help of an adjusting device can be adjusted to allow changes

0 9834/09 7

which is characterized by a different geographical latitude of the Result of the gyro location to compensate. This compensation can of course also be brought about particularly well in this way be that the interval length of the undamped oscillation is adjusted accordingly with an adjusting device.

The method according to the invention for damping the vibrations of a mechanical system in order to bring it to rest or to bring it close to its equilibrium position, «lives proposed that a fixed damping cycle was iteratively applied that is made up of a first interval of undamped movement followed by a second interval a supercritically damped movement. This procedure. is carried out with a sufficient number of steps carried out until the system has approached its equilibrium position as much as desired.

The preferred application of this dampening method happens with meridian pointers, in which the first interval of the undamped movement consists of the free precession of the rotary axis against the meridional plane and on which is followed by the second interval of supercritical damping, which is the running axis closer to the meridional plane than it would if the movement were left to itself. By making these intervals sufficient are often strung together, the axis of the meridian-pointing top can be so close to the meridional plane be brought in as required by the requirements.

The method according to the invention can generally be applied to any mechanical vibratory system with several

909834/097 1

Degrees of freedom are applied, in particular, of course, to those systems whose motion is the differential equation

m. ^ + C. Ο + kx »0 ² German

German

to obey. The movement of such systems, the pendulum-shaped as well as the non-pendulum-shaped meridian pointing Gyroscopic can be represented graphically in a phase plane diagram in which the equation of motion in the l <'orm

^v · ti ^{+ 2} ^ ^{v + x} "° ■

is written. Here χ means the deflection of the system from its equilibrium position, further i3t ν * x ¹ = -j ~, further finally S »- = - equal to the damping ratio T» ω _ο ΐ, and ω, »-u jj is the angular frequency of the undamped Systems and finally t is the time. In this phase diagram, the variable ν is plotted against the deflection χ. Phase plane diagrams are very useful for analyzing oscillatory or vibratory systems. This type of investigation is well known from the relevant literature on mechanical vibrations

If ^ - 0, then the trajectories in the χ, ν-plane are circles whose radii are given by the added values of the deflection Xq. If S ton 0 is different, then the trajectories in the Phasaneben® are partly straight lines with the exception of the neighborhood of an asymptote whose equation is

900834/097

to which all trajectories approach the stable, singular point at the origin of the phase plane huddle asymptotically. A starting point P (x, v), which represents the current state of the system, runs with increasing time on the trajectory for the damped movement that is caused by the initial conditions is determined. When approaching the asymptote, he runs along it towards the origin he is theoretically reached after an infinite amount of time. An exception to this way of approaching the origin is that Trajectory whose equation is

χ ¹ + (0+ "Vd-I) -XO

which practically represents a second asymp. dead of the system and along which the movement comes very quickly to the vicinity of the singular point in the origin advances. These two asymptotes are trajectories of the slowest or the fastest approach to the singular point at the origin.

The inventive method for damping the system whose equilibrium position with the singular point in the Phase level coincides with the fact that the system with the speed 0 of their out of equilibrium located position is left free that the starting point along the Kreisperpherie, which by the initial displacement is determined, progresses until he at the intersection between the trajectory for the undamped and the trajectory for the damped movement, represented by the fast asymptote arrives. At this point the attenuation is switched on

909834/0971

and the starting point P (x, v) moves quickly along the fast asymptote in the vicinity of the stable singular Point at the origin, that of the equilibrium position. of the system. .

The fast asymptote is kind of like this Switching line with the exception that the switching process is not initiated by the fast asymptote, but rather, in that the interval of the undamped movement is predetermined so that at the time of switching on the starting point will be at the fast asymptote.

Due to errors in the timer it can happen that switching from the undamped to the damped state of the system takes place either too early or too late, so that the starting point is along one of the neighboring Orbit curves instead of continuing on the fast asymptote leading directly to the origin, so that he was caught by the -slow asymptote and will never reach the origin or equilibrium. In order to eliminate this failure, the original cycle, which consists of a narrow time interval, is used the free undamped movement and a subsequent second time interval of the damped movement, repeated by adding a new interval of undamped movement from the first position of the starting point to the slow one Asymptote is initiated starting out. After the second cycle has been completed, the point will return to the slow asymptote almost come to rest. The second meeting point of the starting point with the slow asymptote represents a location closer to the origin than the first meeting point at the end of the first dampening cycle. This way it's by iteratively repeating the

909834/09 7

Method possible to get as close to the origin as necessary, despite errors in the temporal Dimensioning the interval of free, undamped movement.

It is obvious, that the slow and the fast Asymptotes, which are characteristics of the system, serve as reference or guide lines, and that in particular the slow asymptote provides a fixed reference line from which the undamped movement is based on each cycle; in this way, a cumulative error in the location of the reference point P representing the state of the system due to a single constant timer error avoided for the interval of undamped movement.

This type of damping method is of particular value for the damping of a meridian-pointing top, due to which it moves quickly and from an initial deflection in or near the meridional plane comes to rest.

The use of the fast and slow asymptotes as switching lines is a preferred implementation of the more general one Procedure for the application of two switching lines, one of which is used to determine the time of application for the supercritical damping and the other for determining the point in time for the cancellation of the damping and the transition to the undamped or proper motion is used.

Pie Determination of the time interval for the starting point to at the end of the initial undamped movement into the merging the preselected switching line is simplified,

'909834/09 71

when the system's transducer starts with no initial speed. This condition is met by that supercritical damping is applied simultaneously with the release of the system from its initial deflection will. This brings the slow asymptote into the. Game so that the starting point, which is now on a trajectory for the muffled movement is running, the slow asymptote cannot intersect, but rather almost to rest on it comes so that the undamped movement from the slow Asymptote is initiated ",

The device with which the damping force is generated and optionally applied comprises a feeler for the Speed with which the transducer moves towards its equilibrium position. The device has also a damper that responds to the sensor and thus to the instantaneous speed of the transducer and generates the damping force which is proportional to the speed of the vibrator. The dampening force is given to the transducer via a timer that determines the time interval in which the damping force is applied, and also the time interval between the individual applications of the damping force in the iterative damping method «,

The time interval between the applications of the damping force as well as the size of the damping force can be set, to compensate for changes in working conditions, e.g. due to changes in geographical Width for the pail show that the transducer consists of the running axis of a meridian pointer.

909834/0971

In another embodiment, the damping force generated can be the square of the instantaneous speed be proportional or it can initially be proportional to the instantaneous speed, if the speed is below a preselected value, and can then be the square of the current speed be proportional if this speed exceeds a second preselected value.

The features and advantages according to the invention are furthermore apparent from the following description of an exemplary embodiment with reference to the accompanying drawings. Show it:

1 shows the phase level diagram of a normalized, undamped oscillation of a vibrator;

2 shows the phase level diagram of a normalized, supercritically damped oscillation of a Schwingers;

3 shows the block diagram of an inventive Damper;

FIGS. 4 and 5 are a plot of the damping ratio versus the time intervals of the iterative damping;

6 shows the phase level diagram of the general

method of iterative damping according to the invention;

7 and 8 the phase level diagram of a preferred embodiment of the invention Method of iterative damping;

9 shows the phase level representation of an undamped movement and a supercritical one subdued movement along the fast asymptote;

90983A / 0971

Pig. 10 shows the phase level representation of the invention iterative damping for the one starting at a negative starting angle Move; and

11 shows the phase plane representation of an undamped, starting with a large starting angle Movement of an oscillator due to a restoring force that is proportional to the sine of the deflection.

Devices with oscillators or vibrators can be analyzed particularly easily by having the Equations of motion of the oscillator and the graphic solution curves of the equations for the movements of the device considered.

In one embodiment according to the invention, the device consists of a vibrator that has a periodic movement executes around a position of equilibrium, from a meridian-seeking top; nevertheless the invention in no way limited to this particular device, but in the same way "to any other device Can be used with a transducer, for example on ordinary gravity pendulums, bifilar and trifilar pendulums, torsion pendulums, spring-centered shafts and spring-mounted shafts Crowds. In the following description, however, only a meridian-seeking top is spoken of.

There are generally two types of meridian-seeking gyroscopes and each of these two types is equally good at Explanation of the invention suitable * It concerns pendulum-shaped tops and around non-pendulum-shaped tops, In the description of the pendulum-shaped, meridian-seeking Roundabout run out.

909834/09 7

Such a gyroscope contains a rotating rotor, a running axis, which is mounted in a stator frame, and a drive device. The top itself sits in a housing, which is the case with a pendulum-shaped top has two degrees of freedom, namely one degree of freedom around an elevation axis and the other degree of freedom around an azimuthal axis. With a pendulum top, on which the description is based, the movement of the barrel axis is synonymous with the movement of the housing, in which the gyro is housed.

For small deflection angles, the equations of motion of a dampened swinging meridian-seeking top can be described in the simplified form:

C & + H- / I4 / - H d £ - 0 (1)

H dp + MO »0 (2)

where C is the damping factor for the azimuthal axis; γ is the azimuth angle, which is counted positive to the east; H the swirl of the gyro rotor around the axis of rotation; —IX is the local horizontal component of the angular velocity COe. the earth; Q is the elevation angle, which is counted positively upwards; M is the torque about the elevation axis; and t the time.

In equations (1) and (2), the attenuation was around the elevation axis and the moments of inertia of the gyro housing and the impeller to the two Running axis, vertical axes neglected. Compared to the other sizes, the mentioned ones are negligible

909834/09 7 1

small and are usually left out of consideration when examining the operation of a pendulum-shaped meridian-seeking top. The absence of these quantities in the following equations in no way invalidates the results of the analysis; rather, this makes the system accessible to a representation in the phase level. Furthermore, it is convenient to normalize equations (1) and (2) by introducing a dimensionless time ^c ] ~~ ■ CO ₀ 1, where 10q is the natural frequency of the undamped system iat LÜo ^? »^, Also § ^> - 2 S and

With these substitutions in equations (1) and (?) We get

2 ά 4 * "" + v - P

Ö.T ι α. f
and

or 3

As is well known, the end of the running axis of an undamped gyroscope moves along an ellipse in a vertical plane which is perpendicular to the meridional plane and the major axis of the ellipse being in the azimuth plane and the minor axis of the ellipse being in the meridional plane. The substitution ~~ q ~ ^s "§ turns the normally traversed ellipse into a circle _$ with the help of which a representation of the movement becomes very simple» The damped movement will of course be changed accordingly _$ since the elevation and azimuthal axes are now the have the same scale factor »

Separation of the variables in equations (3) and (4) leads to

90 9 834/09 / i

German ¹

If

The equation (5) for the azimuthal movement int a differential equation of the second order with the parameter ο which denotes the damping ratio of the system. So <S <1 means a weakly damped system, the solution of which can be expressed with a damped sinusoid. S '= 1 means critical damping, which leads to a linear algebraic function with an attenuator, while ά> 1 represents a heavily damped or supercritically damped system. After all, σ = O means an undamped system, the solution of which is a sinusoidal curve, to which a simple harmonic movement belongs at small angles.

The solutions to equations (5) and (6) are for the undamped case

= Y ₀ cos T - f ο ^{sin r} (5a)

β V ₀ sin T + ^ cos ^r t '(6a)

for o = O; in the supercritically damped case, in which S »1, the following applies

γ ■ «eh ^ cosh - ^ I +

^ «E (fcosh ^ T + -3Ii-I-i2

where ^ r _{0 is} the initial azimuth angle, £ the initial elevation angle and ·> ι ■ ιί ^ - 1.

Equation (5) is the general equation for a 909834/0971

damped linear vibratory structure with a Degree of freedom. An example of such a structure is a helical spring with one degree of freedom. The discussion of the properties of these linear oscillators is well known from the literature. equation (5) also applies to the azimuthal movement of both the pendulum-shaped and the non-pendulum-pointing meridian-pointing Gyroscope, where V "is the angle of azimuth and

0 mean the damping ratio around the azimuth axis. For a non-centrifugal pendeiförmigen the suitability is en-

I ti /) '

frequency of undamped movement. co _o «-W - ^

where I is the moment of inertia in relation to the azimuth axis.

For a better understanding of the invention, the behavior of the gyro is shown in the phase plane representation in which the dimensionless speed (-sTr-) of the barrel axis is plotted against the azimuthal deflection (γ) of the barrel axis. Such phase plane diagrams are also known from the literature and are useful tools for discussing the properties of vibratory structures. If one introduces the abbreviation yr » -j ~~ , then the equation can be transformed

d τ. ο C. _t . , .._ λ (ο}

in which the dimensionless time T has been eliminated to obtain an equation in ψ and y . The solution to equation (7) is the locus for the running axis in the

^ r, y ' plane. In the diagram, the point P serves as the starting point; its position on the locus indicates the deflection and the speed of the end of the axis to a certain time.

909834/0971

If ο ■ is O, then equation (7) is reduced on

(8th)

with the known solutions

y ' ² + γ- ² - C (9)

in which the constant G on the right is determined by the initial conditions. If T »0, ψ »

and ^ »] r _fl, then G" f ₀ and the equation (9) becomes

/ 2 2 iir 2 (9a)

These equations describe a number of concentric circles with the radius If ₀ and correspond to the milling movement of the top due to the effect of the torque caused by the rotation of the earth.

The solution curves of equation (9a) in the phase plane correspond to curves a, b and c in FIG. 1. The reference point P moves clockwise in FIG. 1 at a constant angular velocity on a circle with the radius * y ^r o · ^ ^The current position of the point P is determined by the angle Y, which is conventionally negative. The instantaneous values of y and y ¹ are then given by y » y _o (5-cos T and γ ' » "ψο sin T. Another method for considering the undamped precession movement of the axis of a meridian-pointing top is to determine the deflection |, the proportional to the deflection about the Elevationsach.se is γ against the deflection about the azimuthal axis to apply, ie, the behavior of the gyro with a V, f represent coordinate plane. Since ^ is equal to the negative ψ ¹ (the same

909834/0371

chung 6), this coordinate plane is obtained by rotating FIG. 1 by 180 ° about the ψ axis. This results in the more well-known γ *, f -plane, in which the movement takes place counterclockwise and the angle T is positive.

For supercritically damped systems where o »1, has the equation (7) in a phase plane representation a solution that is substantially different from the case

k ■ 0 as shown in FIG. The solution curves of equation 7 for o »1 form a family of curves shown in FIG. These curves are almost straight and parallel lines (d -.h in FIG. 2) with the exception of the vicinity of the straight lines A1-A1. The equation of the straight line JU - A1 is

The straight line is an asymptote, that of no solution curve can be cut and to which every solution curve approaches asymptotically and to a singular point, the Origin 20, approaching »

The starting point P in Fig _o 2 with the initial conditions ψ '»f ₀

ψ * a Y ₀ is on the curve F from the point Vo "ψ ο starting la toward DIE straight A1-A1 run along and the latter at the origin 2O ₉ of the point of stable equilibrium is toaalierrajg, converge asymptotically.

The movement along the asymptote A1-A1 is the slowest Approaching the origin, that of the creeping movement of the corresponds to the usual strongly damped systems »

909834/09 7

A supercritical damping ratio is used in the present invention. It is assumed that this damping ratio is ten times the critical damping. Such a large value of the damping ratio ( 6 a 10) has the effect that the movement along the straight line A1-A1 is so slow that the setting time of the gyro is several hundred times longer than it can be practically tolerated. As will become apparent from the following description, the otherwise undesirable property of the slow asymptote is used for the method and apparatus according to the invention as a means to stir the oscillating or vibrating element at or near the equilibrium point in a relatively short time bring to.

A curve along the straight line through the origin A2-A2 represents a Curve of the fastest approach to the origin. If a curve begins at this asymptote A2-A2 or it is due to any circumstances intersect, then the starting point P becomes very quickly along the asymptote on the origin to run and get close to it in the shortest possible time. The equation of the straight line A2-A2 is

γ * + (b + γό ² - 'ι) γ

Since the origin is a stable singular point, the starting point P running along the fast asymptote will come to rest near the meridian plane that runs through the origin and is perpendicular to the f axis.

The slow as well as the fast asymptote enclose the angle Od in FIG. 2 with the γ axis and the γ ^{1 axis.} This angle Of depends directly on the one chosen

909834/0971

Damping ratio from and over the definition S. ■ directly dependent on the fundamental properties of the system. If the damping ratio 6 increases, the angle CX becomes smaller and, for an infinitely large damping ratio ο, tends towards 0, so that the fast asymptote with the ψ axis and the slow asymptote with the γ axis of the phase plane in FIG. 2 coincide.

As from the phase level shown in FIG. 2, in which

O has the value 10, it can be seen that the family of solution curves in equation (7) consists of virtually parallel straight lines, except for the neighborhood of the slow asymptote A1-A1. The curves for O = 10 enclose an angle with the γ axis which is closer to 90 ° than is evident from FIG. 2 and the following figures. This is due to an exaggerated representation of the angle Cx. From FIG. 2, values between 6 ° and 7 ° can be read off for the angle, while in the practical case this angle is less than 3 with a damping ratio of 6-10.

If the damping ratio 6 increases above the assumed value of 10, the solution curves become more straight and parallel, until the curves run parallel to the y-axis at an infinite damping ratio. If, on the other hand, the damping ratio becomes less than 10, then the solution curves become less straight and more curved until they merge into a family of concentric circles at ο »0. This behavior of the solution curves as a function of the damping ratio is known from the relevant specialist literature. The shortest possible time in which the axis of the gyro into the

909834/09 7

Meridian plane can be brought, is reached (as can be seen from Fig. 1 and 2) when the starting point P along a circle periphery, which describes the free precession movement, up to the fast asymptote A2-A2 and then the starting point of this asymptote up to the can follow origin located in the meridian plane.

A device for executing the method according to the invention is shown schematically in the block diagram of FIG. 3

shown. For explanation, the device to be controlled was used a meridian-pointing gyroscope is used, its precession movement around both the azimuth and elevation axes takes place.

The mode of operation of the control device according to FIG. 3 is described with reference to the phase plane representation from FIGS. 1 and 2. The azimuthal movement of the rotating axis of the gyroscope is described by equation (7) and agrees with the solutions of this equation for the case b >> 0 or 8 >> 10 according to FIGS. 1 and 2, respectively. The inputs to the gyro, which are shown schematically in FIG. 3, are ί 'and - 2 <S · γ', to which the gyro responds with the outputs y and ιμ- ¹ . If 6 ■ is 0, then the only input is from

£ 'and the top makes a simple harmonic movement from, the precession movement of which is shown in FIG. On the other hand, if ο = 10, then passes the movement of the gyro corresponding to the movements of the reference point P along one of the trajectories from FIG. 2.

The control device works on the azimuthal movement of the running axis, which is the oscillatory or vibratory Element of the meridian-pointing top 1 of FIG. 3

909834/0 97

is. The control comprises a tap 2 which is connected to the azimuthal movement of the running axis of the gyro 1 and has an output which corresponds to the deflection and the speed of the rotary axis in the azimuth plane. The output of the tap 2 is amplified by the amplifier 3 and sent to the motor 4. The output of the motor 4- is fed back to the input of the tap 2 via a speed-reducing mechanism, such as a gear box 5. The deflection output of the gear box combines aich with the deflection output of the gyro and forms a summing connection 6. The coupling between the gear box 5 and the motor 4 and between the gear box 5 and the summing connection 6 is of a mechanical nature, which is indicated by the dash-dotted lines in the drawing The servo system from the tap 2 _$ the amplifier ² I ₉ the motor 4 and the gear 5 of the azimuth movement of the gyro 1 acts in this way.

A typical tap and a 3 servo loop for a meridian-pointing top is described in an American patent application (USSN 5-9 325 of February 23, 1966). For the purposes of explanation it is assumed that the gyro 1, the tap 2, the amplifier 3, the motor 4 and the gearbox 5 from? Ig ₀ 3 are similar to the components described in this application.

The output of the motor 4- is also given to a tachometer generator 7, whose output ep anaung reaches an amplifier and demodulator 8 “The output voltage of the tachometer generator ^ 7 corresponds to the angular velocity and is proportional to the angle Ige schwin · =

90983-4 / 09'M

speed of the running axis in the azimuth plane and is on a timer and attenuation control 9 given that generates a damping torque about the azimuth axis; this moment is proportional to the instantaneous speed of the Running axis in the azimuth plane. The damping torque is on the oscillator, i.e. on the gyro 1 via a torque generator 10.

In the servo device specified above, this enables Gear 5 »that the engine 4 runs at high speed and itself so that results in a more uniform movement. The output voltage increases due to the relatively high number of revolutions of the motor of the speedometer generator 7, which sits on the shaft of the motor 4-. The deflection difference between the part of the tap 2 driven by the gyro and the part of the tap 2 driven by the motor generate an error signal £. This error signal is amplified by the amplifier 3 and sent to the motor 4 in one polarity given that the error signal from the tap is reduced. To improve the servo sensitivity, in phase and amplitude compensation must also be provided for the amplifier *

In addition, the stability of the servo device can be improved by using a speed-dependent Feedback signal from the output of the tachometer generator 7 is passed to the input of the amplifier 3 via a feedback circuit 12.

The output voltage of the tachometer generator 7, the is proportional to the azimuth speed - is amplified and demodulated in the amplifier and demodulator 8 then it goes into the timer and damping control 9, which is the inputs to the torque generator

909834/09 71

BAD OHtQfNAi.

for the gyro controls.

As can be seen in FIG. 3, coils 13 and 14 are provided in the gyro torque generator 10, the axes of which are at right angles to one another. The coil 13 is attached to the gyro housing and carries a constant current I. The coil I ² K sits on the servo slave frame of the gyro and carries a variable current X ₂ «which is proportional to the output voltage of the tachometer generator? is ι which in turn is proportional to the output speed <* gg * ° of the IC gyro. The coil 13 works with the coil 14 · together in a way that, with suitable excitation of the two coils, a torque about the azimuth '= axis of gyroscope is developed ". The gyro torque generator 10 provides in this way the damping expression (2 · 6 ■ y *) about the azimuth axis of the gyro, "the torque that is exerted from one reel to the other, is given by T 'G ^ I ^^" where G ^ a proportional -. tätskonstante Since I ^ constant and I ₂ proportional to γ * , one sees that T »C ₂ ψ ', where G _{2 is} another proportionality constant_. If I * assumes a value with which G ₂ « = G ^ .I ^ « 2S , then it is achieved that T * 2 h ψ '. , which is "equal to the desired instantaneous value of the damping torque ^ es for the gyro", while the damping torque according to Fig. 3 is given to the gyro or the oscillator by a torque generator, it can also be generated in another suitable manner, for example with the help of Coulomb damping or the like the viscosity damping. '

When the gyro has reached its operating speed and the direction of the meridian by other means, such as a magnetic compass, in general

9-0 9834/0971 BATH

has been aligned, then becomes the meridian pointing one Operation initiated by releasing the gyro. When the gyro is released, the control system is activated 5 is given from the voltage source 15 voltage. Then the sequence of time intervals begins, supplied by the timer and damping control 9 will.

The timer and damping control 9 contains a generator 16 for constant current and a generator 17 for variable current, which responds to the output voltage of the tachometer generator 7 via the amplifier 8 and thus to the instantaneous speed · & - of the gyro about the azimuth axis. The outputs of the generators 16 and 17 are given to the torque generator 10 via the transmission gates 18 and 19, respectively. The transmission gates 18 and 19 are controlled by the output of a variable timer 21. If the variable timer has an output signal of a certain polarity, then the gates are put in their on state so that the signal from the associated current generator can pass them can be controlled by programming the variable timer 21. In addition, the application of the first damping pulse can be controlled so that it occurs at the moment of release of the gyroscope, such as shown in Figure 4, or at a later selected time as shown appears after Fig. 5. In the diagrams of Fig. 4 and 5, the application of the damping ratio O is shown over a time scale, the time intervals of which are predetermined by the variable timer 21. The curves 22 and 23 of Figs same

909834/0971

Moment like the output of the variable timer 21, which opens the passage gates 18 and 19. The time scale and the time intervals in FIGS. 4 and 5 are shown using the example of the meridian-pointing gyro, the an undamped period of oscillation of 24-0 seconds of a certain latitude.

Ideally, the gyro precesses during the initial period after releasing without damping as long as that for the movement of the starting point P on the circular trajectory according to FIG. 1 up to the confluence with the fast one Asymptote A2-A2 of Fig. 2 is necessary. At this moment the full damping torque is applied by the timer switched on, so that as a result of this the starting point P ent- ■ long the fast asymptote A2-A2 runs into the meridian plane in which it comes to rest.

A preferred embodiment of the method according to the invention consists in the use of the asymptotes, which result in the deflection-speed representation (FIG. 2) of the movement of the supercritically damped system, as reference or switching lines for determining when the damping is applied and removed again should. These asymptotes, which are determined in the displacement-speed plane of the movement by the size of the supercritical damping ratio of the system, run through the origin of the displacement-speed plane and have the gradients of (- ο - Τ | ό ^ ~ "Ό

(-6 + V & ² ~ 1) for the fast or slow asymptote. For large supercritical damping, the slow asymptote encloses a relatively small angle with the axis of deflection, while the fast asymptote is the same

909834/0971

BAD ORfGiNAL

forms a large angle with the speed axis. Sine Movement that begins on the slow asymptote or flows into it reaches the equilibrium position in infinity great since and is commonly called creeping movement denotes, while the movement along the fast asymptote sees the equilibrium position in the shortest possible time.

Ia represents a preferred embodiment of the method the fast asymptote represents the ideal switching line for the application of the damping torque. Instead of the fast Use asymptote as switching line or etatt die to use fast and slow asymptotes as switching lines, you can also use two arbitrarily selected switching lines in the phase level display 6 see below. The latter shows a combination of circular trajectories from FIG. 1 and a set of trajectories for <S «10 from Fig. 2. Lines A1-A1 and Ä2-A2 represent the slow and fast, respectively Asymptote for a given supercritical damping ratio. I.

S1 and S2 are switching lines running through the origin of the ψ, ψ ¹ T plane and enclose the angle V. The angle γ is proportional to the time interval of the precession movement along the circular trajectory from S1 to S2 in the phase plane for small angles y, see above that the system is essentially linear. By a timer sequence according to the invention, the gyro is released at an initial azimuth angle y and can then precess for an interval T , at the end of which the precession circle 30 intersects the switching line S2 at point Cq. At this point, the supercritical Attenuation

909834 / IiL-Vl

scolded and the starting point P runs along the damped trajectory 51 »which runs parallel to the fast asymptote A.2-A2 as far as IL, which is the intersection of the trajectory for great damping ialt the switching line S1. The attenuation is removed from the gyro, so that it can pre-feed freely and the reference point can pass through the circular trajectory 32 during an interval between the switching lines 61 and 32 determined by the angle T. At the end of this interval, the switching line S2 intersected at point C ^ * If the timing is precise, the side intervals corresponding to the arcs BqC ₀ , B ^ C ₁ , B ₂ C ₂ are all the same size. In a similar way, the attenuated trajectories CqB ^ ₉ C ^ Bg, C ₂ B-, correspond to the same line intervals. Consequently, the starting point of the zigzag line will "run along the connecting lines, until after a sufficient number of cycles 41" the vicinity of the meridian plane is reached "

The ratio between the azimuthal deflection amplitudes of two successive cycles is constant, ie * f "constant. You can then calculate the amplitude after η complete cycles by ψ η « ( ψ, οοαψ ) ξ ^η , where φ is the angle between the switching line S1 and the γ- axis is.

It can be seen from FIG. 6 that ρ for positive η decreases as ώ becomes larger and r smaller, which results in a larger reduction in amplitude after a given number of cycles. Inevitable errors in timing make such an improvement illusory, however, since the absolute error of the time interval under these circumstances can be equal to the length of the interval itself. This means that the switching lines do not remain in their defined predetermined positions,

909834/09 7 1

but move against each other in such a way that the sizes of the angles ώ and / change in a forbidden and indefinite way. To rule out the possibility of these timer errors, the slow asymptote is used alternately as one of the switching lines. In this way, each precession interval will begin at a certain fixed reference line.

Although by using the slow asymptote as a reference line for the introduction of the precession interval ensures that the end of the precession interval and insert the beginning of the following damping interval at the point at which the trajectory of the undamped movement the fast asymptote intersects, other circumstances can cause the precession interval to precede either or ends after the intersection with the fast asymptote. So the timer can be the subject of errors, the exact latitude cannot always be known and the period of the gyro can increase if the Initial amplitude becomes larger, etc., all circumstances that help that, albeit rarely, the damping interval starts on the fast asymptote when they are as Switching line is selected.

Even if the fast asymptote is chosen as the switching line for the application of the damping, the damping will be iteratively, i.e. in individual cycles consisting of a precession interval and a damping interval, and such a cycle is repeated sufficiently often that the amplitude of the gyro is reduced to an acceptable value. The iterative damping that the slow and Fast asymptotes used as switching lines are shown graphically in FIGS. 7, 7 and 10.

90 9 8-3-4 / Oü 7 1

In FIG. 7 it is assumed that the error (corresponding to an error of {Zn i ** real time) of the precession interval

To ""% " 2 0L '

is negative, so that the damping interval is initiated early, ie at B, by an angle ^ *% before the fast asymptote and thus the switching line "S3 runs through point B. As a result, the gedä movement now takes place according to the trajectory 40 through the Point B. The size of the error angle is enlarged in Figures 7, 8 and 10, corresponding to the enlargement of the angle C for ease of illustration limited.

The trajectory 40 is almost parallel to the fast asymptote A2-A2 and is captured at point G by the slow trajectory A1-A1; on which the starting point almost comes to rest and creeps towards the origin at an extraordinarily slow speed. A few seconds after the capture of the starting point by the slow asymptote, the damping is switched off by the lateral encoder and the top continues its free procession so that the starting point P now runs along the circular trajectory 41 on the arc CD. Ba AOB - GOD » β , at the end of the precession time interval, the starting point P at point D of the switching line OB Tbsw. S3 have arrived. This switching line S3 is defined by the equation

ψ + v | / ^g tan ( CC + A ⁴ T) - 0

909834/0 9 71

while the equation of the ideal line of sight, ie the fast asymptote, is given by ψ- + ψ ' ¹ t ** ¹ dC ^m 0 . At the end dta Präeeeeionseeitintervalles the timer 21 switches the damping again, and the reference-point running Jetheth along the trajectory 43 for the gtdäepft · motion by D, it him on Puakt E by the slow asymptote again is captured. This procedure can be repeated several times until the amplitude of the gyro oscillation is reduced to a reasonable value.

If the error is positive and the milling trajectory is an angle ^! * T over the fast asymptote runs out, then the request process takes place in one from the TIg. 6 resulting catfish take place, the understanding of which can be found in the FIg *? iron itself yields; the new Switching line is now through the equation

γ- + * - · tan (^ i -4'C) - 0

given.

In order to determine the decay of the travel amplitude after a certain number of iterations of the damping process, one can start from the following considerations: the angle <x is less than 5 ° at S «10, so that one recognizes with a view to FIGS. 7 and 8, that ψ ^ · -> -. γ ^? "

or · March ₁ ^ ¹ * J. M this ratio for one

given error & * Γ is constant, one can easily get the remaining amplitude of the gyroscopic oscillations after η iterations to 'ψ'- * f _o

909834/0971

- 36--. ■■. ■

For the example of the meridian-pointing top, one can assume that the fourth part of the. PpäcessiöES period is about 60 seconds. The transition to the. Arc between the slow and fast asymptote then takes about 56 seconds at a damping ratio of 10 »If you take a very unfavorable value of

Δ % '* 0.05 rad or At ■ 2 seconds on "then the pre ze ion β int β rwall is about 56 seconds" + 2 seconds «-

(DSHD

An analytical and also graphical check shows ₉ - that 12 seconds are sufficient for the "damping interval" and "are also sufficient for the initial damping interval". The sequence of the time intervals, which is generated by the timer 21, then results from the schematic representation of FIG. 2 seconds was assumed. .

If the initial amplitude is about 5 °, then after four iterations the amplitude of the gyro will be the Damping cycle

Ψ "*! .- 5 ° * (0 * 05) ⁴ - 3.125 χ ΙΟ" ⁵ α * O.lBogen-

secondec

With such a small initial amplitude, sufficient accuracy is obtained in most cases already after three iteration cycles, since ψ ■ * «5 ° · (0.05) ■» * is 2 arc seconds «In many cases there are already two iteration cycles, after which it is br ^ ^β 4-0 arc seconds should be sufficient.

The damping interval along the fast asymptote for a top with an undamped natural period of 240 seconds can be made with the help of the phase display

909834 / uay

Pig. 9 "can be calculated. The two asymptotes become won in the following way. The diagram shows the solution to the equation

By substituting »m and solving equation (77) for γ- ¹ , one obtains

m + 2b

(12)

whereby for every constant value of m a unit of origin

de is defined with the slope * ~ z -. Therefore must

m + d ο

every solution curve or trajectory curve in the bevel plane representation the · isocline according to equation (12) with the slope m cut. By adding m different values, one obtains a family of isoclines, their m-values determine the neifping of the trajectories that they intersect.

There are several special types of m, those of special Are interested. So is the isocline for m »co, namely

ii / '■ 0, i.e. the y-axis; all trajectories must have this Cut the axis at right angles. The case in which the directions of the trajectories correspond to the ι is of particular interest are the same as the sighting of the isocline, or m ■ ——— ■

By substituting this vertex for - in

Equation (12) gives a quadratisc he equal in ung m, whose roots amount m ■ - Q +

- 1 or

m = »- ο + V) with the abbreviation ύ \ *" \ j5 - 1. If you insert these two values of m into equation (12), you get the two isoclines

- (ST ₇ (12b).

9098 3 4/097 1

As the slopes of the trajectories in, each of their points must be parallel to these two isoclines, can do this® They do not intersect trajectories, they only intersect them approximate asymptotically. The equations (12a) and (12b) thus define two asymptotes in the phase plane. BIe Asymptote defined by the equation (12a) has a small negative slope while that by the equation (12b) has a large negative slope. Equation (12a) defines the slow asymptote and equation (12b) determines the fast asymptote. These Equations can also be represented in the following .Veis © will:

slow asymptote

V ⁺ ( ö ( & + yj ) y O or ( P . (^ -Λ - O fast asymptote ) ν * γ ₊ - Ά ) -y ο or Y ^{1 +} + τί O

(i2ai) (12a% 1)

(12b1) (12bl, 1)

These asymptotes are entered in FIG. 9 as slow asymptotes 45 and fast asymptotes 46.

If one assumes that a point P is at the intersection the circular trajectory for the undamped precession starts with the fast asymptote and the damping begins starts at this moment, then the time interval for the damping can be calculated. The equation (12b2) for the quick asymptote (line 46) can be in the form to be written

909834/0971

- - C ί + ff ) γ (133

Solving for T brings

or

-T.-Jf ^ - ■ m _{r +} ο (15)

At the beginning of the steaming interval is TO and γ - y (O) - which means G »-. The dimensional Io se time along the fast asymptote vd.rd then

^. ^ ₇ J L _V (O) -In y J (16)

Ba ot small, namely less than 3 ° "at ο« 10, can

c 1 you put tan (x * t & * ö ~ y) '» '. Furthermore, because of the smallness of α: γ (O) ** γ _ο · οί · »

This finally results for the dimensionless Time T along the fast asymptote as a function of the deflection ur from the origin

¹ Ur

T - m jf - in Ψ

₍₁₇₎

or for real time accordingly

t - ^ln TT "^ ^ (18).

It can be seen that even along the fast asymptote, theoretically an infinitely long time to reach of the origin is required. This fact is not a problem because it is not necessary to know the origin to reach, but because the starting point is only close enough

909834/03 Π

must get to the origin in a reasonable time. In order to be able to express this fact in numbers, one assumes, for example, that the time to approach the origin is down to one arc second (which represents a very small error in the deflection from the equilibrium position) for a linear system with an initial azimuth angle of γ = 0.1 radian is required. The place on the ψ -axis for one arcsecond is then about 5 x 10

If you insert this .Vert for U ^ and the undamped natural period for the frequency oj _Q in the expression for t (equation 18), then the result is

10,000)

—Ψ ") (I ₉ )

or

4th T , ■ (10,000)

For a gyro with the undamped natural period of 240 seconds for T and a damping ratio of 10, the time required to reduce the deflection from 0.1 rad to one arc second

² ^ ⁰ in

^w - ZT O9.95) which leads to t «^ 3» 3 seconds.

For an exemplary initial deflection of _Q = 0.1 J ₀ rad and a remaining deflection of «1 arc second °, the ratio between the damped time interval and the undamped time interval is obtained. ω (20000 ^

* "^ t T In (

. ^ J or, since T »-I is ₁ ,

6.3 - 0.635 in (2 6) ⁶ ~ 6 +

The general expression for the relationship between the time interval of the damped and the time interval the undamped movement applies

'V "

* 8B ⁽ v

The calculations given also apply to negative azimuth angles. A phase representation of the iterative damping for an initial negative azimuth angle and a negative timing error is shown in FIG.

The above considerations and results are based on the assumption that the initial Winkelely of the gyroscopic oscillation is less than 5 °, so that the precession angle T is independent of the size of y, ie that the system is linear. Of course, this assumption is not always valid, especially because magnetic compasses are used for the rough alignment of the meridian-pointing instrument on the meridian; These magnetic compasses can have a large, unknown declination at the place where the instrument is set up, as a result of which the starting angle γ becomes too large to justify the assumption for setting up equation (1), in particular for the assumption that siny »y were. The more precise equation for the precession motion of the gyro reads in phase coordinates

γ 'I ^ ^{+ sin} r- ° ^(22>

Integrate this equation twice and solve for the dimensionless time <T leads to the relationship for the precession interval between two asymptotes

909834/0971

r «COS

These integrals lead to elliptic functions; the lengthy calculation process associated with this can be avoided by restricting it to an approximation. This approximation is based on the following reason: Since the angle ex is small, roughly in the order of magnitude of 3 °, for the sake of simplicity one consider the full arc ("yit ie» the fourth part of a period instead of the arc r ~ y- - 2of If one now uses the length of the quarter period for the case that starting from ψ " ■ 45 ° the zero approaches, one obtains the difference

^ S " ⁽ ^ oVo * 4-5 ° ~ ^ o ^ Yo ⁸⁸ O- 1.633-1.571
* 0.062 rad
or

At ₁ ^ - S- AT ₁ m 2.37 see.

At the end of the first .FräZessionsintervalls C ₀ , the point P will be delayed by an angle ΔΤνοη approximately 0.062 rad in addition to the assumed time error AtT. The ratio of the amplitudes after one cycle of damping then becomes approximately * ΔV + A%. ■ 0.05 + 0.0612 »0.112, so that the initial 45 angle is now reduced to about 5 °. As a result, in the next damping cycles the error 4Έ "attributable to the starting angle will no longer intervene and only the assumed time error of 0.05 rad will remain

909834/0971

0.112 χ (Ο, Ο5) ³ χ

Cs ^. 6.3 χ 10 " ⁴ degrees <2 = ι, 2.27 arc seconds.

It is clear from the above that a rapid decay of the oscillation amplitudes of the gyro can be achieved even with very much larger starting angles. For example, the amplitude for yi-Sö " _{) takes} A ¹ T ₀ = o, o 5 rad

y ₄ α C,.? 5? χ 0.0552 χ (0.05) ² x 90 ° χ 3600 «

Bogense'-ainden.

Of course, as the number of cushioning cycles increases, e.g., five or six cycles, adequate alignment becomes on the meridian at initial angles close to 180 ° for a total alignment time of approximately 8 minutes (η β 7) can be achieved. This means an essential Improvement compared to the very long time of alignment, which is the case with continuously damped gyroscopes with a starting angle close to 180 ° is necessary.

11 shows a phase plane representation of the undamped precession movement of a gyroscope at the starting angles between 0 and + 180 °. Only one quadrant is shown as the curves in the other three quadrants are mirror images of those in the adjacent quadrant. The curves deviate considerably from the circular shape valid for small starting angles when these iSTangles increase above 5 °. This is clear from the dashed curve 50, which represents f const, and intersects all precession curves at points of the same time T "since the release time. If the time of the precession interval is kept constant at the value f , then the damping is switched on at the point on which the relevant

909834/0971

de curve intersects curve 50. As a result, the starting point runs along the damped trajectory curve on the slow one Asymptote 51 to. Whether he got the asymptote before turning on of the precession interval depends on the size the starting angle and the duration of the damping interval. This is the case in the diagram of FIG. 11 explained a gyro that was released at an initial angle of 45 °. A case when discussing the numerical estimation of the setting accuracy was considered. The point F runs along the precession curve 52 during the time interval for the precession movement, Then the damping is applied and the reference point P now runs along the trajectory 53 for the damped movement and reaches the slow asymptote 51 · At the end of this first cycle is the azimuth angle reduced from 4-5 to less than 5. The damping cycle is then repeated until the transducer has arrived within the permissible error range around the meridian plane is. It should be noted that for large angles neither the asymptotes nor the trajectories for the damped Movements are straight lines. However, this is not important for a qualitative assessment of the behavior at large starting angles.

For explanation it was assumed that the damping ratio is ά «10. However, this damping ratio can be varied over a wide range. The greater the damping ratio, the shorter the time interval that is necessary for the withdrawal of the speed of the gyro or oscillator recorded during the precession interval. If in the limit case δ tends towards infinity, the trajectories according to FIG. 2 become parallel straight lines perpendicular to the y- axis, while the slow and fast asymptotes with the y-axis or the y'-axis

909834/0971

coincides.

However, this condition cannot be realized. Furthermore, it does not significantly shorten the time for a cycle. The precession interval is now T _Q ■ -jy- for ^ T- O ₁ while the interval for the trajectory of the damped movement is now 0. For the previously considered exemplary gyro with a natural period of 240 seconds, the precession interval now T s -L · - is 60 seconds, compared to 54 seconds for ό «10 assuming a negative time error of 2 seconds. With four iterations after an initial damping interval of 12 seconds, the total time savings will be about 36 seconds.

Although this case is only of academic interest, it nonetheless shows that very little time is saved using a very large damping ratio. This is of course due to the fact that most of the time for a complete cycle is consumed by the more or less constant precession interval. Furthermore, the power required to generate the damping torque increases with approximately S. If the damping ratio increases from 10 to around ο m 50, at least 25 times the additional power would be required, and larger coils would also be required. With this effort a time saving of only about Ϊ3 % would be achieved.

Now consider the case that the damping ratio is reduced from <S ■ 10 to about S - 2.5. Through this would take the time along the trajectory for the damped Movement by four times that for the damping ratio ο 10, while the length of the

909834/09/1

sion interval would be reduced to approximately 44 seconds for ATa 0. The time for a full cycle including the initial damping interval is now (4) (12) + 44 »92 see. This means an increase of about 35% over the 68 see * per cycle in the case of ο »" 10 {this increase is not acceptable in many applications.

One can choose from reconciliations,} both the practical and theoretical side, consider the conclusion that an optimum range exists the DMmpfungsverhältnisses between S = 5 and ο a 20, although it 7ert no optimal "is the damping ratio per se and although therefore like every Jert about Λ can accept. The assumption of = 10 in the above description can therefore be regarded as representative of the method of iterative damping.

If the meridianal gyro is used at different ideographic latitudes, it will be necessary to adjust the timing and attenuation controls to compensate for changes due to changes in latitude. However, this compensation need not be complete. An error of + or minus 1 ° in the geographical latitude © can easily be tolerated. The need for compensation of the timing iat attributable _s that the period of oscillation of the gyroscope is a Funistion the latitude of the fact:

constant

T ". 2TJ r - Γ? M 60 cos k ^ cos K

U »thus avoiding an error in the precession interval, it is necessary to do the latter in the same way. "■ · how T changes to adapt to latitude;

909834 / D974

!, 3!, '! 1 "11! 1! 1''! 1! 3111! 11! JI ¹ IIIIHi ¹ I' ¹¹¹ ' ^111. J! PI l'! Jl! L

- 4-7 -

instead of keeping the precession time interval t constant, one can vary it in the same way as T.

^L o C 7Γ

^; _Λ "": - " } ~ * τ
⁰ tj " ν. ί-

M CJ cos

Therefore a compensator 25 is provided for the compensation of the geographical latitude in the control system of FIG. 3, which makes the same proportional adjustment of each individual precession time interval from the KLg. 4 and 5 allowed. This setting can take place at several different times, depending on the type of timer. In mechanically or electromechanically operated timers, the speed of the timer can be varied in inverse proportion to the gyro period, ie proportionally to γ cos λ, so that the timer sequence is gathered or stretched accordingly. In the case of an electronically operated timer, either a change in the electronic time constant or a change in the integrator voltage of the timer proportional to the gyro period can be used to set the timer control.

Although in the above a damping control and a method has been described which is generated on the basis of a proportional to the speed of the azimuth movement Torque works, damping torques can of course also be used that are not proportional to the azimuth speed. E.g. a damping moment proportional to the square of the azimuth speed use:

ijr | γ

γ (26).

909834/0971

A damping torque can also be used, which for small azimuth speeds in a first approximation "or mainly proportional to the speed, but that for high azimuth speeds as a first approximation, or mainly proportional to the square the speed is. Such a torque is given by

T- C (1 + k. | \ Jr |) γ. (27),

the value of the constant k being appropriately selected.

There may be other changes in the details of the device and the method carried out v / earth, without thereby of the inventive concept as he is expressed in the following claims, is deviated from. . ■

909834/097 1

Claims (1)

Claims 1. A method for damping the movements of a vibrator oscillating about its equilibrium position »characterized in that that the movement of the vibrator remains undamped in a first preselected time interval and during of a second preselected time interval is supercritically damped. 2. The method according to claim 1, characterized in that the beginning "of the first time interval is set at a point in time at which the oscillator is out of its equilibrium position. " 3. The method according to any one of the preceding claims, characterized in that the first and the second Time interval alternately lined up in a preselected number will. 4. The method according to any one of the preceding claims, characterized in that the movement is initially rejected of a third preselected time interval is supercritical is dampened. 5. The method according to any one of the preceding claims, characterized in that the first time interval is approximately equal to the fourth part of the undamped Sigen period reduced by a time interval which is given by the undamped natural period divided by 4 ¹ JT times the damping ratio. 909834/0971 6. The method according to any one of the preceding claims, characterized in that the second time interval t ^ is calculated by the expression where T is the undamped self-period, γ the initial deflection from the equilibrium position, y the deflection from the equilibrium position air and the end of the second time interval and ο the damping ratio. 7. The method according to any one of the preceding claims, characterized in that the ratio <ΞΓ between the first and second time interval is calculated from T (In w- - In ψ)
<O ■ _ £ ^ 2 __ 8. The method according to any one of the preceding claims, characterized indicates that the supercritical damping depends on the speed of the transducer. 9. The method according to claim'8, characterized in that the supercritical damping proportional to the square of the speed of the oscillator 10. The method according to claim 8 _t, characterized in that the supercritical damping iat proportional to the speed of the oscillator. 909834/097 1 11. The method according to any one of the preceding claims, characterized in that the supercritical damping ratio is between about 5 and about 20. 12. The method according to claim 11, characterized in that the supercritical damping ratio is about 10 « 13. The method according to any one of the preceding claims for an oscillator whose motion is the differential equation _m ^ i ₄ C _D dx _{(x) m 0} obeys, where in d ^J .o bG-vegte mass, λ) the D damping coefficient, f (x) the restoring force acting on the mass, χ the deflection of the Islassese from its equilibrium position and t the time, characterized in that the damping coefficient a It is a function of the speed of the hater and for all escii speeds greater than is necessary for the critical damping of the mass. I ⁷ +. Method according to Claim 13, characterized in that the steaming coefficient is proportional to the square of the speed of the be'vecjten Masae. 15 · Method according to one of the preceding claims, characterized in characterized in that the damping at speeds of the moving mass below a preselected size mainly proportional to the speed and, at speeds above the selected size, mainly proportional to the square of the speed of the moving mass is. 16. The method according to any one of the preceding claims for a meridian-pointing top, the movement of which is in the north 909834/097 BATH ORIGINAL mated azimuth elevation coordinates to the differential equations SSL _{+ γ} _ äJL SSL _{+ γ} _ d V _£
J obeys, where "ψ · the instantaneous azimuth angle of the circle-« -FT " ^Λθγ normalized instantaneous elevation angle of the gyro speed, θ the actual elevation angle, T = <*> t the normal, -i.ie-rth time, the circular freshness of the undamped oscillation of the rotary axis, Jl the local horizontal component of the angular velocity of the earth's rotation, H the \ 7angular ■ Q ΈΚΊί the damping ratio for the movement; the gyro axis in the Azlrautebehe and G the speed proportional Damping coefficient is the azimuth axis, so that the loci are in a phase plane representation of the movement a first asymptote with the equation along which the equilibrium position is reached the slowest becomes, and a second asymptote with the equation along which the equilibrium position is reached the fastest will have, characterized in that the first and second asymptotes are used as switching lines, so that the supercritical damping and the gyro axis are switched off at the first asymptote as a switching line can precess freely until the reference point corresponding to their movement in the phase plane representation in the second Asymptote opens up as a hold line for the application 909834/0971 jmn / vj am ' the supercritical damping on the circular movement is used. 1? · Method according to claim 16, characterized in that that with initial supercritical damping during the third time intervals the compression movement of the barrel axis of the gyro starts from a fixed point with no initial speed. 18. Device for carrying out the method according to one of the preceding claims, characterized by a sensor for the instantaneous speed of the oscillator}, by a damper responsive to the sensor, which has a damping proportional to the instantaneous speed. (& rs * feugtj and by e | u _e control that "lets" the generated supercritical damping act on the transducer in preselected repetition intervals during a preselected time interval \ ■ ■■; '. "·. ' . ] t '■■■ 19. The device according to claim 18 in a Meridianweiser, & 9V tinen pendelförmlgen gyroscope with a horizontal Laufache ", which tends to move due to one of originating Präzeseioösmoraentes uqi a Verin to set a meridian correctly ', j | nkenn a tap which is proportional to the movement of the, Ao ^ ee. ch ai ^ nal ^ ebej ?, 41 · »i% dt» and that » * i $ xl ffaignal ' la a dfr <^ dfcwindigl | »it the Bfwtguog of the Iiaufeohae proportion ·! te «lektrieche» signal convert · In ^ by Z «it- and while Ύ0 ** · * $) ^ 9 Zettiauif a dey the movement d «J? InwIfte ^ iQ pjroporiioü »lt Signal #r «Äuee» | «Nd 4 * #« h einea * ii »dee those Di * thaoaent "r" euger, who * iif den BATH ORIGINAL and at times a morale counteracting the presidential morale Torque developed around the vertical axis. 20. Device according to claim 19. » characterized in that the movements of the running axis of the top are limited to the horizontal aajimut plane » ^: 21. Device according to one of claims 19 or 20, characterized by a rotatable part which is concentric to the vertical axis of the gyro through a tap _t which sends an electrical signal as a function of the relative rotation of the circle with respect to the rotatable. !! Part mn is the vertical axis of the top; May an auxiliary device be used to rotate the rotatable part, the vertical axis _t around the relative movement, between the top and the rotatable in ¹ SmH in the "essential to Hull snusi © ren?" ius? eli © in ©.-Spammnggqu @ lle, whose tension proporliioaal atis -fiak ^ IgeseliwlEdigtoit äe® arehbarea part is ι dtoeli eiisea Iff-eteoi & eatunerssugejff ¹ ? of this tension anapriefetg qIb © überlcritiach «for the Bawegiisag dtis Hj? © is © ts.n® the Tertifeale - AchsMd © mu? en ? eiti @ s Sp; aaaimgsqu © lle verbuad © mn. dtsr-qh an IiSit © Hv © i? i? icfetuBg for dl © - Steueruag Roundabout n «r iiet _f dag the ÄÄsgiflselt ci. © s ruler? 'into' '. - "- 25t
■ dal
is from the BADORtGiNAL quadratic, depends on the voltage if the latter is larger than the preselected iÄfert. 24. Device according to one of claims 19 to 23 »thereby characterized in that the torque generator operates electromagnetically. 25. Device according to one of claims 19 to 24, characterized characterized in that the size of the torque delivered by the torque generator to the geographic Width of the location of the gyro can be adjusted with an adjusting device. 26. Device according to one of claims 18 to 25 » characterized in that the interval length of the undamped Vibration adjusted with an adjusting device to the latitude of the location of the gyro can be. 909834/0971 BAD ORIQttMÄÖtfSO OAS