This invention relates to laser inertial integrating rate sensors and, more specifically, to sensors in which a dither bias is used to obviate the effects of lock-in inherent in such sensors.
The behavior of ring laser inertial integrating rate sensors is well understood by those skilled in the art. Inherent in such sensors is the phenomenon known as "lock-in" in which counter propagating laser beams tend to lock together to a common frequency. Lock-in arises in ring laser inertial integrating rate sensors at low rates of rotation. At such low rates of rotation, the frequency differential between the two beams is relatively small and the beams tend to couple or resonate together so that the two beams oscillate at only one frequency. Because of this lock-in phenomenon, the frequency differential is no longer proportional to the rate of angular rotation, causing performance errors which have deleterious effects in navigation systems.
To avoid or reduce the effects of lock-in, the laser inertial integrating rate sensor may be biased by dither techniques such as those shown and described in U.S. Pat. No. 3,373,650 to J. E. Killpatrick, assigned to the assignee of the present invention and incorporated herein by reference. The biasing technique usually referred to as dithering may be implemented, typically using mechanical schemes, in a variety of ways. Since these biasing techniques directly affect the behavior of the counter propagating laser beams, the sensor output signal contains not only rate information signals due to inertial motion but also contains a signal component related to the biasing of the sensor. This is true whether the output signal generator is mounted directly on the sensor (block mounted) or off the sensor (case mounted).
The sensor output signal dither contribution further includes a base motion component due to dithering, herein referred to as ".theta..sub.B," and a sensor or gyro motion component due to dithering, herein referred to as ".theta..sub.G." The sensor motor component of the dither signal represents the reaction of the sensor to the torque applied by a motive means attached to the base on which the sensor is mounted. The base motion component of the dither signal represents the motion of the base on which the sensor is mounted which results from a reaction torque from the motor means mounted to the base. This torque acting on the base is of equal magnitude but in a direction opposite the direction of a dither torque applied to produce the dither motion in the sensor. The torque acting on the base produces the base motion that is synchronous with the dither motion of the sensor and is opposite in direction.
Frequently, more than one inertial integrating rate sensor is mounted to an object for providing rotational information about the object. Sometimes only one or two inertial integrating rate sensors are mounted to the object as a means for providing angular rotation information to a system. For example, inertial integrating rate sensors may be used to provide rotational information for an optical telescope having one or more axes of rotation. This rotational information is provided to a control system that is capable of selectively activating servo motors to reposition the telescope thus insuring the telescope remains pointed at a selected target.
If dithered inertial integrating rate sensors are used, then the control system is provided rotational information from one or more sensors that are attached to a base which is in turn shock mounted to the telescope. Dithering the inertial integrating rate sensor causes the sensor to react against the base producing base motion. Because the base is moving relative to the telescope, due to dithering, the control system receives rotational information about the telescope that is in error by the amount of base motion due to dithering. Therefore, the control system is not able to maintain a pointing accuracy that is less than the angular rotation of the base due to dither.
If, however, the base motion due to dithering could be determined and supplied to the control system then the error due to base motion can be subtracted from the rotational information. The control system would then be capable of determining the actual angular movement of the telescope. Once the actual angular movement of the telescope are determined by the control system then it is possible for the control system to correct or adjust for angular movements of the telescope that are smaller than angular movements of the base due to dithering.
Thus, there is a need in these circumstances for a means for accurately determining the base motion due to dither. It is necessary that this base motion determining means maintain accuracy during aging and environmental effects such as temperature variation.
Inertial navigation systems usually make use of three or more integrating rate gyros or sensors attached to the same base. Typically, three such inertial integrating rate sensors are coupled to the base having an orientation such that the axes of sensitivity of the inertial integrating rate sensors are substantially mutually orthogonal to one another, as seen in FIG. 1. The sensor configuration shown in FIG. 1 includes a mounting base, 9, having three inertial integrating rate sensors, 10A, 10B, and 10C, attached thereto. Isolation mounts (not shown) tend to prevent the transfer of vibration between the mounting base 9 and the case (not shown) on which it is mounted. Each inertial integrating rate sensor 10A, 10B and 10C produces an output signal that is indicative of the sum total of all the instantaneous angular motion changes the sensor has undergone in its input axis, or axis of sensitivity. The inertial navigation system transforms the sum of all instantaneous angular motions produced by each inertial integrating rate sensor into navigation parameters.
The use of mechanically dithered inertial integrating rate sensors in these navigation systems results in base motion due to the base motion components, .theta..sub.B, of each individual inertial integrating rate sensor. As shown in FIG. 1, the base motion component, .theta..sub.B, of sensor 10A produces a resultant motion of sensor 10C in a plane substantially orthogonal to the axis of sensitivity of sensor 10C. In a similar manner, the base motion component, .theta..sub.B, of sensor 10B produces a resultant motion of sensor 10C in a plane substantially orthogonal to the axis of sensitivity of sensor 10C. Similarly, the base motion components of sensors 10A and 10C each produce a resultant motion of sensor 10B, and the base motion components of sensors 10B and 10C each produce a resultant motion of sensor 10A.
This resultant motion of each of the inertial integrating rate sensors due to the base motion components of each of the other two inertial integrating rate sensors is such that a point in a plane substantially orthogonal to its sensitive axis follows a Lissajous figure. The Lissajous figure produced for one sensor may be a straight line, ellipse or circle depending on the dither phases of each of the other two inertial integrating rate sensors, assuming each is dithered at the same rate. The axis of rotation, or input or sensitive axis, of this third inertial integrating rate sensor more or less follows a cone due to such motion of the base, and so such input motion is generally referred to as "coning." This axis cone motion represents a real input rate to the third gyro in addition to any inertial rotation about this axis and its dither reaction and, if not made insignificant or corrected for, is an error term in the inertial output signal.
The Lissajous figure for one sensor is the result of base motion components in each of two perpendicular axes due to the other sensors. These base motion components are represented by the angular displacement of sensor 10C due to sensor 10A and 10B dither motion, as seen in FIG. 1. The angular displacement of sensor 10C due to sensor 10A dithering can be represented by the following equation: EQU .theta..sub.C-A =A.sub.A sin .OMEGA.t (1)
In equation 1, A.sub.A represents the amplitude of the base motion or oscillations due to sensor 10A dithering. The term fi represents the frequency of the base motion due to sensor 10A dither. The angular displacement of sensor 10C due to sensor 10B dithering can be represented by the following equation: EQU .theta..sub.C-B =A.sub.B sin (.OMEGA.t+.xi.) (2)
In equation 2, A.sub.B represents the amplitude of the base motion due to sensor 10B dithering. The term .OMEGA. represents the frequency of the base motion due to sensor 10B dither. The term .xi. represents the phase shift between the dithering of sensor 10A and the dithering of sensor 10B.
If the motions represented by equations 1 and 2 are assumed, then through standard mathematical translation a known mathematical representation for the mean angular rate sensed by sensor 10C can be derived. The mean angular rate that sensor 10C senses in an axis of sensitivity orthogonal to the axis of sensitivity of both sensors 10A and 10B is represented by the following equation: ##EQU1##
In equation 3, the mean angular rate sensed by sensor 10C as a result of the dither motions of sensors 10A and 10B represents the coning error in the sensor 10C output signal. This coning error is constant with respect to time as long as both the phase shift and frequency of the base motion are constant. The larger of terms A.sub.A and A.sub.B represents the major axis and the smaller term represents the minor axis of an ellipsoid Lissajous figure. If the dither motions produced by sensor 10A and sensor 10B are in phase, the term .xi. is zero and the coning error rate is zero.
If, alternatively, two orthogonally oriented gyros have different dither frequencies, the Lissajous figure in the plane of a third gyro is not constant but goes through both positive and negative phase relations. The volume swept out by the input axis of this third gyro tends to be zero because the area swept out when the phase is positive is cancelled out by the area swept out when the phase is negative. An instantaneous coning or input error exists, but this error does not build up over time. Therefore by running the gyros at different frequencies this coning error is greatly reduced, but not eliminated.
Another technique for reducing coning error has been to make the mass of the base very large relative to the mass of the sensor mounted thereon. In this manner, the base motion due to dither is reduced. The base motion due to dither, however, is not eliminated.
The device base motion due to dither cannot readily be determined precisely from the dither pickoff signal provided by the piezoelectric output device because of the wide variation of the device output due to aging, temperature, and various environmental effects. Hence, here too, there is a need for a means for determining the motion of the base due to dithering. Once the motion of the base due to dithering is known, it can be provided to the remainder of the navigation system which can in turn correct for the error component in the sensor output signal that is due to this base motion.
In addition, the system can correct for any coning error that might be present in a sensor output signal if the actual base motion due to dithering is known. For sensors that are configured such that a coning error input is produced in one of the sensor outputs, the system can compute or determine this error from the base motion components due to dithering resulting from the two orthogonal sensors. Once the coning error that is produced by each sensor is computed, it can then be subtracted from the sensor output thereby eliminating coning errors from the inertial navigation system.