CORRECTED GYROCOMPASS SYNTHESIS AS A SYSTEM WITH CHANGEABLE STRUCTURE FOR AVIATION GRAVIMETRIC SYSTEM WITH PIEZOELECTRIC GRAVIMETER

The present article introduces the development of a corrected gyrocompass with an automatic switch of the gyrocompass into the gyroazimuth mode. The issues of multi-criterion synthesis of the gyrocompass control loop have been studied. The necessity of temporary delay input (with selected values) under the previously mentioned switching is shown. On the basis of given requirements, we chose the parameters which provide the device with a switching-back into the gyrocompass mode under any initial gyrocompass deviations in the horizontal plane. An algorithm of gyrocompass ballistic deviation compensation due to the amendment generated by the special observing device, without recourse to external information regarding the ship’s acceleration, was developed.

A new piezoelectric gravimeter that is a part of the AGS is proposed in (Bezvesilna, Tkachuk 2014;Bezvesilnaya et al. 2013).
Usually, to determine the course on a plane, the gyropolukompas (GPK) is mainly used. However, the real errors of GPK are so great that definite accuracy cannot be obtained.
The purpose of this paper is to provide a corrected gyrocompass synthesis as a system with a changeable structure for the aviation gravimetric system with a piezoelectric gravimeter.

The gyroscope compass
Gyroscope compasses are the principal course-detecting devices for ships. The development of corrected gyrocompasses (CGC) on the basis of a biaxial platform with dynamically tuned gyroscopes has become one of the directions for developing a device that can meet the increased requirements for operational characteristics of navigation equipment. The main advantage of the CGC is the possibility to change the structure and control loop parameters depending on the device's operation mode. In particular, an effective method for decreasing the indication errors while the ship is maneuvering is to switch the device into the gyroazimuth mode, which can be done either manually or automatically. However, automatic switching into the gyroazimuth mode can result in cases when the device is not switched back to the gyrocompass mode. This issue has not been studied in full so far. The synthesis technique for a two-mode gyrocompass control loop remains a problem.
The given report presents the experience of developing such corrected gyrocompasses like CRUISE and SLAVUTICH by the Public Corporation "Kiev Plant of Automation named after G. Petrovsky" and "Marinex Company Limited" (Ukraine). The key aim of the studies was to maximally exhaust the possibilities for an autonomous change of the device operation mode.
Let's consider the peculiarities of CGC dynamics as a two-mode device (Malovichko, Kostitsyn 1992). Equations of motion are as follows: where a, b indicate tilt angles of the main gyro axis from the direction to the North and from the horizon plane; δaccelerometer filter output; γplatform tilt angle; ϕroll angle; x r , z rcoefficients; 1 ( ) 1 p Tp Φ = + transfer function of the accelerometer filter, Tfilter time constant; ξ ω , η ωthe East and North components of the Earth's rotation angular speed; W ηthe North component of ship movement acceleration; 0 ζthe distance from the centre of gyro to the device installation place J η , f γ , n lplatform parameters; ggravitational acceleration.
To decrease the effect of movement acceleration on the device reading, while solving the inequality u δ ≥ , it is switched to the gyroazimuth mode ( 0 x r = ). Here, u indicates a threshold value. If the inequality is u δ < , the device is automatically switched to the gyrocompass mode. However, the accelerometer output signal can also take place as a result of initial device deviation in azimuth. Let's study this question in detail by analyzing the free motion on a fixed base. We shall neglect the influence of time constant, T (that is admitted under the condition 1 z T r -<< ), and accept that (0) 0 b = , 0 (0) a = a . The possible cases of movement are represented on a phase plane a-b (Fig. 1).
indicate the roots of the characteristic equation, the device is constantly operating in the gyrocompass mode (curve 1). If 0 0ã = a (curve 2), then at a certain moment in time, t~, the representing point will be in boundary position A 1 , where 0 a =b =   . Since the movement is being stopped, there is no settling in the meridian.
Curve 3 corresponds to the movement in the case when 0 0ã > a . Point A 2 , is a transfer to the gyroazimuth mode, and further movement may be comfortably characterized by the diagram: The representing point will move down to the equilibrium position A 3 . There is no settling in the meridian.
It is important to find out, when settling in the meridian will occur, under any initial conditions. One of the ways to execute this task is to increase coefficient z r , when u b = . In this case we have , then the CGC will be set in the meridian under any initial angle 0 a . However, an increase of coefficient z r is not enough: it is necessary to also input a temporary delay ga gc -τ switching the device from the gyroazimuth mode to the gyrocompass one. Then, during the delay time interval, the representing point will move upward in the gyroazimuth mode. In point 3 A ′ the device will be switched to the gyrocompass mode. This process is repeated further on. We can see that there is settling in the meridian.
Curve 4 represents the movement after the input of delay gc ga -τ , during the transfer from the gyrocompass mode to the gyroazimuth one. We see that settling in the meridian exists as well. It is efficient to input both delays.
As shown in the results of modeling in figure 2 ( 1 0.03 ), coefficient z r was increased 10 times. Curve 1 corresponds to the delay of switching between the modes due to δ signal lag in the accelerometer filter with respect to angle b. It is accepted that 3 u < angular minutes. Curve 2 corresponds to the input of an additional delay of 90 s, while switching from the gyroazimuth mode to the gyrocompass one. Thus, due to an increase of coefficient z r in the gyroazimuth mode and the input of delay while changing the device operation mode, it is possible to provide its settling in the meridian under any initial terms. Let's consider the efficiency of switching the device to the gyroazimuth mode temporarily for a ship's maneuver. For this, we shall model equations of motion (1) with an acceleration 0.02 W η = m/s 2 for 8 min, which corresponds to speeding-up to 18 knots. We note, that while the ship is maneuvering, there is no need to increase coefficient z r . This follows from the second equation of system (1), because with a = const, while increasing coefficient z r , the main gyro axis tilts faster from the horizon plane. However, to make the device operative under any navigation conditions, the coefficient z r should always be increased while switching the device to the gyroazimuth mode. It should be taken into account that with a considerable increase of coefficient z r the decision nature can be changed: the process will become a light-extinction oscillating one. To exclude this, it is necessary to simultaneously decrease time constant T (accepted 5 T s ′ = ). Figure 3 shows the modeling results. It is accepted that 3 u = angular minutes, 90 ga gc s τ = . Curve 1 corresponds to switching to the gyroazimuth mode with an unchanged x r ; curve 2to z r increased 10 times; curve 3to increased x r and a decreased time constant T to the value T′ . We see that in the third case there will be the least ballistic deviation. It is efficient that the gyrocompass is settled in the meridian much faster in the last case. Let's consider the CGC synthesis technique with a variable structure implemented in the CGC SLAVU-TICH (Sternberg, Schwalm 2007). The task is: to choose such control loop parameters that the dynamic gyrocompass errors while maneuvering and rolling would not exceed the given values under the minimum time for the transient process.
Let's note that while rolling and settling into the meridian, the device must operate in the gyrocompass mode. Therefore, the posed task will be solved in the following way. Taking into account the requirement regarding accuracy while rolling, we shall impose constraints on the gyrocompass parameters x r , z r and T . We select them, finally, minimizing the time for transient process. An admissible error while maneuvering will occur due the device's switching to the gyroazimuth mode. The following inequality can be derived from the expression for the gyrocompass' maximum error while rolling: where max K ∆ indicates admissible error while rolling. The parameters will be selected during the mode of settling in the meridian on the basis of the root method (Sternberg, Schwalm 2007). According to this method the roots of a characteristic equation:  Figure 4 illustrates the plots of transient processes, where curve 1 corresponds to the CGC CRUISE, curve 2to the recommended parameters. It can be seen that, due to the rational selection of the parameters, the time of the transient process is decreased considerably. and maximum ballistic deviation is as follows: where V η ∆ indicates the increment of the northern component of movement rate per maneuver time t м .
Delay gc ga -τ is required to avoid accidental device switching to the gyroazimuth mode while operating (towage, weighing the anchor, etc. According to inequality 1 Delay ga gc -τ will be calculated in the following way. The main gyro axis in the gyroazimuth mode is set quite rapidly in the equilibrium position, and signal δ becomes weaker than threshold value u ( u > δ |). Due to the input of this delay, it is possible not to admit the device to switch to the gyrocompass mode if the ship maneuver is still in progress. Supposing that the maneuver time equals 1-3 min, we will accept that τ = 180s ga gc . Figure 5 represents the plots of ballistic deviations. Curve 1 corresponds to the CGC CRUISE and curve 2to the CGC with recommended parameters. It is evident that maximum deviation values are considerably lower than admissible values for 2°. The CGC with recommended parameters results in less deviation and is settled in the meridian faster. It is obvious that the third stage filter allows decreasing the error while rolling considerably: in comparison with CGC CRUISE error, it was decreased 900 times. This allows installing the device at a considerable distance from the center of rolling (30 m and more).
Error reduction on the basis of information estimation with the help of observing devices is one of the effective methods to increase the accuracy of navigation systems. Let us take under consideration the application of this method to decrease gyrocompass ballistic deviations (Malovichko, Kostitsyn 1992).
It is evident that estimation error ∆a does not depend on the acceleration value and is defined only by its initial value. As physically the gyrocompass is not switched to the gyroazimuth mode, we shall call this concept "the mode of analytical switching to the gyroazimuth mode".
After maneuver termination, we accept that k 1 = k 2 = 0. In this case, the equations of errors with the accuracy up to designations will meet the equations of the gyrocompass free motion.
To change the coefficients of the observing device, it is necessary to have the information about either the availability or absence of ship movement acceleration, which can be obtained by analysing the output signal level of the horizon indicator.
The modeling of the gyrocompass dynamics with an observing device while the ship is moving with an acceleration 0.172 W η = m/s 2 within 1 min., which corresponds to the speeding-up to 20 knots, was carried out to check the efficiency of the proposed ballistic deviation compensation algorithm.
In figure 7, curve 1 corresponds to ballistic deviation under physical switching of the gyrocompass to the gyroazimuth mode and curve 2 to analytical switching. The estimation error of ballistic deviation of the observing device, under permanent operation of the gyrocompass in the main mode (curve 2), is slightly different from ballistic deviation under physical device switching to the gyroazimuth mode.
While using the observing device, the apparatus is operating in the gyrocompass mode all the time; therefore, it is not a problem for the main axis to set in the meridian under large initial deviation angles. There is, hence, no need to increase coefficient z r for the time of operation in the gyroazimuth mode (curve 3). The matters of gyrocompass stabilization system projection will be discussed further (Bohnenberger 1817). The structural scheme of the gyrocompass' stabilization system projection is shown in figure 8, where x and σ indicate the input and output variables; mdisturbance. To exclude static errors, let us regard the stabilization system as a static one according to both input

Сonclusions
The corrected gyrocompass synthesis as a system with a changeable structure for the aviation gravimetric system with a piezoelectric gravimeter is provided in this paper. The experience of developing such corrected gyrocompasses like CRUISE and SLAVUTICH by the Public Corporation "Kiev Plant of Automation named after G. Petrovsky" and "Marinex Company Limited" (Ukraine) are presented.
Modeling was conducted and found that due to an increase of coefficient z r in the gyroazimuth mode and the input of delay while changing the device operation mode, it is possible to provide its settling in the meridian under any initial terms; CGC dynamic characteristics can be considerably improved by changing the structure of the accelerometer's filter; error reduction on the basis of information estimation with the help of observing devices is one of the effective methods to increase the accuracy of navigation systems.