rus
Issue #3/2020
A. A. Medvedev, M. E. Grushin
ZLG Sensors with one Gas Discharge Gap in Each Sensor Half: Correction of Zero Drift
ZLG Sensors with one Gas Discharge Gap in Each Sensor Half: Correction of Zero Drift
DOI: 10.22184/1993-7296.FRos.2020.14.3.226.232
The paper presents the results of correction the non-magnetic component of zero-drift sensors with changing external temperatures and self-heating. Method is shown that allows to adjust the zero-drift improving accuracy characteristics of the device up to 1000 times. For the first time, testing ZLG were obtained results better than 0.01 ° / h at the rate of change the external temperature 0.3 ° / min.
The paper presents the results of correction the non-magnetic component of zero-drift sensors with changing external temperatures and self-heating. Method is shown that allows to adjust the zero-drift improving accuracy characteristics of the device up to 1000 times. For the first time, testing ZLG were obtained results better than 0.01 ° / h at the rate of change the external temperature 0.3 ° / min.
Теги: laser gyroscope temperature correction zero drift zlg дрейф нуля зеемановский лазерный гироскоп температурная коррекция
ZLG Sensors with one Gas Discharge Gap in Each Sensor Half: Correction of Zero Drift
A. A. Medvedev, M. E. Grushin
Research Institute «Polyus» named after M. F. Stelmakh, JSC, Moscow, Russia
The paper presents the results of correction the non-magnetic component of zero-drift sensors with changing external temperatures and self-heating. Method is shown that allows to adjust the zero-drift improving accuracy characteristics of the device up to 103 times. For the first time, testing ZLG were obtained results better than 0.01 ° / h at the rate of change the external temperature 0.3 ° / min.
Key words: Laser Gyroscope, ZLG, zero drift, temperature correction
Received on: 25.02.2020
Accepted on: 08.04.2020
INTRODUCTION
Modern laser gyroscopy, based on the use of interference phenomena, makes it possible to measure angular velocities and angles in inertial space with high accuracy. A special place in the family of laser gyroscopes (LG) is hold by Zeeman laser gyroscopes (ZLG), where a dithering is created due to the Zeeman effect when a longitudinal magnetic field is applied to gas-discharge gaps [1].
It is known that additional ZLG errors are determined by a number of factors. These factors are associated with instability of the pump current of the active medium, interference in the perimeter adjustment system, instability of external and internal magnetic fields. The ZLG must maintain their accuracy and performance in a wide range of temperature effects. The dynamics of the zero bias of ring lasers, its non-magnetic and magnetic components is influenced by the ambient temperature and thermal processes occurring inside the ring lasers.
The asymmetry of the temperature distribution along the active medium has the greatest influence on the zero drift, or rather on its nonmagnetic component. When creating a temperature gradient along the walls, a gas flow arises at its surface, directed from the colder region to the hotter one. This phenomenon is called thermal slip [2].
The issue of temperature correction using the readings of the temperature difference of thermal sensors (from two to five), installed in the hot and cold parts, was considered in [3–5]. In these works, results were presented using thermal correction of zero drift (Ωzd) on LG modifications on a vibro-suspension, without additional external heating element. After mathematical processing, the zero drift error does not exceed 0.01° / h.
The fundamental difference between ZLG sensors and sensors on a vibro-suspension is the presence of coils that create a longitudinal magnetic field in the active medium. When current flows through the coils, heat is released in them, which leads to a redistribution of thermal fields in the resonator.
NEW ZERO DRIFT TEMPERATURE CORRECTION METHOD
In this research, we consider KL‑4M and K‑5M ZLG sensors working with one GDG in each sensor half filled with a 50% mixture of Ne20 Ne22 and He4 isotopes. For this type of ZLG, a temperature correction of zero drift was carried out at a rate of change of external temperature of 0.3 rpm with temperature transitions from 218 to 298 K, from 298 to 348 K, from 348 to 298 K, from 298 to 218 K. During the correction, the data of two temperature sensors were used.
The results of the calculation of the thermal fields of K‑5M ZLG are presented in Fig. 1. A graphical representation shows that the main heat generation occurs in coil samples (items 5 and 9). At this point, a temperature sensor (T2) was installed. The temperature sensor T1 was installed at the bottom of a metal test rig, to which the ZLG is mechanically attached (posit. 2).
The studies were carried out on an untied foundation in the heat and cold chamber of the Aquitas type model ADS-V_TM with outside compressor. ZLG was protected by the design of the magnetic screen to reduce the influence of external magnetic fields on the stability of the output signal. A temperature sensor was installed at the bottom of the magnetic screen to determine the temperature of the cold part of the ZLG. The accuracy parameters of the ZLG were measured at a discharge current of 1.2 mA and a current in the coils of a nonreciprocal device of 0.5 A.
When developing a model of temperature correction, it was proposed to separate the effect of the self-heating of ZLG on the effect caused by heating of the coils of a nonreciprocal device and the effect caused by a change in the external temperature in the heat and cold chamber.
To correct the thermal slip associated with self-heating, we used the temperature difference between the cold and hot regions of the sensor (∆Т = Т2 – Т1). For this, hourly measurements were carried out at stationary values of external temperatures (T). For each external temperature (–55 °C = 218 K, 25 °C = 298 K, 75 °C = 348 K), the dependences of Ωzd on ∆Т were constructed.
Initially, it was postulated that the temperature dependence of the ZLG zero drift obeys the polynomial dependence: Ωzd = А + В ∙ ∆Т + С ∙ ∆Т2. Figure 2 shows the dependences of ZLG zero drift (Ωzd) on the temperature difference between the cold (T1) and hot (T2) parts of the ZLG for three averaged values of external stationary temperatures. It is important to note that the approximating function must be constructed taking into account the weight characteristics (w) of the obtained point results. We assume that w = 1 / i2, where i is the serial number of the point.
The temperature dependence of the coefficients of the second-order polynomials (Ωzd = А + В ∙ ∆Т + С ∙ ∆Т2), approximating the dependence of Ωzd on ∆Т, was determined by the least squares method for each external stationary temperature (Т).
Figure 3 shows the temperature dependences of the coefficients of polynomials of the second order (A, B, C) obtained by approximating Ωzd = А + В ∙ ∆Т + С ∙ ∆Т2. An analysis of the graphical dependencies (Fig. 3) showed that the temperature dependence of the coefficients of the second-order polynomials A, B, C is well described with a linear dependency. We substitute the obtained coefficients into the previously obtained function Ωzd = А + В ∙ ∆Т + С ∙ ∆Т2. As a result, to correct the self-heating of ZLG from the drift, we subtract the function
Ω* = (А1 + А2 ∙ Т2) + (В1 + В2 ∙ Т2) ∙ ∆Т + (С1 + С2 ∙ Т2) ∙ ∆Т2 . (1)
To introduce temperature correction of zero drift at varying external temperatures, zero drift was measured using the following sequence diagram:
Chamber temperature 298K (3 hours) → rate of temperature change 0.3 ° / min
Chamber temperature 218K (3 hours) → rate of temperature change 0.3 ° / min
Chamber temperature 298K (3 hours) → rate of temperature change 0.3 ° / min
Chamber temperature 348K (3 hours) → rate of temperature change 0.3 ° / min
Chamber temperature 298K (3 hours)
After measuring the zero drift according to the above sequence diagram, the exclusion of self-heating was carried out by subtracting the values calculated according to dependence (1).
In this research, for the first time, it was proposed to describe the processes occurring in the heat and cold chamber, the so-called external heating of the device, using the derivative function of the readings of the temperature sensor from a non-reciprocal device coil (∆T2 / dt). For this, after taking into account the self-heating value by the least squares method for all temperature transitions (from 218 to 298 K, from 298 to 348 K, from 348 to 298 K, from 298 to 218 K), the temperature dependence of the coefficients of the second-order polynomials was determined, which approximate the dependence of Ωzd on ΔT2 / dt. Fig. 4 shows the dependence of zero drift after taking into account self-heating and the time derivative of the coil temperature are taken into account as an example for the temperature transition from 218 to 298 K.
As a result of the mathematical procedures performed on the temperature correction functions during self-heating and changes in external temperatures (expression 1), the resulting function is obtained:
Ω*zd = Ωzd – (А1 + А2 ∙ Т2) + (В1 + В2 ∙ Т2) ∙ ∆Т +
+ (С1 + С2 ∙ Т2) ∙ ∆Т2 – [А3 – В3 ∙ (∆T2 / dt) + С3 ∙ (∆T2 / dt2)] . (2)
where А1 + А2 ∙ Т2, В1 + В2 ∙ Т2, С1 + С2 ∙ Т2 are the temperature dependences of the coefficients of polynomials of the second order, approximating the dependence of Ωzd on ∆Т; T2 is the temperature of the temperature sensor installed in the coil groove; ∆Т is the difference between the cold and hot regions of the ZLG sensor; (∆T2 / dt) is the time derivative of the temperature readings of the temperature sensor installed in the coil groove.
The table presents the results of the temperature correction Ωzd, made according to dependence (2) at varying external temperatures (from 218 to 298K, from 298 to 348K, from 348 to 298K, from 298 to 218K).
Fig. 5 shows the example results of the Ωzd correction performed in accordance with dependence (2) with the external temperature varying from 218 to 298 K. From the results presented in the table and in Fig. 5, it becomes obvious that the proposed correction method Ωzd reduces the error caused by the thermal skid effect up to 103 times.
CONCLUSION
For ZLG sensors K‑4M and K‑5M, a temperature correction of zero drift was carried out at a rate of change of external temperature of 0.3 ° / min. ZLG operate with one gas-discharge gap in each sensor half filled with a 50% mixture of the Ne20 Ne22 and He4 isotopes. When developing the temperature correction algorithm, the effect of the self-heating of ZLG was divided into the effect caused by heating of the coils of a non-reciprocal device, and the effect caused by a change in the external temperature in the heat and cold chamber.
For the first time, it was proposed to describe the processes occurring in the heat and cold chamber, the so-called external heating of the device, using the derivative of the temperature difference of the temperature sensor readings from a non-reciprocal device coil (∆T2 / dt). Thus, the method of temperature correction of zero drift using two temperature sensors proposed in the work allows improving the accuracy characteristics of ZLG up to 103 times with changing external temperatures and self-heating.
REFERENCES
Azarova V. V., Golyaev YU. D., Savel’ev I. I. Zeeman laser gyroscopes. Quantum Electronics. 2015; 45(2): 171–179. DOI: 10.1070/QE2015v045n02ABEH015539.
Grew K. E., Ibbs T. L. Thermal diffusion in gases. Cambridge Univ. Press. 1952 RuMoRGB.
Suhanov S. V. Algoritmy kompensacii pogreshnostej vyhodnogo signala lazernogo giroskopa. Vestnik Nizhegorodskogo universiteta im. N. I. Lobachevskogo. 2011; 3–4:134–140.
Han Jeong Youp, Son Seong Hyun. The compensation method for thermal bias of ring laser gyro. Proceedings of LEOS. 2008. 21-st Annual Meeting of the IEEE Lasers and Electro-Optics Society, Acapulco. 2008; 723–724. DOI: 10.1109/LEOS.2008.4688823.
Geng Li, Fei Wang, Guangzong Xiao, Guo Wei, Pengfei Zhang, Xingwu Long. Temperature compensation method using readout signals of ring laser gyroscope. Opt. Express. 2015; 23(10): 13320–13332. DOI: 10.1364/OE.23.013320.
ABOUT AUTHORS
Medvedev Aleksey Aleksandrovich, alexdyn92@yandex.ru, Polyus Research Institute of M. F. Stelmakh JSC; Specialist in inertial navigation and laser gyroscope, Moscow, Russia.
ORCID id: 0000-0002-7308-1839.
Grushin Mikhail Evgenievich, Cand. of Science (Phys.& Math.), mihail.grushin1968@gmail.com, Polyus Research Institute of M. F. Stelmakh JSC (Moscow); Specialist in gas discharge physics, plasma chemistry, plasma medicine and inertial navigation and laser gyroscope, Moscow, Russia.
SCOPUS id:6603354719.
A. A. Medvedev, M. E. Grushin
Research Institute «Polyus» named after M. F. Stelmakh, JSC, Moscow, Russia
The paper presents the results of correction the non-magnetic component of zero-drift sensors with changing external temperatures and self-heating. Method is shown that allows to adjust the zero-drift improving accuracy characteristics of the device up to 103 times. For the first time, testing ZLG were obtained results better than 0.01 ° / h at the rate of change the external temperature 0.3 ° / min.
Key words: Laser Gyroscope, ZLG, zero drift, temperature correction
Received on: 25.02.2020
Accepted on: 08.04.2020
INTRODUCTION
Modern laser gyroscopy, based on the use of interference phenomena, makes it possible to measure angular velocities and angles in inertial space with high accuracy. A special place in the family of laser gyroscopes (LG) is hold by Zeeman laser gyroscopes (ZLG), where a dithering is created due to the Zeeman effect when a longitudinal magnetic field is applied to gas-discharge gaps [1].
It is known that additional ZLG errors are determined by a number of factors. These factors are associated with instability of the pump current of the active medium, interference in the perimeter adjustment system, instability of external and internal magnetic fields. The ZLG must maintain their accuracy and performance in a wide range of temperature effects. The dynamics of the zero bias of ring lasers, its non-magnetic and magnetic components is influenced by the ambient temperature and thermal processes occurring inside the ring lasers.
The asymmetry of the temperature distribution along the active medium has the greatest influence on the zero drift, or rather on its nonmagnetic component. When creating a temperature gradient along the walls, a gas flow arises at its surface, directed from the colder region to the hotter one. This phenomenon is called thermal slip [2].
The issue of temperature correction using the readings of the temperature difference of thermal sensors (from two to five), installed in the hot and cold parts, was considered in [3–5]. In these works, results were presented using thermal correction of zero drift (Ωzd) on LG modifications on a vibro-suspension, without additional external heating element. After mathematical processing, the zero drift error does not exceed 0.01° / h.
The fundamental difference between ZLG sensors and sensors on a vibro-suspension is the presence of coils that create a longitudinal magnetic field in the active medium. When current flows through the coils, heat is released in them, which leads to a redistribution of thermal fields in the resonator.
NEW ZERO DRIFT TEMPERATURE CORRECTION METHOD
In this research, we consider KL‑4M and K‑5M ZLG sensors working with one GDG in each sensor half filled with a 50% mixture of Ne20 Ne22 and He4 isotopes. For this type of ZLG, a temperature correction of zero drift was carried out at a rate of change of external temperature of 0.3 rpm with temperature transitions from 218 to 298 K, from 298 to 348 K, from 348 to 298 K, from 298 to 218 K. During the correction, the data of two temperature sensors were used.
The results of the calculation of the thermal fields of K‑5M ZLG are presented in Fig. 1. A graphical representation shows that the main heat generation occurs in coil samples (items 5 and 9). At this point, a temperature sensor (T2) was installed. The temperature sensor T1 was installed at the bottom of a metal test rig, to which the ZLG is mechanically attached (posit. 2).
The studies were carried out on an untied foundation in the heat and cold chamber of the Aquitas type model ADS-V_TM with outside compressor. ZLG was protected by the design of the magnetic screen to reduce the influence of external magnetic fields on the stability of the output signal. A temperature sensor was installed at the bottom of the magnetic screen to determine the temperature of the cold part of the ZLG. The accuracy parameters of the ZLG were measured at a discharge current of 1.2 mA and a current in the coils of a nonreciprocal device of 0.5 A.
When developing a model of temperature correction, it was proposed to separate the effect of the self-heating of ZLG on the effect caused by heating of the coils of a nonreciprocal device and the effect caused by a change in the external temperature in the heat and cold chamber.
To correct the thermal slip associated with self-heating, we used the temperature difference between the cold and hot regions of the sensor (∆Т = Т2 – Т1). For this, hourly measurements were carried out at stationary values of external temperatures (T). For each external temperature (–55 °C = 218 K, 25 °C = 298 K, 75 °C = 348 K), the dependences of Ωzd on ∆Т were constructed.
Initially, it was postulated that the temperature dependence of the ZLG zero drift obeys the polynomial dependence: Ωzd = А + В ∙ ∆Т + С ∙ ∆Т2. Figure 2 shows the dependences of ZLG zero drift (Ωzd) on the temperature difference between the cold (T1) and hot (T2) parts of the ZLG for three averaged values of external stationary temperatures. It is important to note that the approximating function must be constructed taking into account the weight characteristics (w) of the obtained point results. We assume that w = 1 / i2, where i is the serial number of the point.
The temperature dependence of the coefficients of the second-order polynomials (Ωzd = А + В ∙ ∆Т + С ∙ ∆Т2), approximating the dependence of Ωzd on ∆Т, was determined by the least squares method for each external stationary temperature (Т).
Figure 3 shows the temperature dependences of the coefficients of polynomials of the second order (A, B, C) obtained by approximating Ωzd = А + В ∙ ∆Т + С ∙ ∆Т2. An analysis of the graphical dependencies (Fig. 3) showed that the temperature dependence of the coefficients of the second-order polynomials A, B, C is well described with a linear dependency. We substitute the obtained coefficients into the previously obtained function Ωzd = А + В ∙ ∆Т + С ∙ ∆Т2. As a result, to correct the self-heating of ZLG from the drift, we subtract the function
Ω* = (А1 + А2 ∙ Т2) + (В1 + В2 ∙ Т2) ∙ ∆Т + (С1 + С2 ∙ Т2) ∙ ∆Т2 . (1)
To introduce temperature correction of zero drift at varying external temperatures, zero drift was measured using the following sequence diagram:
Chamber temperature 298K (3 hours) → rate of temperature change 0.3 ° / min
Chamber temperature 218K (3 hours) → rate of temperature change 0.3 ° / min
Chamber temperature 298K (3 hours) → rate of temperature change 0.3 ° / min
Chamber temperature 348K (3 hours) → rate of temperature change 0.3 ° / min
Chamber temperature 298K (3 hours)
After measuring the zero drift according to the above sequence diagram, the exclusion of self-heating was carried out by subtracting the values calculated according to dependence (1).
In this research, for the first time, it was proposed to describe the processes occurring in the heat and cold chamber, the so-called external heating of the device, using the derivative function of the readings of the temperature sensor from a non-reciprocal device coil (∆T2 / dt). For this, after taking into account the self-heating value by the least squares method for all temperature transitions (from 218 to 298 K, from 298 to 348 K, from 348 to 298 K, from 298 to 218 K), the temperature dependence of the coefficients of the second-order polynomials was determined, which approximate the dependence of Ωzd on ΔT2 / dt. Fig. 4 shows the dependence of zero drift after taking into account self-heating and the time derivative of the coil temperature are taken into account as an example for the temperature transition from 218 to 298 K.
As a result of the mathematical procedures performed on the temperature correction functions during self-heating and changes in external temperatures (expression 1), the resulting function is obtained:
Ω*zd = Ωzd – (А1 + А2 ∙ Т2) + (В1 + В2 ∙ Т2) ∙ ∆Т +
+ (С1 + С2 ∙ Т2) ∙ ∆Т2 – [А3 – В3 ∙ (∆T2 / dt) + С3 ∙ (∆T2 / dt2)] . (2)
where А1 + А2 ∙ Т2, В1 + В2 ∙ Т2, С1 + С2 ∙ Т2 are the temperature dependences of the coefficients of polynomials of the second order, approximating the dependence of Ωzd on ∆Т; T2 is the temperature of the temperature sensor installed in the coil groove; ∆Т is the difference between the cold and hot regions of the ZLG sensor; (∆T2 / dt) is the time derivative of the temperature readings of the temperature sensor installed in the coil groove.
The table presents the results of the temperature correction Ωzd, made according to dependence (2) at varying external temperatures (from 218 to 298K, from 298 to 348K, from 348 to 298K, from 298 to 218K).
Fig. 5 shows the example results of the Ωzd correction performed in accordance with dependence (2) with the external temperature varying from 218 to 298 K. From the results presented in the table and in Fig. 5, it becomes obvious that the proposed correction method Ωzd reduces the error caused by the thermal skid effect up to 103 times.
CONCLUSION
For ZLG sensors K‑4M and K‑5M, a temperature correction of zero drift was carried out at a rate of change of external temperature of 0.3 ° / min. ZLG operate with one gas-discharge gap in each sensor half filled with a 50% mixture of the Ne20 Ne22 and He4 isotopes. When developing the temperature correction algorithm, the effect of the self-heating of ZLG was divided into the effect caused by heating of the coils of a non-reciprocal device, and the effect caused by a change in the external temperature in the heat and cold chamber.
For the first time, it was proposed to describe the processes occurring in the heat and cold chamber, the so-called external heating of the device, using the derivative of the temperature difference of the temperature sensor readings from a non-reciprocal device coil (∆T2 / dt). Thus, the method of temperature correction of zero drift using two temperature sensors proposed in the work allows improving the accuracy characteristics of ZLG up to 103 times with changing external temperatures and self-heating.
REFERENCES
Azarova V. V., Golyaev YU. D., Savel’ev I. I. Zeeman laser gyroscopes. Quantum Electronics. 2015; 45(2): 171–179. DOI: 10.1070/QE2015v045n02ABEH015539.
Grew K. E., Ibbs T. L. Thermal diffusion in gases. Cambridge Univ. Press. 1952 RuMoRGB.
Suhanov S. V. Algoritmy kompensacii pogreshnostej vyhodnogo signala lazernogo giroskopa. Vestnik Nizhegorodskogo universiteta im. N. I. Lobachevskogo. 2011; 3–4:134–140.
Han Jeong Youp, Son Seong Hyun. The compensation method for thermal bias of ring laser gyro. Proceedings of LEOS. 2008. 21-st Annual Meeting of the IEEE Lasers and Electro-Optics Society, Acapulco. 2008; 723–724. DOI: 10.1109/LEOS.2008.4688823.
Geng Li, Fei Wang, Guangzong Xiao, Guo Wei, Pengfei Zhang, Xingwu Long. Temperature compensation method using readout signals of ring laser gyroscope. Opt. Express. 2015; 23(10): 13320–13332. DOI: 10.1364/OE.23.013320.
ABOUT AUTHORS
Medvedev Aleksey Aleksandrovich, alexdyn92@yandex.ru, Polyus Research Institute of M. F. Stelmakh JSC; Specialist in inertial navigation and laser gyroscope, Moscow, Russia.
ORCID id: 0000-0002-7308-1839.
Grushin Mikhail Evgenievich, Cand. of Science (Phys.& Math.), mihail.grushin1968@gmail.com, Polyus Research Institute of M. F. Stelmakh JSC (Moscow); Specialist in gas discharge physics, plasma chemistry, plasma medicine and inertial navigation and laser gyroscope, Moscow, Russia.
SCOPUS id:6603354719.
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