CN104793488B - A kind of superfluid gyroscope Control System Design method based on automatic disturbance rejection controller - Google Patents
A kind of superfluid gyroscope Control System Design method based on automatic disturbance rejection controller Download PDFInfo
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Abstract
The superfluid gyroscope Control System Design method based on automatic disturbance rejection controller that the present invention relates to a kind of.According to the working principle of double Weak link superfluid gyroscopes, the mathematical model of superfluid gyroscope is established；Superfluid gyroscope angular speed model is established using amplitude locking compensation method；Automatic disturbance rejection controller is introduced in superfluid control loop, accurate mathematical model has not been required controlled device according to automatic disturbance rejection controller, and the disturbance caused by system model uncertainty can be considered total the characteristics of disturbing and being tracked compensation together with external disturbance, improve the control precision that the locking of film amplitude is realized in hot phase compensation, entire superfluid gyroscope control system performance is promoted, to improve the precision that angular speed solves general formula.The invention belongs to new concept gyro control technical fields, can be applied to the control system optimization design of superfluid gyroscope.
Description
Technical Field
The invention relates to a design method of a superfluid gyroscope control system based on an active disturbance rejection controller, which is suitable for optimizing the superfluid gyroscope control system.
Technical Field
From the end of the 19 th century to the present, gyroscopes have played an important role in military and civilian fields as the main inertial navigation detection devices. The conventional spinning top senses the angular movement of the spinning top shell relative to the inertia space by the moment generated by the rotation of the rotor. In recent years, with the rapid development of the fields of optics, low-temperature physics and the like, a series of novel gyros appear. The gyroscope does not have a rotor rotating at a high speed, but completes the motion measurement of the shell relative to an inertia space based on a novel physical mechanism. The precision of the laser gyro is high, but the processing is complicated and the locking problem exists. The fiber-optic gyroscope has the advantages of simple processing, high precision, poor system stability and large volume. Cold atom beam gyroscopes and superfluid gyroscopes developed based on low temperature physics, wherein the former has great challenges in laser cooling technology and precise control of trapped atoms, and the latter attracts great attention of domestic scholars in recent years by virtue of excellent properties of no viscosity, no friction, high precision and high sensitivity.
Superfluid gyroscope based on AC Josephson effect, using4The measurement of the rotation angle is realized by the substance wave interference effect of the He superfluid in the annular cavity, and the sensitivity can be reachedIs 10 orders of magnitude higher than that of a fiber-optic gyroscope. The range of the gyroscope is too small, the amplitude locking of the superfluid gyroscope is realized by injecting the thermal phase, so that the purpose of expanding the range is achieved, the injection process of the thermal phase is an inertia link, an active disturbance rejection controller does not require an accurate mathematical model for a controlled object, and the disturbance caused by the uncertainty of a system model and the external disturbance can be regarded as the total disturbance and are tracked and compensated together, so that the control precision of the thermal phase compensation for realizing the film amplitude locking is improved, and the precision of the angular velocity solving general formula is improved.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the problem that angular velocity cannot be solved through direct inverse solution of detected film displacement in the superfluid gyroscope is solved, film amplitude locking is achieved through thermal phase compensation, and a general formula for solving the angular velocity is obtained. The active disturbance rejection controller does not require an accurate mathematical model for a controlled object, and disturbance caused by uncertainty of a system model and external disturbance can be regarded as total disturbance and tracked and compensated together, so that the control precision of film amplitude locking realized by thermal phase compensation is improved, the performance of the whole superfluid gyroscope control system is improved, the precision of an angular velocity solving general formula is improved, and high stability and high precision detection of a superfluid gyroscope system are realized.
The technical solution of the invention is as follows: establishing a mathematical model of the superfluid gyroscope according to the working principle of the double-weak connection superfluid gyroscope; establishing a super-fluid gyroscope angular velocity model by using an amplitude locking compensation method; the active disturbance rejection controller is introduced into the superfluid control loop, and according to the characteristics that the active disturbance rejection controller does not require an accurate mathematical model for a controlled object, and disturbance caused by uncertainty of a system model and external disturbance can be regarded as total disturbance and tracked and compensated together, the control precision of realizing film amplitude locking by thermal phase compensation is improved, the performance of the whole superfluid gyroscope control system is improved, and therefore the precision of solving a general formula by angular velocity is improved.
The method specifically comprises the following steps:
(1) according to the working principle of the double weak connection superfluid gyroscope, establishing a mathematical model of the superfluid gyroscope:
wherein,
wherein x (t) is the amplitude of the film, I (t) is the total material wave flow in the annular cavity, rho1In order to be the density of the super-fluid,is a vector of the sensing area, N is the number of holes contained in a single weak link, I0Is a sheetThe strength of the hole critical supercritical fluid, delta u is the chemical potential energy difference formed by the pressure difference and the temperature difference at two sides of the weak connection, delta phi is the phase difference at the double weak connection, and delta phi is the phase difference at the double weak connectionωSagnac phase shift, Δ φ, caused by external rotation angular velocityheatFor the thermal phase of the injection, phi0In order to be the initial phase position,is the total material wave phase in the annular cavity, h is the Planck constant, m is4He exceeds the mass of the atoms of the fluid,is the angular velocity of rotation of the outside world;
(2) establishing an angular velocity model of a superfluid gyroscope
Aiming at the mathematical model of the detection of the superfluid gyroscope obtained in the step (1), setting a working point at pi/3 by using an amplitude locking principle, and injecting a thermal phase into the superfluid gyroscope to obtain a directly-resolved superfluid gyroscope angular velocity solution:
in the formula, p is the maximum value of the compensation amount, and n is the number of times of reaching the maximum compensation amount;
(3) designing an auto-disturbance rejection controller
The tracking differentiator TD is expressed in the form of:
in the formula:v1(t) is a reference input v0(t) tracking signal, v2(t) is v1(t) differentiation, thereby converting v2(t) as v0(t) "approximate differential", R, delta1To track differentiator adjustable parameters;
the extended state observer, ESO, is expressed as:
in the formula:α1、α2、α3、δ2、β1、β2、β3is an adjustable parameter; the third order ESO is the real-time contribution to the state variable coupling of the object and the total disturbance of the object estimated by the object output y, i.e. 3 signals are generated by the system output y: z is a radical of1、z2、z3Wherein z is1A tracking signal of y, e is z1Difference between y and z2(t) is z1(t) differential signal, z3(t) is an estimate of system model coupling and external perturbations;
the expression of the nonlinear state error feedback control law NLSEF is as follows:
in the formula: alpha is alpha4、α5、δ3、b、kp、kdIs an adjustable parameter; e.g. of the type1Is v is1And z1Difference of (e)2Is v is2And z2Difference of u0Is a non-linear combination of errors, u is a control input; by measuring the film amplitude x (t), the thermal phase delta phi of the injection is outputheat。
The principle of the invention is as follows:
in the superfluid gyroscope system, the amplitude locking of the film can be realized by a thermal phase injection compensation method, the measuring range of the superfluid gyroscope is expanded, and the external rotation angular speed can be directly obtained through inverse solution. The problem of inertia delay of thermal phase injection is considered, real-time injection compensation of the thermal phase can be realized by designing a proper control system of the superfluid gyroscope, and high-precision detection of the angular velocity of the superfluid gyroscope is realized.
The annular cavity of the superfluid gyroscope is filled with4He superfluid changes the temperature and pressure in the annular cavity through a heating resistance wire, and the constant driving potential energy formed at the two ends of the weak connection is as follows:
Δu＝m(Δp/ρ-sΔT)
the resulting thermal drive potential will drive the superfluid flow through the two weak connections, resulting in a total flow in the pipe of:
I(t)＝2I cos((Δφ0-Δφ1)/2)sin((Δφ0+Δφ1)/2)
when the external part is at angular velocityThe phase difference formed by the superfluid at the weak link is delta phi during rotationω：
Considering that the injected thermal phase also forms a certain phase difference at the weak link, the phase difference formed by the whole process is considered comprehensively as follows:
the phase relation of the thermal driving potential energy matter wave is as follows:
and dividing the volume of the ring cavity to obtain the total material wave phase in the ring cavity as follows:
the total material wave flow in the annular cavity obtained by combining the formula is as follows:
the change of the membrane displacement in the superfluid loop is related to the superfluid by:
the amplitude of the vibration signal of the superfluid mass wave generated at the weak connection in phase due to external rotation is modulated, and the expression of the modulation quantity A is as follows:
A＝2NI0|cos(Δφω)|
knowing that the modulation amount is a periodic function and the period is pi, the conditions for directly solving the external rotation angular velocity are as follows: delta phiωIn the interval (k pi/2, (k +1) pi/2), if delta phiωIs greater than pi/2, then delta phiωExpressed as:
Δφω＝kπ/2+Δφy
by inversely solving the displacement amount of the film detected by the sensor, the obtained angular velocity amount is only the margin Δ ΦyCannot directly obtain the actual delta phi through inverse solutionωAnd the k value is difficult to determine, so that the obtained speed solution is an incomplete solution, and the normal operation of the superfluid gyroscope can be realized only by limiting delta phiωIn the interval (0, pi/2), this necessarily results in a very small range of detectable angular velocities of the gyroscope.
In a double weak connection superfluid gyroscope system with thermal phase injection, the phase of a working point of the system is set to be pi/3, and the thermal phase compensation quantity is delta phiheatThen, the following conditions are satisfied in the work:
the compensation quantity obtained by subtracting the current moment of the system from the phase of the working point is the phase caused by the detected current input angular velocity: the resolution of the input angular velocity is then:
and in practical operation, the maximum value of the phase which can be compensated by adopting the thermal compensation can not exceed 500 pi, then the constraint is that:
when the actual compensation amount is larger than p, the compensation amount is required to be subtracted from the original compensation amount by the maximum value p of the compensation amount, and the number n of times of subtracting p is stored, so that the universal phase difference caused by external rotation can be obtained:
the external rotation angular velocity can be directly obtained by inverse solution:
the injection approximation of the thermal phase is considered to be a first order inertial elementThe requirement of locking the amplitude of the superfluid on the expected amplitude can be controlled and realized by designing the superfluid gyroscope of the active disturbance rejection controller, the influence of inertia delay on the stability and the detection precision of a superfluid gyroscope system is avoided, the active disturbance rejection controller does not require an accurate mathematical model for a controlled object, the disturbance caused by the uncertainty of the system model and the external disturbance can be regarded as total disturbance and are tracked and compensated together, the control precision of locking the film amplitude by thermal phase compensation is improved, the performance of the whole superfluid gyroscope control system is improved, and therefore the precision of solving a general formula by angular velocity is improved.
The tracking differentiator TD is expressed in the form of:
in the formula:v1(t) is a reference input v0(t) tracking signal, v2(t) is v1(t) differentiation, thereby converting v2(t) as v0(t) "approximate differential", R, delta1To track differentiator adjustable parameters;
the extended state observer, ESO, is expressed as:
in the formula:α1、α2、α3、δ2、β1、β2、β3is an adjustable parameter; the third order ESO is the real-time contribution to the state variable coupling of the object and the total disturbance of the object estimated by the object output y, i.e. 3 signals are generated by the system output y: z is a radical of1、z2、z3Wherein z is1A tracking signal of y, e is z1Difference between y and z2(t) is z1(t) differential signal, z3(t) is an estimate of system model coupling and external perturbations;
the expression of the nonlinear state error feedback control law NLSEF is as follows:
in the formula: alpha is alpha4、α5、δ3、b、kp、kdIs an adjustable parameter; e.g. of the type1Is v is1And z1Difference of (e)2Is v is2And z2Difference of u0Is a non-linear combination of errors, u is a control input; by measuring the film amplitude x (t), the thermal phase delta phi of the injection is outputheat。
Compared with the prior art, the scheme of the invention has the main advantages that:
(1) although the existing control scheme provides a film displacement relation model, when the rotation phase exceeds pi/2, the angular velocity obtained by model resolving is only reflected by the rotation phase margin and cannot obtain a complete solution of an angular velocity solution, the invention locks the film amplitude by injection compensation of the thermal phase, and the complete solution of the angular velocity solution is obtained while the double weak connection superfluid gyroscope range is enlarged;
(2) an active disturbance rejection controller is introduced into a superfluid control loop, an accurate mathematical model is not required for a controlled object according to the active disturbance rejection controller, disturbance caused by uncertainty of a system model and external disturbance can be regarded as total disturbance and tracked and compensated together, control precision of film amplitude locking achieved by thermal phase compensation is improved, performance of a whole superfluid gyroscope control system is improved, and precision of a general formula for solving angular velocity is improved.
Drawings
FIG. 1 is a block diagram of an active disturbance rejection controller;
FIG. 2 is a flow chart of the present invention;
FIG. 3 is a waveform of the amplitude of the thin film;
fig. 4 is a waveform diagram of measured angular velocity.
Detailed description of the preferred embodiments
The implementation object of the invention is a double-weak-connection superfluid gyroscope, the specific implementation scheme is shown in fig. 2, and the specific implementation steps are as follows:
(1) according to the working principle of the double weak connection superfluid gyroscope, establishing a mathematical model of the superfluid gyroscope:
wherein,
wherein x (t) is the amplitude of the film, I (t) is the total material wave flow in the annular cavity, rho1In order to be the density of the super-fluid,is a vector of the sensing area, N is the number of holes contained in a single weak link, I0For single-hole critical supercritical fluid strength, Δ u is the chemical potential energy difference formed by the pressure difference and temperature difference at two sides of the weak connection, Δ φ is the phase difference at the double weak connection, Δ φωSagnac phase shift, Δ φ, caused by external rotation angular velocityheatFor the thermal phase of the injection, phi0In order to be the initial phase position,is the total material wave phase in the annular cavity, h is the Planck constant, m is4He exceeds the mass of the atoms of the fluid,is the angular velocity of rotation of the outside world;
(2) establishing an angular velocity model of a superfluid gyroscope
Aiming at the mathematical model of the detection of the superfluid gyroscope obtained in the step (1), setting a working point at pi/3 by using an amplitude locking principle, and injecting a thermal phase into the superfluid gyroscope to obtain a directly-resolved superfluid gyroscope angular velocity solution:
in the formula, p is the maximum value of the compensation amount, and n is the number of times of reaching the maximum compensation amount;
(3) designing an auto-disturbance rejection controller
The tracking differentiator TD is expressed in the form of:
in the formula:v1(t) is a reference input v0(t) tracking signal, v2(t) is v1(t) differentiation, thereby converting v2(t) as v0(t) "approximate differential", R, delta1To track differentiator adjustable parameters;
the extended state observer, ESO, is expressed as:
in the formula:α1、α2、α3、δ2、β1、β2、β3is an adjustable parameter; the third order ESO is the real-time contribution to the state variable coupling of the object and the total disturbance of the object estimated by the object output y, i.e. 3 signals are generated by the system output y: z is a radical of1、z2、z3Wherein z is1A tracking signal of y, e is z1Difference between y and z2(t) is z1(t) differential signal, z3(t) is an estimate of system model coupling and external perturbations;
the expression of the nonlinear state error feedback control law NLSEF is as follows:
in the formula: alpha is alpha4、α5、δ3、b、kp、kdIs an adjustable parameter; e.g. of the type1Is v is1And z1Difference of (e)2Is v is2And z2Difference of u0Is a non-linear combination of errors, u is a control input; by measuring the film amplitude x (t), the thermal phase delta phi of the injection is outputheat。
As can be seen from fig. 3 and 4, after the control is stabilized, the film amplitude does not change with the change of the measured angular velocity, which shows that the film amplitude locking effect based on the active disturbance rejection controller is better.
Those skilled in the art will appreciate that the details of the present invention not described in detail herein are well within the skill of those in the art.
Claims (1)
1. A design method of a superfluid gyroscope control system based on an active disturbance rejection controller is characterized by comprising the following steps: establishing a mathematical model of the superfluid gyroscope according to the working principle of the double-weak connection superfluid gyroscope; establishing a super-fluid gyroscope angular velocity model by using an amplitude locking compensation method; introducing an active disturbance rejection controller into a superfluid control loop, improving the control precision of realizing film amplitude locking by thermal phase compensation according to the characteristics that the active disturbance rejection controller does not require an accurate mathematical model for a controlled object, and disturbance caused by uncertainty of a system model and external disturbance can be regarded as total disturbance and tracked and compensated together, and improving the performance of a whole superfluid gyroscope control system, thereby improving the precision of solving a general formula by angular velocity, and specifically comprising the following steps:
(1) according to the working principle of the double weak connection superfluid gyroscope, establishing a mathematical model of the superfluid gyroscope:
wherein,
wherein x (t) is the amplitude of the film, I (t) is the total material wave flow in the annular cavity, rho1In order to be the density of the super-fluid,is a vector of the sensing area, N is the number of holes contained in a single weak link, I0For single-hole critical supercritical fluid strength, Δ u is the chemical potential energy difference formed by the pressure difference and temperature difference at two sides of the weak connection, Δ φ is the phase difference at the double weak connection, Δ φωSagnac phase shift, Δ φ, caused by external rotation angular velocityheatFor the thermal phase of the injection, phi0In order to be the initial phase position,is the total material wave phase in the annular cavity, h is the Planck constant, m is4He exceeds the mass of the atoms of the fluid,is the angular velocity of rotation of the outside world;
(2) establishing an angular velocity model of a superfluid gyroscope
Aiming at the mathematical model of the detection of the superfluid gyroscope obtained in the step (1), setting a working point at pi/3 by using an amplitude locking principle, and injecting a thermal phase into the superfluid gyroscope to obtain a directly-resolved superfluid gyroscope angular velocity solution:
in the formula, p is the maximum value of the compensation amount, and n is the number of times of reaching the maximum compensation amount;
(3) designing an auto-disturbance rejection controller
The tracking differentiator TD is expressed in the form of:
in the formula:v1(t) is a reference input v0(t) tracking signal, v2(t) is v1(t) differentiation, thereby converting v2(t) as v0(t) "approximate differential", R, delta1To track differentiator adjustable parameters;
the extended state observer, ESO, is expressed as:
in the formula:α1、α2、α3、δ2、β1、β2、β3is an adjustable parameter; the third order ESO is the real-time contribution to the state variable coupling of the object and the total disturbance of the object estimated by the object output y, i.e. 3 signals are generated by the system output y: z is a radical of1、z2、z3Wherein z is1A tracking signal of y, e is z1Difference between y and z2(t) is z1(t) differential signal, z3(t) is an estimate of system model coupling and external perturbations;
the expression of the nonlinear state error feedback control law NLSEF is as follows:
in the formula: alpha is alpha4、α5、δ3、b、kp、kdIs an adjustable parameter; e.g. of the type1Is v is1And z1Difference of (e)2Is v is2And z2Difference of u0Is a non-linear combination of errors, u is a control input; by measuring the film amplitude x (t), the heat injected is outputPhase delta phiheat。
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| CN105066981B (en) * | 2015-07-27 | 2017-10-03 | 中国人民解放军装备学院 | A kind of superfluid gyroscope device based on light wave thermal compensation |
| CN105182750B (en) * | 2015-09-02 | 2018-06-26 | 中国人民解放军军械工程学院 | A kind of linear/non-linear Active Disturbance Rejection Control system method for handover control |
| CN105159065B (en) * | 2015-09-02 | 2018-06-26 | 中国人民解放军军械工程学院 | A kind of non-linear Active Disturbance Rejection Control system stability judgment method |
| CN109459007A (en) * | 2018-09-20 | 2019-03-12 | 中国人民解放军战略支援部队航天工程大学 | Inhibit fan-shaped superfluid interference grid gyro to measure angular speed Noise Method and its device |
| CN111431456B (en) * | 2020-03-10 | 2021-12-17 | 浙江工业大学 | Permanent magnet synchronous motor finite set multi-step model prediction current control method |
| CN113138612A (en) * | 2020-07-28 | 2021-07-20 | 西安天和防务技术股份有限公司 | Active disturbance rejection control method and device for astronomical navigation and electronic equipment |
| CN112666825A (en) * | 2020-12-30 | 2021-04-16 | 西安建筑科技大学 | Micromechanical gyroscope amplitude control system based on ADRC |
| CN113848721B (en) * | 2021-10-09 | 2023-05-16 | 九江学院 | Cold atom gravity meter active vibration isolation method based on high-gain observer sliding mode control |
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