CN104793488A - Superfluid gyroscope control system design method based on active disturbance rejection controller - Google Patents

Abstract

The invention relates to a superfluid gyroscope control system design method based on an active disturbance rejection controller. The method comprises the steps of establishing a mathematic model of a superfluid gyroscope according to the working principle of a double weak connection superfluid gyroscope, establishing a superfluid gyroscope angular velocity model by an amplitude locking compensation method, and introducing an active disturbance rejection controller in a superfluid control circuit. The active disturbance rejection controller does not require an accurate mathematical model for a controlled object, and disturbance caused by system model uncertainties and external disturbance are regarded as the total disturbance and are tracked and compensated at the same time. Thus, thermal phase compensation is improved to realize the control precision of film amplitude locking, enhance the performance of a whole superfluid gyroscope control system and improve the accuracy of an angular velocity solving general formula. The superfluid gyroscope control system design method of the invention belongs to the technical field of new-concept gyroscope control, and can be used to design a superfluid gyroscope control system in an optimized manner.

Description

A kind of superfluid gyroscope Control System Design method based on automatic disturbance rejection controller

Technical field

The present invention relates to a kind of superfluid gyroscope Control System Design method based on automatic disturbance rejection controller, be applicable to the optimization of superfluid gyroscope control system.

Technical background

From 19 end of the centurys till now, gyroscope, as main inertial navigation checkout equipment, plays an important role in military, civilian field.The gyro of traditional concept is the angular motion being produced the momentum moment responsive gyro housing relative inertness space by rotor turns.In recent years along with the fast development in the field such as optics, cryophysics, there is the gyro of series of new.The rotor of High Rotation Speed had no longer by this gyro, but completes the motion measurement in housing relative inertness space based on novel Physical Mechanism.The precision of laser gyro is higher, but processed complex and there is latch-up problem.Optical fibre gyro processing is simple, precision is high, but system stability is poor, and volume is large.What grow up based on cryophysics has cold atomic beam gyro and superfluid gyroscope, wherein the former laser-cooling technology and catch atom accurate control in there is huge challenge, the latter relies on it without glutinousness, without friction, high precision, highly sensitive premium properties, causes the very big concern of domestic scholars in recent years.

Based on the superfluid gyroscope of ac josephson effect, utilize ⁴he superfluid realizes the measurement to angle of rotation in the matter wave interference effect of ring cavity, and sensitivity can reach 10 orders of magnitude higher than optical fibre gyro.But this gyro range ability is too small, the amplitude locking of superfluid gyroscope is realized by injecting hot phase place, thus reach the object of expansion range, the injection process of hot phase place is an inertial element, automatic disturbance rejection controller does not require accurate mathematical model to controlled device, and total disturbance and together tracked compensation can be considered by the system model disturbance that causes of uncertainty and external disturbance, thus improve the control accuracy that hot phase compensation realizes the locking of film amplitude, therefore lifting angle speed solves the precision of general formula.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome in superfluid gyroscope, the problem that angular velocity cannot be tried to achieve by the direct anti-solution of membrane displacement detected, and realizes the locking of film amplitude, obtain the general formula that angular velocity solves by hot phase compensation.Automatic disturbance rejection controller does not require accurate mathematical model to controlled device, and the feature of total disturbance and together tracked compensation can be considered by the system model disturbance that causes of uncertainty and external disturbance, improve the control accuracy that hot phase compensation realizes the locking of film amplitude, promote whole superfluid gyroscope control system performance, thus improve the precision that angular velocity solves general formula, and then realize high stable and the high precision test of superfluid gyroscope system.

Technical solution of the present invention is: according to the principle of work of two Weak link superfluid gyroscope, set up the mathematical model of superfluid gyroscope; Utilize amplitude to lock compensation method and set up superfluid gyroscope angular velocity model; Automatic disturbance rejection controller is introduced in superfluid control loop, according to automatic disturbance rejection controller, accurate mathematical model is not required to controlled device, and the feature of total disturbance and together tracked compensation can be considered by the system model disturbance that causes of uncertainty and external disturbance, improve the control accuracy that hot phase compensation realizes the locking of film amplitude, promote whole superfluid gyroscope control system performance, thus improve the precision that angular velocity solves general formula.

Specifically comprise the following steps:

(1) according to the principle of work of two Weak link superfluid gyroscope, the mathematical model of superfluid gyroscope is set up:

$x\left(t\right)=\frac{1}{{\mathrm{\ρ}}_1\stackrel{\→}{A}}{\∫}_0^{t}I\left(t\right)\mathrm{dt}$

Wherein,

$\mathrm{\Δ\φ}={\mathrm{\Δ\φ}}_{\mathrm{\ω}}+\mathrm{\Δ}{\mathrm{\φ}}_{\mathrm{heat}}=\frac{2\mathrm{\πm}}{h}\stackrel{\→}{\mathrm{\ω}}\·\stackrel{\→}{A}+{\mathrm{\Δ\φ}}_{\mathrm{heat}}$

In formula, x (t) is film amplitude, the matter wave flow that I (t) is annular cavity total, ρ ₁for superfluid density, for the vector of induction area, the hole count of N contained by single Weak link, I ₀for the critical superfluid intensity of single hole, Δ u is that the chemical potential energy formed by Weak link pressure at both sides difference and temperature difference is poor, and Δ φ is the phase differential at two Weak link place, Δ φ _ωfor the Sagnac phase shift that outer buttons tarnsition velocity causes, Δ φ _heatfor the hot phase place injected, φ ₀for initial phase, for the matter wave phase place of annular cavity total, h is Planck's constant, and m is ⁴the quality of He superfluid atom, for the angular velocity of rotation in the external world;

(2) superfluid gyroscope angular velocity model is set up

The mathematical model that the superfluid gyroscope obtained for step (1) detects, utilizes amplitude locking principle to set working point at π/3 place, injects hot phase place to superfluid gyroscope, and obtaining can the superfluid gyroscope angular velocity solution of directly calculation:

$\stackrel{\→}{\mathrm{\ω}}=\frac{h}{2\mathrm{\πm}\stackrel{\→}{A}}(\frac{\mathrm{\π}}{3}-{\mathrm{\Δ\φ}}_{\mathrm{heat}}-\mathrm{nm})$

In formula, m is compensation rate maximal value, and n is the number of times reaching maximum compensation rate;

(3) automatic disturbance rejection controller is designed

The expression-form of Nonlinear Tracking Differentiator TD is:

$\left\{\begin{array}{c}{\stackrel{\·}{v}}_1=v_2\\ {\stackrel{\·}{v}}_2=-\mathrm{Rsat}(A,{\mathrm{\δ}}_1)\end{array}\right.$

In formula: $A=v_1-v_0+\frac{v_2\left|v_2\right|}{2R},$ $\mathrm{sat}(A,{\mathrm{\&delta;}}_1)=\left\{\begin{array}{c}\mathrm{sign}\left(A\right),\left|A\right|\&GreaterEqual;{\mathrm{\&delta;}}_1\\ A/{\mathrm{\&delta;}}_1,\left|A\right|<{\mathrm{\&delta;}}_1\end{array}\right.,$ V ₁t () is reference input v ₀the tracking signal of (t), v ₂t () is v ₁the differential of (t), thus v ₂t () is as v ₀" approximate differential " of (t), R, δ ₁for Nonlinear Tracking Differentiator adjustable parameter;

The expression-form of extended state observer ESO is:

$\left\{\begin{array}{c}e=z_1-y\\ {\stackrel{\&CenterDot;}{z}}_1=z_2-{\mathrm{\&beta;}}_1\mathrm{fal}(e,{\mathrm{\&alpha;}}_1,{\mathrm{\&delta;}}_2)\\ {\stackrel{\&CenterDot;}{z}}_2=z_3-{\mathrm{\&beta;}}_2\mathrm{fal}(e,{\mathrm{\&alpha;}}_2,{\mathrm{\&delta;}}_2)+\mathrm{bu}\\ {\stackrel{\&CenterDot;}{z}}_3=-{\mathrm{\&beta;}}_3\mathrm{fal}(e,{\mathrm{\&alpha;}}_3,{\mathrm{\&delta;}}_2)\end{array}\right.$

In formula: $\left\{\begin{array}{c}e=z_1-y\\ {\stackrel{\&CenterDot;}{z}}_1=z_2-{\mathrm{\&beta;}}_1\mathrm{fal}(e,{\mathrm{\&alpha;}}_1,{\mathrm{\&delta;}}_2)\\ {\stackrel{\&CenterDot;}{z}}_2=z_3-{\mathrm{\&beta;}}_2\mathrm{fal}(e,{\mathrm{\&alpha;}}_2,{\mathrm{\&delta;}}_2)+\mathrm{bu}\\ {\stackrel{\&CenterDot;}{z}}_3=-{\mathrm{\&beta;}}_3\mathrm{fal}(e,{\mathrm{\&alpha;}}_3,{\mathrm{\&delta;}}_2)\end{array}\right.,$ α ₁, α ₂, α ₃, δ ₂, β ₁, β ₂, β ₃for adjustable parameter; Three rank ESO export y by object to estimate the state variable coupling of object and the real-time effect amount of the total disturbance of object, namely export y by system and produce 3 signal: z ₁, z ₂, z ₃, wherein z ₁for the tracking signal of y, e is z ₁with the difference of y, z ₂t () is z ₁the differential signal of (t), z ₃t () is the estimation to system model coupling and outer disturbance;

The expression formula of nonlinear state Error Feedback control law NLSEF is:

$\left\{\begin{array}{c}{e}_1=v_1-z_1\\ e_2=v_2-z_2\\ u_0=k_r\mathrm{fal}(e_1,{\mathrm{\&alpha;}}_4,{\mathrm{\&delta;}}_3)+k_d\mathrm{fal}(e_2,{\mathrm{\&alpha;}}_5,{\mathrm{\&delta;}}_3)\\ u=u_0-\frac{z_3}{b_0}\end{array}\right.$

In formula: α ₄, α ₅, δ ₃, b, k _r, k _dfor adjustable parameter; e ₁for v ₁and z ₁difference, e ₂for v ₂and z ₂difference, u ₀for the nonlinear combination of error, u is control inputs; By measuring film amplitude x (t), the hot phase delta phi of output injection _heat.

Principle of the present invention is:

In superfluid gyroscope system, the amplitude locking of film can be realized by the method for hot phase place injecting compensating, not only extend the range of superfluid gyroscope, direct anti-solution can also obtain outside rotational angular velocity.Consider the inertial delay problem that hot phase place is injected, the real-time injecting compensating of hot phase place can be realized by the control system that design superfluid gyroscope is suitable, thus realize the high-precision detection of superfluid gyroscope angular velocity.

Be filled with in the ring cavity of superfluid gyroscope ⁴he superfluid, changes the temperature and pressure in ring cavity by resistive heater, and the constant drive potential energy that Weak link two ends are formed is:

Δu＝m(Δp/ρ-sΔT)

The thermal drivers potential energy formed can drive superfluid to flow through two Weak link, and the total flow of the formation in pipeline is:

I(t)＝2Icos((Δφ ₀-Δφ ₁)/2)sin((Δφ ₀+Δφ ₁)/2)

When outside is with angular velocity during rotation, the phase differential formed at Weak link place superfluid is Δ φ _ω:

${\mathrm{\&Delta;\&phi;}}_{\mathrm{\&omega;}}=\frac{4\mathrm{\&pi;m}}{h}\stackrel{\&RightArrow;}{\mathrm{\&omega;}}\&CenterDot;\stackrel{\&RightArrow;}{A}$

Consider that the hot phase place of injection can form certain phase differential at Weak link place equally, then considering integrally formed phase differential is:

$\mathrm{\&Delta;\&phi;}={\mathrm{\&Delta;\&phi;}}_0-\mathrm{\&Delta;}{\mathrm{\&phi;}}_1=\frac{4\mathrm{\&pi;m}}{h}\stackrel{\&RightArrow;}{\mathrm{\&omega;}}\&CenterDot;\stackrel{\&RightArrow;}{A}+{\mathrm{\&Delta;\&phi;}}_{\mathrm{heat}}$

Thermal drivers potential energy matter wave phase relation has again:

$\frac{\mathrm{d\&phi;}}{\mathrm{dt}}=-\frac{\mathrm{\&Delta;u}}{h}$

Annularly cavity volume is divided and is obtained matter wave phase place total in loop and be:

${\mathrm{\&Delta;\&phi;}}_0+{\mathrm{\&Delta;\&phi;}}_1=\frac{-4\mathrm{\&pi;t\&Delta;u}}{h}$

The matter wave flow that comprehensive above-mentioned formula can obtain annular cavity total is:

$I\left(t\right)=2{\mathrm{NI}}_0\cos (\mathrm{\&Delta;\&phi;}/2)\sin (-2\mathrm{\&pi;t}\frac{\mathrm{\&Delta;u}}{h})$

In superfluid loop, the change of membrane displacement and superfluid pass are:

$x\left(t\right)=\frac{1}{\mathrm{\&rho;A}}{\&Integral;}_0^{t}I\left(t\right)\mathrm{dt}$

The amplitude of the superfluid matter wave vibration signal that the phase place that external rotating causes produces at Weak link place is modulated, and the expression formula of modulation voltage A is:

A＝2NI ₀|cos(Δφ _ω)|

${\mathrm{\&Delta;\&phi;}}_{\mathrm{\&omega;}}=\frac{2\mathrm{\&pi;m}}{h}\stackrel{\&RightArrow;}{\mathrm{\&omega;}}\&CenterDot;\stackrel{\&RightArrow;}{A}$

Known modulation voltage is periodic function, and its cycle is π, can anti-condition of separating outer buttons tarnsition velocity be directly: Δ φ _ωinterval at (k pi/2, (k+1) pi/2), if Δ φ _ωvalue be greater than pi/2, then Δ φ _ωbe expressed as:

Δφ _ω＝kπ/2+Δφ _y

Membrane displacement amount then by detecting sensor is counter separates, and the angular velocity amount that obtains is surplus Δ φ _yembodiment, cannot directly obtain actual Δ φ by anti-solution _ω, and k value is difficult to determine, the velocity solution obtained like this is incomplete solution, and the normal work wanting to realize superfluid gyroscope can only by restriction Δ φ _ωon interval (0, pi/2), this just must cause gyro can detection angle velocity range very little.

In two Weak link superfluid gyroscope systems that hot phase place is injected, the working point phase place of initialization system is π/3, and hot phase compensation amount is Δ φ _heat, then meet in working:

$\frac{2\mathrm{\&pi;m}}{h}\stackrel{\&RightArrow;}{\mathrm{\&omega;}}\&CenterDot;\stackrel{\&RightArrow;}{A}+{\mathrm{\&Delta;\&phi;}}_{\mathrm{heat}}=\mathrm{\&pi;}/3$

The compensation rate that working point phase place deducts system current time is the phase place that the current input angular velocity that detects causes: then the amount of resolving of input angular velocity is:

$\mathrm{\&omega;}=\frac{h}{2\mathrm{\&pi;m}\stackrel{\&RightArrow;}{A}}(\mathrm{\&pi;}/3-{\mathrm{\&Delta;\&phi;}}_{\mathrm{heat}})$

And in practical operation, adopt the compensable phase place maximal value of thermal compensation more than 500 π, then must not to retrain and have:

$\frac{2\mathrm{\&pi;m}}{h}{\stackrel{\&RightArrow;}{\mathrm{\&omega;}}}_{\max }\&CenterDot;\stackrel{\&RightArrow;}{A}\&le;\mathrm{\&pi;}/500$

When the compensation rate of reality is greater than m, then need compensation rate to deduct compensation rate maximal value m from original basis, store the frequency n deducting m simultaneously, now just can obtain the general phase differential quoted by outer buttons:

${\mathrm{\&Delta;\&phi;}}_{\mathrm{\&omega;}}=\frac{2\mathrm{\&pi;m}}{h}\stackrel{\&RightArrow;}{\mathrm{\&omega;}}\&CenterDot;\stackrel{\&RightArrow;}{A}=\mathrm{\&pi;}/3-{\mathrm{\&Delta;\&phi;}}_{\mathrm{heat}}-\mathrm{mn}$

Now direct anti-solution can obtain external rotating angular velocity:

$\mathrm{\&omega;}=\frac{h}{2\mathrm{\&pi;m}\stackrel{\&RightArrow;}{A}}(\mathrm{\&pi;}/3-{\mathrm{\&Delta;\&phi;}}_{\mathrm{heat}}-\mathrm{mn})$

The injection of hot phase place is approximate thinks first order inertial loop by designing the superfluid gyroscope of automatic disturbance rejection controller, the superfluid amplitude of control realization can lock the requirement expecting amplitude, avoid inertial delay on the impact of superfluid gyroscope system stability and accuracy of detection, automatic disturbance rejection controller does not require accurate mathematical model to controlled device, and total disturbance and together tracked compensation can be considered by the system model disturbance that causes of uncertainty and external disturbance, improve the control accuracy that hot phase compensation realizes the locking of film amplitude, promote whole superfluid gyroscope control system performance, thus improve the precision that angular velocity solves general formula.

The expression-form of Nonlinear Tracking Differentiator TD is:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{v}}_1=v_2\\ {\stackrel{\&CenterDot;}{v}}_2=-\mathrm{Rsat}(A,{\mathrm{\&delta;}}_1)\end{array}\right.$

In formula: $A=v_1-v_0+\frac{v_2\left|v_2\right|}{2R},$ $\mathrm{sat}(A,{\mathrm{\&delta;}}_1)=\left\{\begin{array}{c}\mathrm{sign}\left(A\right),\left|A\right|\&GreaterEqual;{\mathrm{\&delta;}}_1\\ A/{\mathrm{\&delta;}}_1,\left|A\right|<{\mathrm{\&delta;}}_1\end{array}\right.,$ V ₁t () is reference input v ₀the tracking signal of (t), v ₂t () is v ₁the differential of (t), thus v ₂t () is as v ₀" approximate differential " of (t), R, δ ₁for Nonlinear Tracking Differentiator adjustable parameter;

The expression-form of extended state observer ESO is:

$\left\{\begin{array}{c}e=z_1-y\\ {\stackrel{\&CenterDot;}{z}}_1=z_2-{\mathrm{\&beta;}}_1\mathrm{fal}(e,{\mathrm{\&alpha;}}_1,{\mathrm{\&delta;}}_2)\\ {\stackrel{\&CenterDot;}{z}}_2=z_3-{\mathrm{\&beta;}}_2\mathrm{fal}(e,{\mathrm{\&alpha;}}_2,{\mathrm{\&delta;}}_2)+\mathrm{bu}\\ {\stackrel{\&CenterDot;}{z}}_3=-{\mathrm{\&beta;}}_3\mathrm{fal}(e,{\mathrm{\&alpha;}}_3,{\mathrm{\&delta;}}_2)\end{array}\right.$

In formula: $\left\{\begin{array}{c}e=z_1-y\\ {\stackrel{\&CenterDot;}{z}}_1=z_2-{\mathrm{\&beta;}}_1\mathrm{fal}(e,{\mathrm{\&alpha;}}_1,{\mathrm{\&delta;}}_2)\\ {\stackrel{\&CenterDot;}{z}}_2=z_3-{\mathrm{\&beta;}}_2\mathrm{fal}(e,{\mathrm{\&alpha;}}_2,{\mathrm{\&delta;}}_2)+\mathrm{bu}\\ {\stackrel{\&CenterDot;}{z}}_3=-{\mathrm{\&beta;}}_3\mathrm{fal}(e,{\mathrm{\&alpha;}}_3,{\mathrm{\&delta;}}_2)\end{array}\right.,$ α ₁, α ₂, α ₃, δ ₂, β ₁, β ₂, β ₃for adjustable parameter; Three rank ESO export y by object to estimate the state variable coupling of object and the real-time effect amount of the total disturbance of object, namely export y by system and produce 3 signal: z ₁, z ₂, z ₃, wherein z ₁for the tracking signal of y, e is z ₁with the difference of y, z ₂t () is z ₁the differential signal of (t), z ₃t () is the estimation to system model coupling and outer disturbance;

The expression formula of nonlinear state Error Feedback control law NLSEF is:

$\left\{\begin{array}{c}{e}_1=v_1-z_1\\ e_2=v_2-z_2\\ u_0=k_r\mathrm{fal}(e_1,{\mathrm{\&alpha;}}_4,{\mathrm{\&delta;}}_3)+k_d\mathrm{fal}(e_2,{\mathrm{\&alpha;}}_5,{\mathrm{\&delta;}}_3)\\ u=u_0-\frac{z_3}{b_0}\end{array}\right.$

In formula: α ₄, α ₅, δ ₃, b, k _r, k _dfor adjustable parameter; e ₁for v ₁and z ₁difference, e ₂for v ₂and z ₂difference, u ₀for the nonlinear combination of error, u is control inputs; By measuring film amplitude x (t), the hot phase delta phi of output injection _heat.

The solution of the present invention is compared with existing scheme, and major advantage is:

(1) although existing control program gives the relational model of membrane displacement, but when rotation phase exceedes pi/2, the angular velocity obtained by Models computed is only the embodiment of rotation phase surplus, the solution completely of angular velocity solution can not be obtained, the present invention is by the injecting compensating locking film amplitude of hot phase place, while the two Weak link superfluid gyroscope range of expansion, obtain the solution completely of angular velocity solution;

(2) in superfluid control loop, automatic disturbance rejection controller is introduced, according to automatic disturbance rejection controller, accurate mathematical model is not required to controlled device, and total disturbance and together tracked compensation can be considered by the system model disturbance that causes of uncertainty and external disturbance, improve the control accuracy that hot phase compensation realizes the locking of film amplitude, improve whole superfluid gyroscope control system performance, thus improve the precision that angular velocity solves general formula.

Accompanying drawing explanation

Fig. 1 is automatic disturbance rejection controller structural drawing;

Fig. 2 is process flow diagram of the present invention;

Fig. 3 is film amplitude oscillogram;

Fig. 4 is institute's angular velocity oscillogram.

Specific embodiments

Objective for implementation of the present invention is the superfluid gyroscope of two Weak link, and as shown in Figure 2, concrete implementation step is as follows for specific embodiments:

(1) according to the principle of work of two Weak link superfluid gyroscope, the mathematical model of superfluid gyroscope is set up:

$x\left(t\right)=\frac{1}{{\mathrm{\&rho;}}_1\stackrel{\&RightArrow;}{A}}{\&Integral;}_0^{t}I\left(t\right)\mathrm{dt}$

Wherein,

$\mathrm{\&Delta;\&phi;}={\mathrm{\&Delta;\&phi;}}_{\mathrm{\&omega;}}+\mathrm{\&Delta;}{\mathrm{\&phi;}}_{\mathrm{heat}}=\frac{2\mathrm{\&pi;m}}{h}\stackrel{\&RightArrow;}{\mathrm{\&omega;}}\&CenterDot;\stackrel{\&RightArrow;}{A}+{\mathrm{\&Delta;\&phi;}}_{\mathrm{heat}}$

In formula, x (t) is film amplitude, the matter wave flow that I (t) is annular cavity total, ρ ₁for superfluid density, for the vector of induction area, the hole count of N contained by single Weak link, I ₀for the critical superfluid intensity of single hole, Δ u is that the chemical potential energy formed by Weak link pressure at both sides difference and temperature difference is poor, and Δ φ is the phase differential at two Weak link place, Δ φ _ωfor the Sagnac phase shift that outer buttons tarnsition velocity causes, Δ φ _heatfor the hot phase place injected, φ ₀for initial phase, for the matter wave phase place of annular cavity total, h is Planck's constant, and m is ⁴the quality of He superfluid atom, for the angular velocity of rotation in the external world;

(2) superfluid gyroscope angular velocity model is set up

The mathematical model that the superfluid gyroscope obtained for step (1) detects, utilizes amplitude locking principle to set working point at π/3 place, injects hot phase place to superfluid gyroscope, and obtaining can the superfluid gyroscope angular velocity solution of directly calculation:

$\stackrel{\&RightArrow;}{\mathrm{\&omega;}}=\frac{h}{2\mathrm{\&pi;m}\stackrel{\&RightArrow;}{A}}(\frac{\mathrm{\&pi;}}{3}-{\mathrm{\&Delta;\&phi;}}_{\mathrm{heat}}-\mathrm{nm})$

In formula, m is compensation rate maximal value, and n is the number of times reaching maximum compensation rate;

(3) automatic disturbance rejection controller is designed

The expression-form of Nonlinear Tracking Differentiator TD is:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{v}}_1=v_2\\ {\stackrel{\&CenterDot;}{v}}_2=-\mathrm{Rsat}(A,{\mathrm{\&delta;}}_1)\end{array}\right.$

In formula: $A=v_1-v_0+\frac{v_2\left|v_2\right|}{2R},$ $\mathrm{sat}(A,{\mathrm{\&delta;}}_1)=\left\{\begin{array}{c}\mathrm{sign}\left(A\right),\left|A\right|\&GreaterEqual;{\mathrm{\&delta;}}_1\\ A/{\mathrm{\&delta;}}_1,\left|A\right|<{\mathrm{\&delta;}}_1\end{array}\right.,$ V ₁t () is reference input v ₀the tracking signal of (t), v ₂t () is v ₁the differential of (t), thus v ₂t () is as v ₀" approximate differential " of (t), R, δ ₁for Nonlinear Tracking Differentiator adjustable parameter;

The expression-form of extended state observer ESO is:

$\left\{\begin{array}{c}e=z_1-y\\ {\stackrel{\&CenterDot;}{z}}_1=z_2-{\mathrm{\&beta;}}_1\mathrm{fal}(e,{\mathrm{\&alpha;}}_1,{\mathrm{\&delta;}}_2)\\ {\stackrel{\&CenterDot;}{z}}_2=z_3-{\mathrm{\&beta;}}_2\mathrm{fal}(e,{\mathrm{\&alpha;}}_2,{\mathrm{\&delta;}}_2)+\mathrm{bu}\\ {\stackrel{\&CenterDot;}{z}}_3=-{\mathrm{\&beta;}}_3\mathrm{fal}(e,{\mathrm{\&alpha;}}_3,{\mathrm{\&delta;}}_2)\end{array}\right.$

In formula: $\left\{\begin{array}{c}e=z_1-y\\ {\stackrel{\&CenterDot;}{z}}_1=z_2-{\mathrm{\&beta;}}_1\mathrm{fal}(e,{\mathrm{\&alpha;}}_1,{\mathrm{\&delta;}}_2)\\ {\stackrel{\&CenterDot;}{z}}_2=z_3-{\mathrm{\&beta;}}_2\mathrm{fal}(e,{\mathrm{\&alpha;}}_2,{\mathrm{\&delta;}}_2)+\mathrm{bu}\\ {\stackrel{\&CenterDot;}{z}}_3=-{\mathrm{\&beta;}}_3\mathrm{fal}(e,{\mathrm{\&alpha;}}_3,{\mathrm{\&delta;}}_2)\end{array}\right.,$ α ₁, α ₂, α ₃, δ ₂, β ₁, β ₂, β ₃for adjustable parameter; Three rank ESO export y by object to estimate the state variable coupling of object and the real-time effect amount of the total disturbance of object, namely export y by system and produce 3 signal: z ₁, z ₂, z ₃, wherein z ₁for the tracking signal of y, e is z ₁with the difference of y, z ₂t () is z ₁the differential signal of (t), z ₃t () is the estimation to system model coupling and outer disturbance;

The expression formula of nonlinear state Error Feedback control law NLSEF is:

$\left\{\begin{array}{c}{e}_1=v_1-z_1\\ e_2=v_2-z_2\\ u_0=k_r\mathrm{fal}(e_1,{\mathrm{\&alpha;}}_4,{\mathrm{\&delta;}}_3)+k_d\mathrm{fal}(e_2,{\mathrm{\&alpha;}}_5,{\mathrm{\&delta;}}_3)\\ u=u_0-\frac{z_3}{b_0}\end{array}\right.$

In formula: α ₄, α ₅, δ ₃, b, k _r, k _dfor adjustable parameter; e ₁for v ₁and z ₁difference, e ₂for v ₂and z ₂difference, u ₀for the nonlinear combination of error, u is control inputs; By measuring film amplitude x (t), the hot phase delta phi of output injection _heat.

As can be seen from Fig. 3, Fig. 4, after control is stable, film amplitude does not change with the change of the angular velocity measured, and illustrates that the film amplitude locking effect based on automatic disturbance rejection controller is better.

The content be not described in detail in present disclosure belongs to the known prior art of professional and technical personnel in the field.

Claims (1)

1. based on a superfluid gyroscope Control System Design method for automatic disturbance rejection controller, it is characterized in that: according to the principle of work of two Weak link superfluid gyroscope, set up the mathematical model of superfluid gyroscope; Utilize amplitude to lock compensation method and set up superfluid gyroscope angular velocity model; Automatic disturbance rejection controller is introduced in superfluid control loop, according to automatic disturbance rejection controller, accurate mathematical model is not required to controlled device, and the feature of total disturbance and together tracked compensation can be considered by the system model disturbance that causes of uncertainty and external disturbance, improve the control accuracy that hot phase compensation realizes the locking of film amplitude, promote whole superfluid gyroscope control system performance, thus improve the precision that angular velocity solves general formula, specifically comprise the following steps:

(1) according to the principle of work of two Weak link superfluid gyroscope, the mathematical model of superfluid gyroscope is set up:

$x\left(t\right)=\frac{1}{{\mathrm{\&rho;}}_1\stackrel{\&RightArrow;}{A}}{\&Integral;}_0^{t}I\left(t\right)\mathrm{dt}$

Wherein,

$\mathrm{\&Delta;\&phi;}=\mathrm{\&Delta;}{\mathrm{\&phi;}}_{\mathrm{\&omega;}}+\mathrm{\&Delta;}{\mathrm{\&phi;}}_{\mathrm{heat}}=\frac{2\mathrm{\&pi;m}}{h}\stackrel{\&RightArrow;}{\mathrm{\&omega;}}\&CenterDot;\stackrel{\&RightArrow;}{A}+\mathrm{\&Delta;}{\mathrm{\&phi;}}_{\mathrm{heat}}$

In formula, x (t) is film amplitude, the matter wave flow that I (t) is annular cavity total, ρ ₁for superfluid density, for the vector of induction area, the hole count of N contained by single Weak link, I ₀for the critical superfluid intensity of single hole, Δ u is that the chemical potential energy formed by Weak link pressure at both sides difference and temperature difference is poor, and Δ φ is the phase differential at two Weak link place, Δ φ _ωfor the Sagnac phase shift that outer buttons tarnsition velocity causes, Δ φ _heatfor the hot phase place injected, φ ₀for initial phase, for the matter wave phase place of annular cavity total, h is Planck's constant, and m is ⁴the quality of He superfluid atom, for the angular velocity of rotation in the external world;

(2) superfluid gyroscope angular velocity model is set up

The mathematical model that the superfluid gyroscope obtained for step (1) detects, utilizes amplitude locking principle to set working point at π/3 place, injects hot phase place to superfluid gyroscope, and obtaining can the superfluid gyroscope angular velocity solution of directly calculation:

$\stackrel{\&RightArrow;}{\mathrm{\&omega;}}=\frac{h}{2\mathrm{\&pi;m}\stackrel{\&RightArrow;}{A}}(\frac{\mathrm{\&pi;}}{3}-\mathrm{\&Delta;}{\mathrm{\&phi;}}_{\mathrm{heat}}-\mathrm{nm})$

In formula, m is compensation rate maximal value, and n is the number of times reaching maximum compensation rate;

(3) automatic disturbance rejection controller is designed

The expression-form of Nonlinear Tracking Differentiator TD is:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{v}}_1=v_2\\ {\stackrel{\&CenterDot;}{v}}_2=-\mathrm{Rsat}(A,{\mathrm{\&delta;}}_1)\end{array}\right.$

In formula: $A=v_1-v_0+\frac{v_2\left|v_2\right|}{2R},\mathrm{sat}(A,{\mathrm{\&delta;}}_1)=\left\{\begin{array}{c}\mathrm{sign}\left(A\right),\left|A\right|\&GreaterEqual;{\mathrm{\&delta;}}_1\\ A/{\mathrm{\&delta;}}_1,\left|A\right|<{\mathrm{\&delta;}}_1\end{array}\right.,$ V ₁t () is reference input v ₀the tracking signal of (t), v ₂t () is v ₁the differential of (t), thus v ₂t () is as v ₀" approximate differential " of (t), R, δ ₁for Nonlinear Tracking Differentiator adjustable parameter;

The expression-form of extended state observer ESO is:

$\left\{\begin{array}{c}e=z_1-y\\ {\stackrel{\&CenterDot;}{z}}_1=z_2-{\mathrm{\&beta;}}_1\mathrm{fal}(e,{\mathrm{\&alpha;}}_1,{\mathrm{\&delta;}}_2)\\ {\stackrel{\&CenterDot;}{z}}_2=z_3-{\mathrm{\&beta;}}_2\mathrm{fal}(e,{\mathrm{\&alpha;}}_2,{\mathrm{\&delta;}}_2)+\mathrm{bu}\\ {\stackrel{\&CenterDot;}{z}}_3=-{\mathrm{\&beta;}}_3\mathrm{fal}(e,{\mathrm{\&alpha;}}_3,{\mathrm{\&delta;}}_2)\end{array}\right.$

In formula: $\left\{\begin{array}{c}e=z_1-y\\ {\stackrel{\&CenterDot;}{z}}_1=z_2-{\mathrm{\&beta;}}_1\mathrm{fal}(e,{\mathrm{\&alpha;}}_1,{\mathrm{\&delta;}}_2)\\ {\stackrel{\&CenterDot;}{z}}_2=z_3-{\mathrm{\&beta;}}_2\mathrm{fal}(e,{\mathrm{\&alpha;}}_2,{\mathrm{\&delta;}}_2)+\mathrm{bu}\\ {\stackrel{\&CenterDot;}{z}}_3=-{\mathrm{\&beta;}}_3\mathrm{fal}(e,{\mathrm{\&alpha;}}_3,{\mathrm{\&delta;}}_2)\end{array}\right.,$ α ₁, α ₂, α ₃, δ ₂, β ₁, β ₂, β ₃for adjustable parameter; Three rank ESO export y by object to estimate the state variable coupling of object and the real-time effect amount of the total disturbance of object, namely export y by system and produce 3 signal: z ₁, z ₂, z ₃, wherein z ₁for the tracking signal of y, e is z ₁with the difference of y, z ₂t () is z ₁the differential signal of (t), z ₃t () is the estimation to system model coupling and outer disturbance;

The expression formula of nonlinear state Error Feedback control law NLSEF is:

$\left\{\begin{array}{c}{e}_1=v_1-z_1\\ e_2=v_2-z_2\\ u_0=k_p\mathrm{fal}(e_1,{\mathrm{\&alpha;}}_4,{\mathrm{\&delta;}}_3)+k_d\mathrm{fal}(e_2,{\mathrm{\&alpha;}}_5,{\mathrm{\&delta;}}_3)\\ u=u_0-\frac{z_3}{b_0}\end{array}\right.$

In formula: α ₄, α ₅, δ ₃, b, k _p, k _dfor adjustable parameter; e ₁for v ₁and z ₁difference, e ₂for v ₂and z ₂difference, u ₀for the nonlinear combination of error, u is control inputs; By measuring film amplitude x (t), the hot phase delta phi of output injection _heat.