CN104777842A - Satellite single-axis measurement and control integrated method based on magnetic levitation control sensitive gyroscope - Google Patents

Abstract

The invention relates to a satellite single-axis measurement and control integrated method based on a magnetic levitation control sensitive gyroscope. The satellite single-axis measurement and control integrated method comprises the following steps: detecting an attitude angle velocity of a satellite under high-frequency small-amplitude disturbance by the magnetic levitation control sensitive gyroscope, identifying and removing the attitude angle velocity generated by the high-frequency small-amplitude disturbance by using a self-adaptive wave trap with a center trapped wave frequency changing with a disturbance frequency, figuring out a compensation moment required by compensation disturbance, figuring out a magnetic levitation rotor radial control moment required by amplitude control according to a corresponding amplitude control rule, and designing an integrated steering rule of a magnetic levitation rotor by combining disturbance inhibition and amplitude control to ensure that a rotor rotation shaft deflects and outputs a required radial two-degree-of-freedom micro-framing stress moment, so that high-precision amplitude control and disturbance inhibition of a single axis of a satellite are realized.

Description

A kind of satellite single shaft measurement and control integration method based on the responsive gyro of magnetic suspension control

Technical field

The present invention relates to a kind of satellite single shaft measurement and control integration method based on the responsive gyro of magnetic suspension control, be applicable to the high-precision attitude Measurement & Control of satellite.

Technical background

Along with the development of high resolving power earth observation technology, more and more higher to the requirement of satellite gravity anomaly and vibration suppression.The detection and control of tradition posture control system is separated, and whole attitude control system is the limited bandwidth of the structure of a single closed loop, posture control system.Therefore, the small size disturbance of the high frequency for satellite, existing posture control system is difficult to suppress.In addition, the Detection & Controling of existing attitude control system are separated, and add the flexible structure of satellite itself, this just must cause dystopy control problem, thus inevitably affects stability and the robustness of whole attitude control system.

In order to solve the problem, Zheng Shiqiang, by double-frame magnetic suspension control moment gyro, moment execution and attitude measurement are combined, but this research will be measured and control time-sharing multiplex, the magnetic suspension control torque gyroscope a certain moment can only be operated in a kind of state, and measurement and control fail to carry out simultaneously; Liu Bin proposes a kind of design proposal of magnetically suspended gyroscope flywheel, although magnetically suspended gyroscope flywheel control and measurement can carry out simultaneously, but this method does not obtain the analytical expression of three-axis attitude angular velocity, not only practicality is strong, and is not easy to analyze relation between attitude angular velocity and systematic parameter from mechanism.

The responsive gyro of magnetic suspension control is that one has merged angular rate gyroscope rate detection and inertia actuator moment exports dual-use function, integrate attitude responsive with control, vibration detection and the multifunctional novel concept inertial mechanism that suppresses.Just because of the introducing of the responsive gyro of magnetic suspension control, changing the large closed loop configuration of existing posture control system, is three closed loop appearance control structures by its topology.Each ring, for different controlled devices, with different control bandwidth, respectively to platform stance, Platform Vibration and gyro itself vibrates, carries out three ring fused controllings.Breach existing single closed loop attitude system, control degree of stability limited, the limitation of Vibration Active Control cannot be carried out, make the high stability of satellite and super quiet control become possibility.

Summary of the invention

Technology of the present invention is dealt with problems and is: cannot suppress high frequency small amplitude disturbance to overcome existing satellite, and posture control system, due to the detection and control altogether problem such as the dystopy control that causes of position, proposes a kind of satellite single shaft measurement and control integration method based on the responsive gyro of magnetic suspension control.The method not only can suppress the high frequency small amplitude disturbance of satellite by micro-Frame research moment, and the high precision can carrying out attitude controls, achieve the integration of attitude detection, Disturbance Rejection and gesture stability, the high-precision attitude for satellite controls to provide a kind of brand-new technological approaches.

Technical solution of the present invention is: by the attitude angular velocity of satellite under the disturbance of magnetic suspension control responsive gyro detection high frequency small amplitude, the adaptive notch filter that use center trap frequency changes with forcing frequency, identification and removal are carried out to the attitude angular velocity that high frequency small amplitude disturbance produces, calculate compensating torque needed for compensating disturbance, according to corresponding attitude control law, calculate the radial control moment of magnetic suspension rotor needed for appearance control, in conjunction with Disturbance Rejection and gesture stability, design the integrated operation rule of magnetic suspension rotor, rotor turning axle is made to deflect the micro-Frame research moment of radial two degrees of freedom needed for exporting, thus the high-precision attitude realizing satellite single shaft detects, control and Disturbance Rejection, specifically comprise the following steps:

(1) according to rigid dynamics and principle of coordinate transformation magnetic suspension rotor kinetics equation be:

$M^r={\stackrel{\·}{H}}^r+{\mathrm{\ω}}_{\mathrm{ir}}^r\×H^r$

Wherein:

H ^r＝IΩ ⁱ

${\stackrel{\·}{H}}^r=I{\stackrel{\·}{\mathrm{\Ω}}}^i$

${\mathrm{\Ω}}^i={\mathrm{\Ω}}^r+{\mathrm{\ω}}_{\mathrm{ir}}^r$

$I\left[\begin{array}{ccc}{I}_r& 0& 0\\ 0& I_z& 0\\ 0& 0& I_r\end{array}\right],{\mathrm{\Ω}}^r=\left[\begin{array}{c}0\\ \mathrm{\Ω}\\ 0\end{array}\right]$

${\mathrm{\ω}}_{\mathrm{ir}}^r={\mathrm{\ω}}_{\mathrm{rf}}^r+{\mathrm{\ω}}_{\mathrm{icmg}}^r=C_f^r{\mathrm{\ω}}_{\mathrm{rf}}^f+C_f^r{C}_g^f{C}_g^f{C}_{\mathrm{cmg}}^g{\mathrm{\ω}}_{\mathrm{icmg}}^{\mathrm{cmg}}$

${\mathrm{\ω}}_{\mathrm{icmg}}^{\mathrm{cmg}}=C_b^{\mathrm{cmg}}{\mathrm{\ω}}_{\mathrm{ib}}^b+{\mathrm{\ω}}^{\mathrm{cmg}}$

In formula, M ^rrepresent magnetic suspension rotor bonding force square, H ^rrepresent the angular momentum at rotor system lower rotor part, represent the angular momentum at rotor system lower rotor part, I represents the moment of inertia that rotor rotates around the responsive gyro reference frame of magnetic suspension control, I _rrepresent rotor radial moment of inertia, I _zrepresent rotor axial moment of inertia, Ω represents rotor axial rotating speed, Ω ^rrepresent rotor speed, Ω ⁱrepresent the absolute angular velocities of rotor, represent the absolute angular velocities rate of change of rotor, represent the absolute angular velocities of rotor coordinate, namely relative to the rotating speed of inertial space, represent the deflection speed of the relative magnetic bearing of rotor, for the responsive gyro reference frame of magnetic suspension control is relative to the speed of inertial space, for rotor is relative to the angular velocity of inertial space, ω ^cmgfor frame corners speed, for magnetic bearing coordinate is tied to the transformation matrix of rotor coordinate, for frame coordinates is tied to the transformation matrix of magnetic bearing coordinate system, for the responsive gyro of magnetic suspension control is with reference to the transformation matrix being tied to frame coordinates system, for celestial body is tied to the transformation matrix of the responsive gyro reference frame of magnetic suspension control;

At magnetic bearing, system, frame coordinates system are installed, the responsive gyro reference frame of magnetic suspension control overlaps and satellite only has single shaft angular speed ${\mathrm{\ω}}_{\mathrm{ib}}^b={\left[\begin{array}{ccc}{\mathrm{\ω}}_{\mathrm{ibx}}^b& 0& 0\end{array}\right]}^T$ Condition under:

${\mathrm{\ω}}_{\mathrm{ir}}^r={\mathrm{\ω}}_{\mathrm{rf}}^r+{\mathrm{\ω}}_{\mathrm{icmg}}^r=C_f^r{\mathrm{\ω}}_{\mathrm{rf}}^f+C_f^r{\mathrm{\ω}}_{\mathrm{icmg}}^{\mathrm{cmg}}$

α, β are very little,

Again ${\mathrm{\ω}}_{\mathrm{icmg}}^{\mathrm{cmg}}=\left[\begin{array}{c}{\mathrm{\ω}}_{\mathrm{ibx}}^b\\ 0\\ 0\end{array}\right],{\mathrm{\ω}}_{\mathrm{rf}}^f=\left[\begin{array}{c}\stackrel{\·}{\mathrm{\α}}\\ 0\\ \stackrel{\·}{\mathrm{\β}}\end{array}\right],{\mathrm{\ω}}_{\mathrm{ir}}^r=\left[\begin{array}{c}{\mathrm{\ω}}_{\mathrm{ibx}}^b+\stackrel{\·}{\mathrm{\α}}\\ 0\\ \stackrel{\·}{\mathrm{\β}}\end{array}\right],$ Then:

${\mathrm{\Ω}}^i=\left[\begin{array}{c}{\mathrm{\ω}}_{\mathrm{ibx}}^b+\stackrel{\·}{\mathrm{\α}}\\ \mathrm{\Ω}\\ \stackrel{\·}{\mathrm{\β}}\end{array}\right],H^r=\left[\begin{array}{c}{I}_r({\mathrm{\ω}}_{\mathrm{ibx}}^b+\stackrel{\·}{\mathrm{\α}})\\ I_z\mathrm{\Ω}\\ I_r\stackrel{\·}{\mathrm{\β}}\end{array}\right],{\stackrel{\·}{H}}^r=\left[\begin{array}{c}{I}_r({\stackrel{\·}{\mathrm{\ω}}}_{\mathrm{ibx}}^b+\stackrel{\·\·}{\mathrm{\α}})\\ 0\\ I_r\stackrel{\·\·}{\mathrm{\β}}\end{array}\right],M^r=\left[\begin{array}{c}{I}_r{\stackrel{\·}{\mathrm{\ω}}}_{\mathrm{ibx}}^b+I_r\stackrel{\·\·}{\mathrm{\α}}-\stackrel{\·}{\mathrm{\β}}{I}_z\mathrm{\Ω}\\ \stackrel{\·}{\mathrm{\α}}{I}_z\mathrm{\Ω}+I_z\mathrm{\Ω}{\mathrm{\ω}}_{\mathrm{ibx}}^b+I_r\stackrel{\·\·}{\mathrm{\β}}\end{array}\right]$

Rotor radial bonding force square expression formula is:

$M_x^r=I_r{\stackrel{\·}{\mathrm{\ω}}}_{\mathrm{ibx}}^b+I_r\stackrel{\·\·}{\mathrm{\α}}-\stackrel{\·}{\mathrm{\β}}{I}_z\mathrm{\Ω},M_z^r=\stackrel{\·}{\mathrm{\α}}{I}_z\mathrm{\Ω}+I_z\mathrm{\Ω}{\mathrm{\ω}}_{\mathrm{ibx}}^b+I_r\stackrel{\·}{\mathrm{\β}}$

Suffered by magnetic suspension rotor, bonding force square is:

$M_x^r=l_m(f_{\mathrm{by}}-f_{\mathrm{ay}}),M_z^r=l_m(f_{\mathrm{ax}}-f_{\mathrm{bx}})$

Magnetic force suffered by magnetic suspension rotor can be expressed as following linear forms:

f _λ＝k _iλi _λ+k _hλh _λ(λ＝ax，ay，bc，by)

In formula, k _{i λ}and k _{h λ}(λ=ax, ay, bx, by) represents current stiffness and the displacement rigidity of radial ax, ay, bx and by passage of magnetic suspension rotor respectively, can demarcate by experiment; i _ax, i _bx, i _ayand i _bythe winding current of four radial passages, h _ax, h _bx, h _ayand h _bythe linear displacement amount of magnetic suspension rotor respectively on ax, bx, ay and by direction, l _mrepresent from magnetic suspension rotor center to the distance at radial direction magnetic bearing center; h _ax, h _bx, h _ay, h _bycan be measured by eddy current displacement sensor, i _ax, i _bx, i _ay, i _bycan current sensor measurement be passed through, thus bonding force square suffered by rotor can be calculated

The expression formula of rotor deflection angle is:

α＝(h _ay-h _by)/(2l _m)，β＝(h _ax-h _bx)/(2l _m)

H _ax, h _bx, h _ayand h _bythe linear displacement amount of magnetic suspension rotor respectively on Ax, Bx, Ay and By direction, l _mrepresent from magnetic suspension rotor center to the distance at radial direction magnetic bearing center, h _ax, h _bx, h _ay, h _aycan be measured by eddy current displacement sensor, thus can calculate rotor deflection information α, β, $\stackrel{\·}{\mathrm{\α}},\stackrel{\·}{\mathrm{\β}},\stackrel{\·\·}{\mathrm{\α}},\stackrel{\·\·}{\mathrm{\β}};$

Attitude of satellite angular speed, angular acceleration are:

${\mathrm{\ω}}_{\mathrm{ibx}}^b=M_z^r-\stackrel{\·}{\mathrm{\α}}{I}_z\mathrm{\Ω}-I_r\stackrel{\·\·}{\mathrm{\β}},{\stackrel{\·}{\mathrm{\ω}}}_{\mathrm{ibx}}^b=(M_x^r-I_r\stackrel{\·\·}{\mathrm{\α}}+\stackrel{\·}{\mathrm{\β}}{I}_z\mathrm{\Ω})/I_r$

Under there is no orbit angular velocity condition, order when θ, ψ are undisturbed, celestial body coordinate system is relative to the attitude angle of orbital coordinate system, then represent all directions attitude angle acceleration, represent all directions angular velocity, represent the angular acceleration that disturbance produces and angular velocity, represent total angular acceleration and angular velocity, then:

(2) in measuring satellite angular velocities, Mach angle Speed identification and disturbing moment compensate

In attitude angular velocity, the sinusoidal angular velocity of the generation of high frequency small amplitude disturbing moment and forcing frequency same frequency, can adopt adaptive notch filter to carry out identification and removal to it; The core of trapper N is depression feedback element Nf, and its centre frequency can change according to forcing frequency W change, and ε determines speed of convergence and the center notch bandwidth of trapper N, K _h/ K _ifor the scale-up factor of disturbance compensation;

If ω (t) is the input of depression feedback element Nf, the output that c (t) is Nf, then have:

$c\left(t\right)=\left[\begin{array}{cc}\sin \left(\mathrm{Wt}\right)& \cos \left(\mathrm{Wt}\right)\end{array}\right]\·\left[\begin{array}{c}\∫\sin \left(\mathrm{Wt}\right)\·\mathrm{\ω}\left(t\right)\mathrm{dt}\\ \∫\cos \left(\mathrm{Wt}\right)\·\mathrm{\ω}\left(t\right)\mathrm{dt}\end{array}\right]$

C and ω meets the following differential equation:

$\stackrel{\·\·}{c}+W^{2}c=\stackrel{\·}{\mathrm{\ω}}$

The transport function of depression feedback element Nf is:

$N_f\left(s\right)=\frac{c\left(s\right)}{\mathrm{\ω}\left(s\right)}=\frac{s}{s^2+W^2}$

Trapper inputs export to depression feedback element Nf biography letter No be:

Make s=j ω, consider the frequency characteristic of No, when ε ≠ 0:

N _O(jω)≈0，[ω∈(0，W-Δω)∪(W+Δω，∞)]

N _O(jω)＝1，[ω∈(W-Δω，W+Δω)]

Namely, when ε ≠ 0, the output of No will level off to input medium frequency is the component of W

The output of depression feedback element Nf for:

$A=\sqrt{{r_1}^2+{r_2}^2},\mathrm{\λ}=\arctan \left(\frac{r_2}{r_1}\right)$

Namely after feedback element convergence, the output valve of depression feedback element Nf integrator is the amplitude with the sine and cosine component of forcing frequency amount in attitude angular velocity, which achieves the attitude angular velocity produced disturbance in attitude angular velocity signal identification;

By compensating proportion COEFFICIENT K _h/ K _i, compensating torque is introduced in direction eliminate disturbance to the impact of attitude;

(3) magnetic suspension rotor integrated operation rule

Under the effect of single shaft high frequency small amplitude disturbing moment, using the responsive gyro of magnetic suspension control as the Dynamical Attitude Equations of topworks be:

$J{\stackrel{\·}{\mathrm{\ω}}}_{\mathrm{ib}}^b+{\mathrm{\ω}}_{\mathrm{ib}}^b\×J{\mathrm{\ω}}_{\mathrm{ib}}^b+{\stackrel{\·}{H}}^r+\mathrm{\ω}\×H^r=T_d$

In formula, J represents satellite moment of inertia matrix, T _d=[T _dx0 0] represent single shaft high frequency small amplitude disturbing moment, under little attitude angle condition using magnetic suspension rotor as the Dynamical Attitude Equations of attitude control actuator be:

$J_y\stackrel{\·\·}{\mathrm{\θ}}+{\stackrel{\·}{h}}_y=0,$

Wherein, J _x, J _y, J _zrepresent the moment of inertia of each axle of satellite, h _yrepresent rotor axial momentum, the Dynamical Attitude Equations in rotor radial two directions is:

Therefore need the disturbance torque of the β rotation direction of going compensation to cause because of disturbance, therefore:

Order for the speed of the β rotation direction that posture adjustment needs, then have after compensation:

α rotation direction does not need to compensate, order for the speed of the α rotation direction that posture adjustment needs, therefore the Dynamical Attitude Equations in rotor radial two directions is:

After adding disturbance compensation, according to satellite dynamics equation, posture adjustment object attitude angle is ψ _r=0, design uneoupled control rule is:

K _px, k _dx, k _pz, k _dzfor PD controller parameter; Dynamical Attitude Equations is:

Satellite does not have the single-axis attitude angle information in disturbance situation for:

Satellite only has single shaft angular speed when,

Satellite gravity anomaly amount is realized by the micro-framework control moment of rotor radial:

$U_x=-{\stackrel{\·}{\mathrm{\β}}}_c{h}_y,U_z={\stackrel{\·}{\mathrm{\α}}}_c{h}_y$

Therefore in conjunction with disturbance compensation, the integrated operation rule that magnetic suspension rotor controls is:

$\stackrel{\·}{\mathrm{\α}}={\stackrel{\·}{\mathrm{\α}}}_c=U_z/h_y,$

The control reference quantity that in reality, magnetic bearing applies is h _axr, h _bxr, h _ayr, h _byr, and h _bxr=-h _axr, h _byr=-h _ayr, therefore:

$h_{\mathrm{ayr}}={\mathrm{\αl}}_m=-l_m\∫(M_z^r-\stackrel{\·}{\mathrm{\α}}{I}_z\mathrm{\Ω}-I_r\stackrel{\·\·}{\mathrm{\β}})$

$h_{\mathrm{byr}}={-\mathrm{\αl}}_m=l_m\∫(M_z^r-\stackrel{\·}{\mathrm{\α}}{I}_z\mathrm{\Ω}-I_r\stackrel{\·\·}{\mathrm{\β}})$

Principle of the present invention is: according to inertia theorem of moments, the outside moment suffered by it is only depended in the change of high speed rotor angular momentum in inertial space direction, moment suffered by magnetic suspension rotor is rotated by satellite, rotor relatively deflects and causes, and the size of magnetic suspension rotor Moment, uniquely determined by magnetic axis load, satellite resolves and obtains can detect magnetic bearing electric current and rotor displacement by real-time high-precision by the attitude angular velocity under high frequency small amplitude interference.By the attitude angular velocity of satellite under the disturbance of magnetic suspension control responsive gyro self detection high frequency small amplitude, the adaptive notch filter that use center trap frequency changes with forcing frequency, identification and removal are carried out to the attitude angular velocity that high frequency small amplitude disturbance produces, calculate compensating torque needed for compensating disturbance, according to corresponding attitude control law, calculate the radial control moment of magnetic suspension rotor needed for appearance control, in conjunction with Disturbance Rejection and gesture stability, design the integrated operation rule of magnetic suspension rotor, rotor turning axle is made to deflect the micro-Frame research moment of radial two degrees of freedom needed for exporting, thus realize gesture stability and the Disturbance Rejection of satellite single shaft.

The installation of satellite and the responsive gyro of magnetic suspension control as shown in Figure 1, radial direction magnetic bearing installation site relative rotor barycenter is symmetrical, rotor realizes suspend control by 5DOF magnetic bearing, radial 4 magnetic bearings (use ax, ay, bx respectively, by represents) control magnetic suspension rotor two radial translational degree of freedom and two rotational freedoms, axially (representing with z) bearing control translational degree of freedom, its rotational freedom is driven by motor, provides rotor angular momentum.Application euler dynamical equations, then under can obtaining rotor system, magnetic suspension rotor kinetics equation is:

$M^r={\stackrel{\·}{H}}^r+{\mathrm{\ω}}_{\mathrm{ir}}^r\×H^r$

Wherein:

H ^r＝IΩ ⁱ

${\stackrel{\·}{H}}^r=I{\stackrel{\·}{\mathrm{\Ω}}}^i$

${\mathrm{\Ω}}^i={\mathrm{\Ω}}^r+{\mathrm{\ω}}_{\mathrm{ir}}^r$

$I\left[\begin{array}{ccc}{I}_r& 0& 0\\ 0& I_z& 0\\ 0& 0& I_r\end{array}\right],{\mathrm{\Ω}}^r=\left[\begin{array}{c}0\\ \mathrm{\Ω}\\ 0\end{array}\right]$

${\mathrm{\ω}}_{\mathrm{ir}}^r={\mathrm{\ω}}_{\mathrm{rf}}^r+{\mathrm{\ω}}_{\mathrm{icmg}}^r=C_f^r{\mathrm{\ω}}_{\mathrm{rf}}^f+C_f^r{C}_g^f{C}_g^f{C}_{\mathrm{cmg}}^g{\mathrm{\ω}}_{\mathrm{icmg}}^{\mathrm{cmg}}$

${\mathrm{\ω}}_{\mathrm{icmg}}^{\mathrm{cmg}}=C_b^{\mathrm{cmg}}{\mathrm{\ω}}_{\mathrm{ib}}^b+{\mathrm{\ω}}^{\mathrm{cmg}}$

At magnetic bearing, system, frame coordinates system are installed, the responsive gyro reference frame of magnetic suspension control overlaps and satellite only has single shaft angular speed ${\mathrm{\ω}}_{\mathrm{ib}}^b={\left[\begin{array}{ccc}{\mathrm{\ω}}_{\mathrm{ibx}}^b& 0& 0\end{array}\right]}^T$ Condition under:

${\mathrm{\ω}}_{\mathrm{ir}}^r={\mathrm{\ω}}_{\mathrm{rf}}^r+{\mathrm{\ω}}_{\mathrm{icmg}}^r=C_f^r{\mathrm{\ω}}_{\mathrm{rf}}^f+C_f^r{\mathrm{\ω}}_{\mathrm{icmg}}^{\mathrm{cmg}}$

α, β are very little, $C_f^r=E,$ Again ${\mathrm{\ω}}_{\mathrm{icmg}}^{\mathrm{cmg}}=\left[\begin{array}{c}{\mathrm{\ω}}_{\mathrm{ibx}}^b\\ 0\\ 0\end{array}\right],{\mathrm{\ω}}_{\mathrm{rf}}^f=\left[\begin{array}{c}\stackrel{\·}{\mathrm{\α}}\\ 0\\ \stackrel{\·}{\mathrm{\β}}\end{array}\right],{\mathrm{\ω}}_{\mathrm{ir}}^r=\left[\begin{array}{c}{\mathrm{\ω}}_{\mathrm{ibx}}^b+\stackrel{\·}{\mathrm{\α}}\\ 0\\ \stackrel{\·}{\mathrm{\β}}\end{array}\right],$ Then:

${\mathrm{\Ω}}^i=\left[\begin{array}{c}{\mathrm{\ω}}_{\mathrm{ibx}}^b+\stackrel{\·}{\mathrm{\α}}\\ \mathrm{\Ω}\\ \stackrel{\·}{\mathrm{\β}}\end{array}\right],H^r=\left[\begin{array}{c}{I}_r({\mathrm{\ω}}_{\mathrm{ibx}}^b+\stackrel{\·}{\mathrm{\α}})\\ I_z\mathrm{\Ω}\\ I_r\stackrel{\·}{\mathrm{\β}}\end{array}\right],{\stackrel{\·}{H}}^r=\left[\begin{array}{c}{I}_r({\stackrel{\·}{\mathrm{\ω}}}_{\mathrm{ibx}}^b+\stackrel{\·\·}{\mathrm{\α}})\\ 0\\ I_r\stackrel{\·\·}{\mathrm{\β}}\end{array}\right],M^r=\left[\begin{array}{c}{I}_r{\stackrel{\·}{\mathrm{\ω}}}_{\mathrm{ibx}}^b+I_r\stackrel{\·\·}{\mathrm{\α}}-\stackrel{\·}{\mathrm{\β}}{I}_z\mathrm{\Ω}\\ \stackrel{\·}{\mathrm{\α}}{I}_z\mathrm{\Ω}+I_z\mathrm{\Ω}{\mathrm{\ω}}_{\mathrm{ibx}}^b+I_r\stackrel{\·\·}{\mathrm{\β}}\end{array}\right]$

Rotor radial bonding force square expression formula is:

$M_x^r=I_r{\stackrel{\·}{\mathrm{\ω}}}_{\mathrm{ibx}}^b+I_r\stackrel{\·\·}{\mathrm{\α}}-\stackrel{\·}{\mathrm{\β}}{I}_z\mathrm{\Ω},M_z^r=\stackrel{\·}{\mathrm{\α}}{I}_z\mathrm{\Ω}+I_z\mathrm{\Ω}{\mathrm{\ω}}_{\mathrm{ibx}}^b+I_r\stackrel{\·}{\mathrm{\β}}$

Suffered by magnetic suspension rotor, bonding force square is:

$M_x^r=l_m(f_{\mathrm{by}}-f_{\mathrm{ay}}),M_z^r=l_m(f_{\mathrm{ax}}-f_{\mathrm{bx}})$

Magnetic force suffered by magnetic suspension rotor can be expressed as following linear forms:

f _λ＝k _iλi _λ+k _hλh _y(λ＝ax，ay，bx，by)

H _ax, h _bx, h _ay, h _bycan be measured by eddy current displacement sensor, i _ax, i _bx, i _ay, i _bycan current sensor measurement be passed through, thus bonding force square suffered by rotor can be calculated

The expression formula of rotor deflection angle is:

α＝(h _ay-h _by)/(2l _m)，β＝(h _ax-h _bx)/(2l _m)

H _ax, h _bx, h _ay, h _bycan be measured by eddy current displacement sensor, thus can calculate rotor deflection information α, β,

Attitude of satellite angular speed, angular acceleration are:

${\mathrm{\ω}}_{\mathrm{ibx}}^b=M_z^r-\stackrel{\·}{\mathrm{\α}}{I}_z\mathrm{\Ω}-I_r\stackrel{\·\·}{\mathrm{\β}},{\stackrel{\·}{\mathrm{\ω}}}_{\mathrm{ibx}}^b=(M_x^r-I_r\stackrel{\·\·}{\mathrm{\α}}+\stackrel{\·}{\mathrm{\β}}{I}_z\mathrm{\Ω})/I_r$

Under there is no orbit angular velocity condition, order when θ, ψ are undisturbed, celestial body coordinate system is relative to the attitude angle of orbital coordinate system, then represent all directions attitude angle acceleration, represent all directions angular velocity, represent the angular acceleration that disturbance produces and angular velocity, represent total angular acceleration and angular velocity, then:

In attitude angular velocity, the sinusoidal angular velocity of the generation of high frequency small amplitude disturbing moment and forcing frequency same frequency, can adopt adaptive notch filter to carry out identification and removal to it; The core of trapper N is depression feedback element Nf, and its centre frequency can change according to forcing frequency W change, and ε determines speed of convergence and the center notch bandwidth of trapper N, K _h/ K _ifor the scale-up factor of disturbance compensation;

If ω (t) is the input of depression feedback element Nf, the output that c (t) is Nf, then have:

$c\left(t\right)=\left[\begin{array}{cc}\sin \left(\mathrm{Wt}\right)& \cos \left(\mathrm{Wt}\right)\end{array}\right]\·\left[\begin{array}{c}\∫\sin \left(\mathrm{Wt}\right)\·\mathrm{\ω}\left(t\right)\mathrm{dt}\\ \∫\cos \left(\mathrm{Wt}\right)\·\mathrm{\ω}\left(t\right)\mathrm{dt}\end{array}\right]$

C and ω meets the following differential equation:

$\stackrel{\·\·}{c}+W^{2}c=\stackrel{\·}{\mathrm{\ω}}$

The transport function of depression feedback element Nf is:

$N_f\left(s\right)=\frac{c\left(s\right)}{\mathrm{\ω}\left(s\right)}=\frac{s}{s^2+W^2}$

Trapper inputs export to depression feedback element Nf biography letter No be:

Make s=j ω, consider the frequency characteristic of No, when ε ≠ 0:

N _O(jω)≈0，[ω∈(0，W-Δω)∪(W+Δω，∞)]

N _O(jω)＝1，[ω∈(W-Δω，W+Δω)]

Namely, when ε ≠ 0, the output of No will level off to input medium frequency is the component of W

The output of depression feedback element Nf for:

$A=\sqrt{{r_1}^2+{r_2}^2},\mathrm{\λ}=\arctan \left(\frac{r_2}{r_1}\right)$

Namely after feedback element convergence, the output valve of depression feedback element Nf integrator is the amplitude with the sine and cosine component of forcing frequency amount in attitude angular velocity, which achieves the attitude angular velocity produced disturbance in attitude angular velocity signal identification;

By compensating proportion COEFFICIENT K _h/ K _i, compensating torque is introduced in direction eliminate disturbance to the impact of attitude;

Under the effect of single shaft high frequency small amplitude disturbing moment, using the responsive gyro of magnetic suspension control as the Dynamical Attitude Equations of topworks be:

$J{\stackrel{\·}{\mathrm{\ω}}}_{\mathrm{ib}}^b+{\mathrm{\ω}}_{\mathrm{ib}}^b\×J{\mathrm{\ω}}_{\mathrm{ib}}^b+{\stackrel{\·}{H}}^r+\mathrm{\ω}\×H^r=T_d$

In formula, J represents satellite moment of inertia matrix, T _d=[T _dx0 0] represent single shaft high frequency small amplitude disturbing moment, under little attitude angle condition using magnetic suspension rotor as the Dynamical Attitude Equations of attitude control actuator be:

$J_y\stackrel{\·\·}{\mathrm{\θ}}+{\stackrel{\·}{h}}_y=0,$

Wherein, J _x, J _y, J _zrepresent the moment of inertia of each axle of satellite, h _yrepresent rotor axial momentum, the Dynamical Attitude Equations of rotor radial both direction is:

Therefore need the disturbance torque of the β rotation direction of going compensation to cause because of disturbance, therefore:

Order for the speed of the β rotation direction that posture adjustment needs, then have after compensation:

α rotation direction does not need to compensate, order for the speed of the α rotation direction that posture adjustment needs, therefore the Dynamical Attitude Equations of rotor radial both direction is:

After adding disturbance compensation, according to satellite dynamics equation, posture adjustment object attitude angle is ψ _r=0, design uneoupled control rule is:

K _px, k _dx, k _pz, k _dzfor PD controller parameter; Dynamical Attitude Equations is:

Satellite does not have the single-axis attitude angle information in disturbance situation for:

Satellite only has single shaft angular speed when,

Satellite gravity anomaly amount is realized by the micro-framework control moment of rotor radial:

$U_x=-{\stackrel{\·}{\mathrm{\β}}}_c{h}_y,U_z={\stackrel{\·}{\mathrm{\α}}}_c{h}_y$

Therefore in conjunction with disturbance compensation, the integrated operation rule that magnetic suspension rotor controls is:

$\stackrel{\·}{\mathrm{\α}}={\stackrel{\·}{\mathrm{\α}}}_c=U_z/h_y,$

The control reference quantity that in reality, magnetic bearing applies is h _axr, h _bxr, h _ayr, h _byr, and h _bxr=-h _axr, h _byr=-h _ayr, therefore:

$h_{\mathrm{ayr}}={\mathrm{\αl}}_m=-l_m\∫(M_z^r-\stackrel{\·}{\mathrm{\α}}{I}_z\mathrm{\Ω}-I_r\stackrel{\·\·}{\mathrm{\β}})$

$h_{\mathrm{byr}}={-\mathrm{\αl}}_m=l_m\∫(M_z^r-\stackrel{\·}{\mathrm{\α}}{I}_z\mathrm{\Ω}-I_r\stackrel{\·\·}{\mathrm{\β}})$

So far, exporting micro-Frame research moment by controlling magnetic bearing rotor displacement, achieving the measurement and control integration of satellite single-axis attitude.

The solution of the present invention is compared with existing scheme, major advantage is: be difficult to suppress high frequency small amplitude disturbance to overcome existing satellite, with posture control system due to the detection and control altogether problem such as the dystopy control that causes of position, propose a kind of based on satellite single-axis attitude measurement and control integration method under the high frequency small amplitude disturbance of the responsive gyro of magnetic suspension control.The method is on the basis realizing attitude angular rate high precision test, the high frequency small amplitude disturbance of satellite not only can be suppressed by micro-Frame research moment, and can gesture stability be carried out, achieve that attitude of satellite angular speed detects, the integration of gesture stability and Disturbance Rejection, the high-precision attitude for satellite controls to provide a kind of brand-new technological approaches.

Accompanying drawing explanation

The mounting structure schematic diagram of the responsive gyro of Fig. 1 magnetic suspension control on satellite;

Fig. 2 is trapper structural drawing;

Fig. 3 is theory diagram of the present invention;

Fig. 4 is that PD controls undisturbed suppression compensation satellite single-axis attitude angle;

Fig. 5 is that PD controls undisturbed suppression compensation satellite single-axis attitude angular speed;

Fig. 6 is that PD controls have Disturbance Rejection to compensate satellite single-axis attitude angle;

Fig. 7 is that PD controls have Disturbance Rejection to compensate satellite single-axis attitude angular speed.

Specific embodiments

Objective for implementation of the present invention as shown in Figure 1, radial direction magnetic bearing installation site relative rotor barycenter is symmetrical, radial 4 magnetic bearings (use ax respectively, ay, bx, by represent) control magnetic suspension rotor two radial translational degree of freedom and two rotational freedoms, the structure of the trapper of design is as shown in Figure 2, as shown in Figure 3, concrete implementation step is as follows for specific embodiment of the invention scheme:

(1) according to rigid dynamics and principle of coordinate transformation magnetic suspension rotor kinetics equation be:

$M^r={\stackrel{\·}{H}}^r+{\mathrm{\ω}}_{\mathrm{ir}}^r\×H^r$

Wherein:

H ^r＝IΩ ⁱ

${\stackrel{\·}{H}}^r=I{\stackrel{\·}{\mathrm{\Ω}}}^i$

${\mathrm{\Ω}}^i={\mathrm{\Ω}}^r+{\mathrm{\ω}}_{\mathrm{ir}}^r$

$I\left[\begin{array}{ccc}{I}_r& 0& 0\\ 0& I_z& 0\\ 0& 0& I_r\end{array}\right],{\mathrm{\Ω}}^r=\left[\begin{array}{c}0\\ \mathrm{\Ω}\\ 0\end{array}\right]$

${\mathrm{\ω}}_{\mathrm{ir}}^r={\mathrm{\ω}}_{\mathrm{rf}}^r+{\mathrm{\ω}}_{\mathrm{icmg}}^r=C_f^r{\mathrm{\ω}}_{\mathrm{rf}}^f+C_f^r{C}_g^f{C}_g^f{C}_{\mathrm{cmg}}^g{\mathrm{\ω}}_{\mathrm{icmg}}^{\mathrm{cmg}}$

${\mathrm{\ω}}_{\mathrm{icmg}}^{\mathrm{cmg}}=C_b^{\mathrm{cmg}}{\mathrm{\ω}}_{\mathrm{ib}}^b+{\mathrm{\ω}}^{\mathrm{cmg}}$

In formula, M ^rrepresent magnetic suspension rotor bonding force square, H ^rrepresent the angular momentum at rotor system lower rotor part, represent the angular momentum at rotor system lower rotor part, I represents the moment of inertia that rotor rotates around the responsive gyro reference frame of magnetic suspension control, I _rrepresent rotor radial moment of inertia, I _zrepresent rotor axial moment of inertia, Ω represents rotor axial rotating speed, Ω ^rrepresent rotor speed, Ω ⁱrepresent the absolute angular velocities of rotor, represent the absolute angular velocities rate of change of rotor, represent the absolute angular velocities of rotor coordinate, namely relative to the rotating speed of inertial space, represent the deflection speed of the relative magnetic bearing of rotor, for the responsive gyro reference frame of magnetic suspension control is relative to the speed of inertial space, for rotor is relative to the angular velocity of inertial space, ω ^cmgfor frame corners speed, for magnetic bearing coordinate is tied to the transformation matrix of rotor coordinate, for frame coordinates is tied to the transformation matrix of magnetic bearing coordinate system, for the responsive gyro of magnetic suspension control is with reference to the transformation matrix being tied to frame coordinates system, for celestial body is tied to the transformation matrix of the responsive gyro reference frame of magnetic suspension control;

At magnetic bearing, system, frame coordinates system are installed, the responsive gyro reference frame of magnetic suspension control overlaps and satellite only has single shaft angular speed ${\mathrm{\ω}}_{\mathrm{ib}}^b={\left[\begin{array}{ccc}{\mathrm{\ω}}_{\mathrm{ibx}}^b& 0& 0\end{array}\right]}^T$ Condition under:

${\mathrm{\ω}}_{\mathrm{ir}}^r={\mathrm{\ω}}_{\mathrm{rf}}^r+{\mathrm{\ω}}_{\mathrm{icmg}}^r=C_f^r{\mathrm{\ω}}_{\mathrm{rf}}^f+C_f^r{\mathrm{\ω}}_{\mathrm{icmg}}^{\mathrm{cmg}}$

α, β are very little,

Again ${\mathrm{\ω}}_{\mathrm{icmg}}^{\mathrm{cmg}}=\left[\begin{array}{c}{\mathrm{\ω}}_{\mathrm{ibx}}^b\\ 0\\ 0\end{array}\right],{\mathrm{\ω}}_{\mathrm{rf}}^f=\left[\begin{array}{c}\stackrel{\·}{\mathrm{\α}}\\ 0\\ \stackrel{\·}{\mathrm{\β}}\end{array}\right],{\mathrm{\ω}}_{\mathrm{ir}}^r=\left[\begin{array}{c}{\mathrm{\ω}}_{\mathrm{ibx}}^b+\stackrel{\·}{\mathrm{\α}}\\ 0\\ \stackrel{\·}{\mathrm{\β}}\end{array}\right],$ Then:

${\mathrm{\Ω}}^i=\left[\begin{array}{c}{\mathrm{\ω}}_{\mathrm{ibx}}^b+\stackrel{\·}{\mathrm{\α}}\\ \mathrm{\Ω}\\ \stackrel{\·}{\mathrm{\β}}\end{array}\right],H^r=\left[\begin{array}{c}{I}_r({\mathrm{\ω}}_{\mathrm{ibx}}^b+\stackrel{\·}{\mathrm{\α}})\\ I_z\mathrm{\Ω}\\ I_r\stackrel{\·}{\mathrm{\β}}\end{array}\right],{\stackrel{\·}{H}}^r=\left[\begin{array}{c}{I}_r({\stackrel{\·}{\mathrm{\ω}}}_{\mathrm{ibx}}^b+\stackrel{\·\·}{\mathrm{\α}})\\ 0\\ I_r\stackrel{\·\·}{\mathrm{\β}}\end{array}\right],M^r=\left[\begin{array}{c}{I}_r{\stackrel{\·}{\mathrm{\ω}}}_{\mathrm{ibx}}^b+I_r\stackrel{\·\·}{\mathrm{\α}}-\stackrel{\·}{\mathrm{\β}}{I}_z\mathrm{\Ω}\\ \stackrel{\·}{\mathrm{\α}}{I}_z\mathrm{\Ω}+I_z\mathrm{\Ω}{\mathrm{\ω}}_{\mathrm{ibx}}^b+I_r\stackrel{\·\·}{\mathrm{\β}}\end{array}\right]$

Rotor radial bonding force square expression formula is:

$M_x^r=I_r{\stackrel{\·}{\mathrm{\ω}}}_{\mathrm{ibx}}^b+I_r\stackrel{\·\·}{\mathrm{\α}}-\stackrel{\·}{\mathrm{\β}}{I}_z\mathrm{\Ω},M_z^r=\stackrel{\·}{\mathrm{\α}}{I}_z\mathrm{\Ω}+I_z\mathrm{\Ω}{\mathrm{\ω}}_{\mathrm{ibx}}^b+I_r\stackrel{\·}{\mathrm{\β}}$

Suffered by magnetic suspension rotor, bonding force square is:

$M_x^r=l_m(f_{\mathrm{by}}-f_{\mathrm{ay}}),M_z^r=l_m(f_{\mathrm{ax}}-f_{\mathrm{bx}})$

Magnetic force suffered by magnetic suspension rotor can be expressed as following linear forms:

f _λ＝k _iλi _λ+k _hλh _λ(λ＝ax，ay，bx，by)

In formula, k _{i λ}and k _{h λ}(λ=ax, ay, bx, by) represents current stiffness and the displacement rigidity of radial ax, ay, bx and by passage of magnetic suspension rotor respectively, can demarcate by experiment; i _ax, i _bx, i _ayand i _bythe winding current of four radial passages, h _ax, h _bx, h _ayand h _aythe linear displacement amount of magnetic suspension rotor respectively on ax, bx, ay and by direction, l _mrepresent from magnetic suspension rotor center to the distance at radial direction magnetic bearing center; h _ax, h _bx, h _ay, h _bycan be measured by eddy current displacement sensor, i _ax, i _bx, i _ay, i _bycan current sensor measurement be passed through, thus bonding force square suffered by rotor can be calculated

The expression formula of rotor deflection angle is:

α＝(h _ay-h _by)/(2l _m)，β＝(h _ax-h _bx)/(2l _m)

H _ax, h _ax, h _ayand h _bythe linear displacement amount of magnetic suspension rotor respectively on ax, bx, ay and by direction, l _mrepresent from magnetic suspension rotor center to the distance at radial direction magnetic bearing center, h _ax, h _bx, h _ay, h _bycan be measured by eddy current displacement sensor, thus can calculate rotor deflection information α, β, $\stackrel{\·}{\mathrm{\α}},\stackrel{\·}{\mathrm{\β}},\stackrel{\·\·}{\mathrm{\α}},\stackrel{\·\·}{\mathrm{\β}};$

Attitude of satellite angular speed, angular acceleration are:

${\mathrm{\ω}}_{\mathrm{ibx}}^b=M_z^r-\stackrel{\·}{\mathrm{\α}}{I}_z\mathrm{\Ω}-I_r\stackrel{\·\·}{\mathrm{\β}},{\stackrel{\·}{\mathrm{\ω}}}_{\mathrm{ibx}}^b=(M_x^r-I_r\stackrel{\·\·}{\mathrm{\α}}+\stackrel{\·}{\mathrm{\β}}{I}_z\mathrm{\Ω})/I_r$

Under there is no orbit angular velocity condition, order when θ, ψ are undisturbed, celestial body coordinate system is relative to the attitude angle of orbital coordinate system, then represent all directions attitude angle acceleration, represent all directions angular velocity, represent the angular acceleration that disturbance produces and angular velocity, represent total angular acceleration and angular velocity, then:

(2) in measuring satellite angular velocities, Mach angle Speed identification and disturbing moment compensate

In attitude angular velocity, the sinusoidal angular velocity of the generation of high frequency small amplitude disturbing moment and forcing frequency same frequency, can adopt adaptive notch filter to carry out identification and removal to it; The core of trapper N is depression feedback element Nf, and its centre frequency can change according to forcing frequency W change, and ε determines speed of convergence and the center notch bandwidth of trapper N, K _h/ K _ifor the scale-up factor of disturbance compensation;

If ω (t) is the input of depression feedback element Nf, the output that c (t) is Nf, then have:

$c\left(t\right)=\left[\begin{array}{cc}\sin \left(\mathrm{Wt}\right)& \cos \left(\mathrm{Wt}\right)\end{array}\right]\·\left[\begin{array}{c}\∫\sin \left(\mathrm{Wt}\right)\·\mathrm{\ω}\left(t\right)\mathrm{dt}\\ \∫\cos \left(\mathrm{Wt}\right)\·\mathrm{\ω}\left(t\right)\mathrm{dt}\end{array}\right]$

C and ω meets the following differential equation:

$\stackrel{\·\·}{c}+W^{2}c=\stackrel{\·}{\mathrm{\ω}}$

The transport function of depression feedback element Nf is:

$N_f\left(s\right)=\frac{c\left(s\right)}{\mathrm{\ω}\left(s\right)}=\frac{s}{s^2+W^2}$

Trapper inputs export to depression feedback element Nf biography letter No be:

Make s=j ω, consider the frequency characteristic of No, when ε ≠ 0:

N _O(jω)≈0，[ω∈(0，W-Δω)∪(W+Δω，∞)]

N _O(jω)＝1，[ω∈(W-Δω，W+Δω)]

Namely, when ε ≠ 0, the output of No will level off to input medium frequency is the component of W

The output of depression feedback element Nf for:

$A=\sqrt{{r_1}^2+{r_2}^2},\mathrm{\λ}=\arctan \left(\frac{r_2}{r_1}\right)$

Namely after feedback element convergence, the output valve of depression feedback element Nf integrator is the amplitude with the sine and cosine component of forcing frequency amount in attitude angular velocity, which achieves the attitude angular velocity produced disturbance in attitude angular velocity signal identification;

By compensating proportion COEFFICIENT K _h/ K _i, compensating torque is introduced in direction eliminate disturbance to the impact of attitude;

(3) magnetic suspension rotor integrated operation rule

Under the effect of single shaft high frequency small amplitude disturbing moment, using the responsive gyro of magnetic suspension control as the Dynamical Attitude Equations of topworks be:

$J{\stackrel{\·}{\mathrm{\ω}}}_{\mathrm{ib}}^b+{\mathrm{\ω}}_{\mathrm{ib}}^b\×J{\mathrm{\ω}}_{\mathrm{ib}}^b+{\stackrel{\·}{H}}^r+\mathrm{\ω}\×H^r=T_d$

In formula, J represents satellite moment of inertia matrix, T _d=[T _dx0 0] represent single shaft high frequency small amplitude disturbing moment, under little attitude angle condition using magnetic suspension rotor as the Dynamical Attitude Equations of attitude control actuator be:

$J_y\stackrel{\·\·}{\mathrm{\θ}}+{\stackrel{\·}{h}}_y=0,$

Wherein, J _x, J _y, J _zrepresent the moment of inertia of each axle of satellite, h _yrepresent rotor axial momentum, the Dynamical Attitude Equations in rotor radial two directions is:

Therefore need the disturbance torque of the β rotation direction of going compensation to cause because of disturbance, therefore:

Order for the speed of the β rotation direction that posture adjustment needs, then have after compensation:

α rotation direction does not need to compensate, order for the speed of the α rotation direction that posture adjustment needs, therefore the Dynamical Attitude Equations in rotor radial two directions is:

After adding disturbance compensation, according to satellite dynamics equation, posture adjustment object attitude angle is ψ _r=0, design uneoupled control rule is:

K _px, k _dx, k _pz, k _dzfor PD controller parameter; Dynamical Attitude Equations is:

Satellite does not have the single-axis attitude angle information in disturbance situation for:

Satellite only has single shaft angular speed when,

Satellite gravity anomaly amount is realized by the micro-framework control moment of rotor radial:

$U_x=-{\stackrel{\·}{\mathrm{\β}}}_c{h}_y,U_z={\stackrel{\·}{\mathrm{\α}}}_c{h}_y$

Therefore in conjunction with disturbance compensation, the integrated operation rule that magnetic suspension rotor controls is:

$\stackrel{\·}{\mathrm{\α}}={\stackrel{\·}{\mathrm{\α}}}_c=U_z/h_y,$

The control reference quantity that in reality, magnetic bearing applies is h _axr, h _bxr, h _ayr, h _byr, and h _bxr=-h _axr, h _byr=-h _ayr, therefore:

$h_{\mathrm{ayr}}={\mathrm{\αl}}_m=-l_m\∫(M_z^r-\stackrel{\·}{\mathrm{\α}}{I}_z\mathrm{\Ω}-I_r\stackrel{\·\·}{\mathrm{\β}})$

$h_{\mathrm{byr}}={-\mathrm{\αl}}_m=l_m\∫(M_z^r-\stackrel{\·}{\mathrm{\α}}{I}_z\mathrm{\Ω}-I_r\stackrel{\·\·}{\mathrm{\β}})$

In order to verify the effect of the method, the attitude angle before and after Disturbance Rejection being compensated and attitude angular velocity contrast, and test findings is respectively as shown in Fig. 4, Fig. 5, Fig. 6, Fig. 7.

Abscissa representing time in Fig. 4, Fig. 6, unit is s, and ordinate represents roll angle, and unit is °, abscissa representing time in Fig. 5, Fig. 7, and unit is s, and ordinate represents rate of roll, and unit is °/s.Attitude angle before and after contrast Disturbance Rejection compensates and attitude angular velocity, can find out the suppression adopting the present invention well to achieve high frequency small amplitude disturbance, and calculating realizes comparatively simple, and engineering is strong.

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. the present invention relates to a kind of satellite single shaft measurement and control integration method based on the responsive gyro of magnetic suspension control, by the attitude angular velocity of satellite under the disturbance of magnetic suspension control responsive gyro detection high frequency small amplitude, the adaptive notch filter that use center trap frequency changes with forcing frequency, identification and removal are carried out to the attitude angular velocity that high frequency small amplitude disturbance produces, calculate compensating torque needed for compensating disturbance, and according to corresponding attitude control law, calculate the radial control moment of magnetic suspension rotor needed for appearance control, in conjunction with Disturbance Rejection and gesture stability, design the integrated operation rule of magnetic suspension rotor, rotor turning axle is made to deflect the micro-Frame research moment of radial two degrees of freedom needed for exporting, thus realize gesture stability and the Disturbance Rejection of satellite single shaft, specifically comprise the following steps:

(1) according to rigid dynamics and principle of coordinate transformation magnetic suspension rotor kinetics equation be:

$M^r={\stackrel{\·}{H}}^r+{\mathrm{\ω}}_{\mathrm{ir}}^r\×H^r$

Wherein:

H ^r＝IΩ ⁱ

${\stackrel{\·}{H}}^r=I{\stackrel{\·}{\mathrm{\Ω}}}^i$

${\mathrm{\Ω}}^i={\mathrm{\Ω}}^r+{\mathrm{\ω}}_{\mathrm{ir}}^r$

$I=\left[\begin{array}{ccc}{I}_r& 0& 0\\ 0& I_z& 0\\ 0& 0& I_r\end{array}\right],{\mathrm{\Ω}}^r=\left[\begin{array}{c}0\\ \mathrm{\Ω}\\ 0\end{array}\right]$

${\mathrm{\ω}}_{\mathrm{ir}}^r={\mathrm{\ω}}_{\mathrm{rf}}^r+{\mathrm{\ω}}_{\mathrm{icmg}}^r=C_f^r{\mathrm{\ω}}_{\mathrm{rf}}^f+C_f^r{C}_g^f{C}_{\mathrm{cmg}}^g{\mathrm{\ω}}_{\mathrm{icmg}}^{\mathrm{cmg}}$

${\mathrm{\ω}}_{\mathrm{icmg}}^{\mathrm{cmg}}=C_b^{\mathrm{cmg}}{\mathrm{\ω}}_{\mathrm{ib}}^b+{\mathrm{\ω}}^{\mathrm{cmg}}$

In formula, M ^rrepresent magnetic suspension rotor bonding force square, H ^rrepresent the angular momentum at rotor system lower rotor part, represent the angular momentum at rotor system lower rotor part, I represents the moment of inertia that rotor rotates around the responsive gyro reference frame of magnetic suspension control, I _rrepresent rotor radial moment of inertia, I _zrepresent rotor axial moment of inertia, Ω represents rotor axial rotating speed, Ω ^rrepresent rotor speed, Ω ⁱrepresent the absolute angular velocities of rotor, represent the absolute angular velocities rate of change of rotor, represent the absolute angular velocities of rotor coordinate, namely relative to the rotating speed of inertial space, represent the deflection speed of the relative magnetic bearing of rotor, for the responsive gyro reference frame of magnetic suspension control is relative to the speed of inertial space, for rotor is relative to the angular velocity of inertial space, ω ^cmgfor frame corners speed, for magnetic bearing coordinate is tied to the transformation matrix of rotor coordinate, for frame coordinates is tied to the transformation matrix of magnetic bearing coordinate system, for the responsive gyro of magnetic suspension control is with reference to the transformation matrix being tied to frame coordinates system, for celestial body is tied to the transformation matrix of the responsive gyro reference frame of magnetic suspension control;

At magnetic bearing, system, frame coordinates system are installed, the responsive gyro reference frame of magnetic suspension control overlaps and satellite only has single shaft angular speed ${\mathrm{\ω}}_{\mathrm{ib}}^b={\left[\begin{array}{ccc}{\mathrm{\ω}}_{\mathrm{ibx}}^b& 0& 0\end{array}\right]}^T$ Condition under:

${\mathrm{\ω}}_{\mathrm{ir}}^r={\mathrm{\ω}}_{\mathrm{rf}}^r+{\mathrm{\ω}}_{\mathrm{icmg}}^r=C_f^r{\mathrm{\ω}}_{\mathrm{rf}}^f+C_f^r{\mathrm{\ω}}_{\mathrm{icmg}}^{\mathrm{cmg}}$

α, β are very little,

Again ${\mathrm{\ω}}_{\mathrm{icmg}}^{\mathrm{cmg}}=\left[\begin{array}{c}{\mathrm{\ω}}_{\mathrm{ibx}}^b\\ 0\\ 0\end{array}\right],{\mathrm{\ω}}_{\mathrm{rf}}^f=\left[\begin{array}{c}\stackrel{\·}{\mathrm{\α}}\\ 0\\ \stackrel{\·}{\mathrm{\β}}\end{array}\right],{\mathrm{\ω}}_{\mathrm{ir}}^r=\left[\begin{array}{c}{\mathrm{\ω}}_{\mathrm{ibx}}^b+\stackrel{\·}{\mathrm{\α}}\\ 0\\ \stackrel{\·}{\mathrm{\β}}\end{array}\right],$ Then:

${\mathrm{\Ω}}^i=\left[\begin{array}{c}{\mathrm{\ω}}_{\mathrm{ibx}}^b+\stackrel{\·}{\mathrm{\α}}\\ \mathrm{\Ω}\\ \stackrel{\·}{\mathrm{\β}}\end{array}\right],H^r=\left[\begin{array}{c}{I}_r({\mathrm{\ω}}_{\mathrm{ibx}}^b+\stackrel{\·}{\mathrm{\α}})\\ I_z\mathrm{\Ω}\\ I_r\stackrel{\·}{\mathrm{\β}}\end{array}\right],{\stackrel{\·}{H}}^r=\left[\begin{array}{c}{I}_r({\stackrel{\·}{\mathrm{\ω}}}_{\mathrm{ibx}}^b+\stackrel{\·\·}{\mathrm{\α}})\\ 0\\ I_r\stackrel{\·\·}{\mathrm{\β}}\end{array}\right],=M^r\left[\begin{array}{c}{I}_r{\stackrel{\·}{\mathrm{\ω}}}_{\mathrm{ibx}}^b+I_r\stackrel{\·\·}{\mathrm{\α}}-\stackrel{\·}{\mathrm{\β}}{I}_z\mathrm{\Ω}\\ 0\\ \stackrel{\·}{\mathrm{\α}}{I}_z\mathrm{\Ω}+I_z\mathrm{\Ω}{\mathrm{\ω}}_{\mathrm{ibx}}^b+I_r\stackrel{\·\·}{\mathrm{\β}}\end{array}\right]$

Rotor radial bonding force square expression formula is:

$M_x^r=I_r{\stackrel{\·}{\mathrm{\ω}}}_{\mathrm{ibx}}^b+I_r\stackrel{\·\·}{\mathrm{\α}}-\stackrel{\·}{\mathrm{\β}}{I}_z\mathrm{\Ω},M_z^r=\stackrel{\·}{\mathrm{\α}}{I}_z\mathrm{\Ω}+I_z\mathrm{\Ω}{\mathrm{\ω}}_{\mathrm{ibx}}^b+I_r\stackrel{\·\·}{\mathrm{\β}}$

Suffered by magnetic suspension rotor, bonding force square is:

$M_x^r=l_m(f_{\mathrm{by}}-f_{\mathrm{ay}}),M_z^r=l_m(f_{\mathrm{ax}}-f_{\mathrm{bx}})$

Magnetic force suffered by magnetic suspension rotor can be expressed as following linear forms:

f _λ＝k _iλi _λ+k _hλh _λ(λ＝ax，ay，bx，by)

In formula, k _{i λ}and k _{h λ}(λ=ax, ay, bx, by) represents current stiffness and the displacement rigidity of radial ax, ay, bx and by passage of magnetic suspension rotor respectively, can demarcate by experiment; i _ax, i _bx, i _ayand i _bythe winding current of four radial passages, h _ax, h _bx, h _ayand h _bythe linear displacement amount of magnetic suspension rotor respectively on ax, bx, ay and by direction, l _mrepresent from magnetic suspension rotor center to the distance at radial direction magnetic bearing center; h _ax, h _bx, h _ay, h _bycan be measured by eddy current displacement sensor, i _ax, i _bx, i _ay, i _bycan current sensor measurement be passed through, thus bonding force square suffered by rotor can be calculated

The expression formula of rotor deflection angle is:

α＝(h _ay-h _by)/(2l _m)，β＝(h _ax-h _bx)/(2l _m)

Wherein, h _ax, h _bx, h _ayand h _bythe linear displacement amount of magnetic suspension rotor respectively on ax, bx, ay and by direction, l _mrepresent from magnetic suspension rotor center to the distance at radial direction magnetic bearing center, h _ax, h _bx, h _ay, h _bycan be measured by eddy current displacement sensor, thus can calculate rotor deflection information α, β,

Attitude of satellite angular speed, angular acceleration are:

${\mathrm{\ω}}_{\mathrm{ibx}}^b=M_z^r-\stackrel{\·}{\mathrm{\α}}{I}_z\mathrm{\Ω}-I_r\stackrel{\·\·}{\mathrm{\β}},{\stackrel{\·}{\mathrm{\ω}}}_{\mathrm{ibx}}^{\text{b}}=(M_x^r-I_r\stackrel{\·\·}{\mathrm{\α}}+\stackrel{\·}{\mathrm{\β}}{I}_z\mathrm{\Ω})/I_r$

Under there is no orbit angular velocity condition, order when θ, Ψ are undisturbed, celestial body coordinate system is relative to the attitude angle of orbital coordinate system, then represent all directions attitude angle acceleration, represent all directions angular velocity, represent the angular acceleration that disturbance produces and angular velocity, represent total angular acceleration and angular velocity, then:

(2) in measuring satellite angular velocities, Mach angle Speed identification and disturbing moment compensate

In attitude angular velocity, the sinusoidal angular velocity of the generation of high frequency small amplitude disturbing moment and forcing frequency same frequency, can adopt adaptive notch filter to carry out identification and removal to it; The core of trapper N is depression feedback element Nf, and its centre frequency can change according to forcing frequency W change, and ε determines speed of convergence and the center notch bandwidth of trapper N, K _h/ K _ifor the scale-up factor of disturbance compensation;

If ω (t) is the input of depression feedback element Nf, the output that c (t) is Nf, then have:

$c\left(t\right)=\left[\begin{array}{cc}\sin \left(\mathrm{Wt}\right)& \cos \left(\mathrm{Wt}\right)\end{array}\right]\·\left[\begin{array}{c}\∫\sin \left(\mathrm{Wt}\right)\·\mathrm{\ω}\left(t\right)\mathrm{dt}\\ \∫\cos \left(\mathrm{Wt}\right)\·\mathrm{\ω}\left(t\right)\mathrm{dt}\end{array}\right]$

C and ω meets the following differential equation:

$\stackrel{\·\·}{c}+W^{2}c=\stackrel{\·}{\mathrm{\ω}}$

The transport function of depression feedback element Nf is:

$N_f\left(s\right)=\frac{c\left(s\right)}{\mathrm{\ω}\left(s\right)}=\frac{s}{s^2+W^2}$

Trapper inputs export to depression feedback element Nf biography letter No be:

Make s=j ω, consider the frequency characteristic passing letter No, when ε ≠ 0,

N _O(jω)≈0，[ω∈(0，W-Δω)∪(W+Δω，∞)]

N _O(jω)＝1，[ω∈(W-Δω，W+Δω)]

Namely, when ε ≠ 0, the output of No will level off to input medium frequency is the component of W

The output of depression feedback element Nf for:

$A=\sqrt{r_1^2+r_2^2},\mathrm{\λ}=\arctan \left(\frac{r_2}{r_1}\right)$

Namely after feedback element convergence, the output valve of depression feedback element Nf integrator is the amplitude with the sine and cosine component of forcing frequency amount in attitude angular velocity, which achieves the attitude angular velocity produced disturbance in attitude angular velocity signal identification;

By compensating proportion COEFFICIENT K _h/ K _i, compensating torque is introduced in direction eliminate disturbance to the impact of attitude;

(3) magnetic suspension rotor integrated operation rule

Under the effect of single shaft high frequency small amplitude disturbing moment, using the responsive gyro of magnetic suspension control as the Dynamical Attitude Equations of topworks be:

$J{\stackrel{\·}{\mathrm{\ω}}}_{\mathrm{ib}}^b+{\mathrm{\ω}}_{\mathrm{ib}}^b\×J{\mathrm{\ω}}_{\mathrm{ib}}^b+{\stackrel{\·}{H}}^r+\mathrm{\ω}\×H^r=T_d$

In formula, J represents satellite moment of inertia matrix, T _d=[T _dx0 0] represent single shaft high frequency small amplitude disturbing moment, under little attitude angle condition using magnetic suspension rotor as the Dynamical Attitude Equations of attitude control actuator be:

$J_y\stackrel{\·\·}{\mathrm{\θ}}+{\stackrel{\·}{h}}_y=0,$

Wherein, J _x, J _y, J _zrepresent the moment of inertia of each axle of satellite, h _yrepresent rotor axial momentum, the Dynamical Attitude Equations in rotor radial two directions is:

Therefore need the disturbance torque of the β rotation direction of going compensation to cause because of disturbance, therefore:

Order for the speed of the β rotation direction that posture adjustment needs, then have after compensation:

α rotation direction does not need to compensate, order for the speed of the α rotation direction that posture adjustment needs, therefore the Dynamical Attitude Equations of rotor radial both direction is:

After adding disturbance compensation, according to satellite dynamics equation, posture adjustment object attitude angle is Ψ _r=0, design uneoupled control rule is:

K _px, k _dx, k _pz, k _dzfor PD controller parameter; Dynamical Attitude Equations is:

$J_z\stackrel{\·\·}{\mathrm{\ψ}}+k_{\mathrm{pz}}({\mathrm{\ψ}}_r-\mathrm{\ψ})+k_{\mathrm{dz}}(0-\stackrel{\·}{\mathrm{\ψ}})=0$

Satellite does not have the single-axis attitude angle information in disturbance situation for:

Satellite only has single shaft angular speed when,

Satellite gravity anomaly amount is realized by the micro-framework control moment of rotor radial:

$U_x=-{\stackrel{\·}{\mathrm{\β}}}_c{h}_y,U_z={\stackrel{\·}{\mathrm{\α}}}_c{h}_y$

Therefore in conjunction with disturbance compensation, the integrated operation rule that magnetic suspension rotor controls is:

$\stackrel{\·}{\mathrm{\α}}={\stackrel{\·}{\mathrm{\α}}}_c=U_z/h_y,$

The control reference quantity that in reality, magnetic bearing applies is h _axr, h _bxr, h _ayr, h _byr, and h _bxr=-h _axr, h _byr=-h _ayr, therefore:

$h_{\mathrm{ayr}}={\mathrm{\αl}}_m=-l_m\∫(M_z^r-\stackrel{\·}{\mathrm{\α}}{I}_z\mathrm{\Ω}-I_r\stackrel{\·\·}{\mathrm{\β}})$

$h_{\mathrm{byr}}={-\mathrm{\αl}}_m=l_m\∫(M_z^r-\stackrel{\·}{\mathrm{\α}}{I}_z\mathrm{\Ω}-I_r\stackrel{\·\·}{\mathrm{\β}}).$