CN105059568A - Eight-rod six-degree-of-freedom satellite platform for ultra-precise ultra-stable satellites, and decoupling control method of eight-rod six-degree-of-freedom satellite platform - Google Patents

Abstract

The invention discloses an eight-rod six-degree-of-freedom satellite platform for ultra-precise ultra-stable satellites, and a decoupling control method of the eight-rod six-degree-of-freedom satellite platform. The eight-rod six-degree-of-freedom satellite platform for ultra-precise ultra-stable satellites comprises a load cabin, a platform cabin and a suspension device, wherein the suspension device is arranged between the load cabin and the platform cabin; the load cabin and the platform cabin are in non-contact arrangement through the suspension device. Besides, the invention further discloses a decoupling control method of the eight-rod six-degree-of-freedom satellite platform for ultra-precise ultra-stable satellites. The eight-rod six-degree-of-freedom satellite platform disclosed by the invention is simple to mount; only eight magnetic-suspension mechanisms need to be symmetrically mounted, so that the operation is simple and easy; the decoupling can be measured and controlled by reasonably allocating the number and the layout of the magnetic-suspension mechanisms and judging whether the distribution force is dynamically output or not in a real-time manner, and judging the size and the direction of the distribution force; the decoupling control method can be completely realized through algorithms; the redundant design of the eight magnetic-suspension mechanisms is high in reliability.

Description

Two super satellite eight bar six degree of freedom satellite platform and decoupling control method thereof

Technical field

The present invention relates to satellite platform small movements control technology field, particularly, relate to a kind of two super satellite eight bar six degree of freedom satellite platform and decoupling control method thereof

Background technology

The traditionally method of designing that is connected of load and satellite platform, load is pointed to and is relied on satellite platform control system to realize with degree of stability, but because satellite platform high frequency micro vibration is inevitable, and control system product bandwidth, precision etc. are limited in one's ability, the technical bottleneck of micro-vibration " difficult survey, difficult control " is made to be difficult to break through.The two super satellite (" superfinishing is super steady " satellite) designed for this problem realizes the sound isolation in two cabins by non-contact magnetically float means, physically directly eliminates platform cabin high frequency micro vibration to the adverse effect in load cabin.

The high precision ACTIVE CONTROL in load cabin and the relative position in two cabins control all to be realized by magnetic floating mechanism, if appearance control power and relative position control effort influence each other namely are coupled, and just cannot realize the super steady control of superfinishing in load cabin.Therefore must accomplish to make the relative position control effort in the ACTIVE CONTROL moment in load cabin and two cabins full decoupled.Orthodox method generally adopts six rod models, with the form uniform layout of equilateral triangle, and two magnetic floating mechanisms angle angle mount in 90 ° of same position, this model measurement, control decoupling zero and mechanism install all very complicated, irredundant, and poor reliability.

Summary of the invention

For the above-mentioned problems in the prior art, the present invention proposes a kind of two super satellite eight bar six degree of freedom satellite platform and decoupling control method thereof of symmetrical mounting arrangement, this satellite platform and control method are by reasonable disposition magnetic floating mechanism quantity and layout, and the output of real-time dynamic assignment power realizes six degree of freedom uneoupled control with or without, size and Orientation, the method can pass through algorithm realization completely.

For achieving the above object, the present invention is achieved by the following technical solutions.

According to an aspect of the present invention, provide a kind of two super satellite eight bar six degree of freedom satellite platform, comprise load cabin, platform cabin and levitation device, described levitation device is arranged between load cabin and platform cabin, and described load cabin and platform cabin are arranged by levitation device noncontact.

Preferably, described levitation device comprises multiple magnetic floating mechanism, wherein each magnetic floating mechanism includes: coil 31, magnet steel 32, yoke 33 and support 34, wherein, described coil 31 is connected to platform cabin by support 34, described magnet steel 32 is connected with load cabin, and without physical connection between described support 34 and yoke 33, thus the noncontact achieved between load cabin and platform cabin is arranged.Arranged by noncontact, the vibration in platform cabin 2 and interference can not transfer to load cabin 1, reach capacity weight 14 dynamic in get quiet, the effect that load cabin and platform cabin sound are isolated.

Preferably, described coil 31 is equal everywhere to the distance of magnet steel 32 radial direction, forms the balance position of coil 31.

Preferably, described magnetic floating mechanism also comprises relative position sensor 35, described relative position sensor and magnetic floating mechanism integrated design, and relative position sensor (edd current transducer) measures the displacement of magnetic floating mechanism respectively.

Preferably, described relative position sensor and magnetic floating mechanism are 8.

Preferably, described magnetic floating mechanism is eight, be respectively magnetic floating mechanism A1, A2, A3, A4, B1, B2, B3, B4, eight magnetic floating mechanism A1, A2, A3, A4, B1, B2, B3, B4 symmetric configurations are on platform cabin, wherein, magnetic floating mechanism A1, A2, A3, A4 are positioned at four corner locations in platform cabin, and direction is along Z-direction; Magnetic floating mechanism B1, B2, B3, B4 are positioned at four limit point midways of satellite platform, and wherein, magnetic floating mechanism B1, B3 direction is along Y direction, and magnetic floating mechanism B2, B4 direction is along X-direction.

According to another aspect of the present invention, provide a kind of decoupling control method of above-mentioned two super satellite eight bar six degree of freedom satellite platform, comprise the steps:

A () sets up load cabin attitude dynamic equations:

$I_p{\stackrel{\·}{\mathrm{\ω}}}_p+{\mathrm{\ω}}_p\×\left(I_p{\mathrm{\ω}}_p\right)=\underset{i=1}{\overset{8}{\Σ}}{l}_i\×F_i+T_{d1}$

Wherein, F _ifor the appearance control power that magnetic floating mechanism produces, T _d1for extraneous long periodic noise, can be eliminated by the effect of magnetic floating mechanism; I _pfor the inertia matrix in load cabin, for load cabin angular acceleration, ω _pfor load cabin cireular frequency, l _ifor the arm of force of each magnetic floating mechanism;

B () sets up platform cabin attitude dynamic equations:

$I_s\stackrel{\·}{\mathrm{\ω}}+\mathrm{\ω}\×\left(I_s\mathrm{\ω}\right)+C_{af1}{\stackrel{\·\·}{q}}_{f1}+C_{af1}{\stackrel{\·\·}{q}}_{f2}=T_c-\underset{i=1}{\overset{8}{\Σ}}{l}_i^{\′}\×F_i+T_{d2}$

${\stackrel{\·\·}{q}}_{f1}+2{\mathrm{\ζ}}_f{\mathrm{\Λ}}_f{\stackrel{\·}{q}}_{f1}+{\mathrm{\Λ}}_f^2{q}_{f1}+C_{af1}^T\stackrel{\·}{\mathrm{\ω}}=0$

${\stackrel{\·\·}{q}}_{f2}+2{\mathrm{\ζ}}_f{\mathrm{\Λ}}_f{\stackrel{\·}{q}}_{f2}+{\mathrm{\Λ}}_f^2{q}_{f2}+C_{af2}^T\stackrel{\·}{\mathrm{\ω}}=0$

In formula, I _sfor platform cabin inertia matrix, ω is platform cabin cireular frequency, C _af1for the coefficient of coupling battle array that the vibration of+Y-direction solar array is rotated satellite hub body, C _af2for the coefficient of coupling battle array that the vibration of-Y-direction solar array is rotated satellite hub body, q _f1for+Y-direction solar array modal coordinate, q _f2for-Y-direction solar array modal coordinate, T _cfor flywheel control torque, T _d2for windsurfing rotates disturbance torque, Λ _ffor solar array model frequency diagonal matrix, ζ _ffor solar array modal damping coefficient; for platform cabin angular acceleration, for the second derivative of+Y-direction solar array modal coordinate, for the second derivative of-Y-direction solar array modal coordinate, for the first derivative of+Y-direction solar array modal coordinate, for the first derivative of-Y-direction solar array modal coordinate, l ' is the arm of force of each magnetic floating mechanism, for the vibration of+Y-direction solar array is to the transposition of the coefficient of coupling battle array that satellite hub body rotates, for the vibration of-Y-direction solar array is to the transposition of the coefficient of coupling battle array that satellite hub body rotates;

C () is set up load freight space and is put governing equation:

$M_p{a}_p=\underset{i=1}{\overset{8}{\Σ}}{F}_i$

In formula, M _pfor load cabin quality, α _pfor load cabin acceleration/accel;

(d) load cabin in the x-direction translation time, magnetic floating mechanism B2, B4 produce relative position control effort be respectively Δ F _x; In the y-direction during translation, the relative position control effort that magnetic floating mechanism B1, B3 produce is respectively Δ F _y; In the z-direction during translation, the relative position control effort that magnetic floating mechanism A1, A2, A3, A4 produce is respectively Δ F _z; In like manner, the appearance control power produced when magnetic floating mechanism A1, A2, A3, A4, B1, B2, B3, B4 makes load rotate is respectively F _a1, F _a2, F _a3, F _a4, F _b1, F _b2, F _b3, F _b4;

Translation control effort F in the x-direction _sxfor:

F _sx＝F _B2+ΔF _x+F _B4+ΔF _x＝F _B2+F _B4+2ΔF _x；

Now for translation control effort F _sxconstraint condition be: produce the moment around y-axis by magnetic floating mechanism A1, A2, A3, A4, offset by Δ F _xthe moment produced;

Translation control effort F in the y-direction _syfor:

F _sy＝F _B1+ΔF _y+F _B3+ΔF _y＝F _B1+F _B3+2ΔF _y；

Now to translation control effort F _syconstraint condition be: produce the moment around x-axis by magnetic floating mechanism A1, A2, A3, A4, offset by Δ F _ythe moment produced;

Translation control effort F in the z-direction _szfor:

F _sz＝F _A1+ΔF _z+F _A2+ΔF _z+F _A3+ΔF _z+F _A4+ΔF _z＝F _A1+F _A2+F _A3+F _A4+4ΔF _z；

By making F _b2=-F _b4, F _b1=-F _b3, F _a1+ F _a2+ F _a3+ F _a4=0, guarantee appearance control power to the translation in load cabin without any impact;

Around the rotation control effort T in x direction _rxfor:

$\begin{array}{c}{T}_{rx}=(F_{A1}+{\mathrm{\ΔF}}_z)\frac{l_1}{2}+(F_{A2}+{\mathrm{\ΔF}}_z)\frac{l_1}{2}-(F_{A3}+{\mathrm{\ΔF}}_z)\frac{l_1}{2}-(F_{A4}+{\mathrm{\ΔF}}_z)\frac{l_1}{2}\\ =(F_{A1}+F_{A2}-F_{A3}-F_{A4})\frac{l_1}{2}=(F_{A1}+F_{A2})l_1\end{array}$

In formula, l ₁for the length of magnetic floating mechanism attachment face;

Around the rotation control effort T in y direction _ryfor:

$\begin{array}{c}{T}_{ry}=-(F_{A1}+{\mathrm{\ΔF}}_z)\frac{l_3}{2}+(F_{A2}+{\mathrm{\ΔF}}_z)\frac{l_3}{2}+(F_{A3}+{\mathrm{\ΔF}}_z)\frac{l_3}{2}-(F_{A4}+{\mathrm{\ΔF}}_z)\frac{l_3}{2}\\ =(-F_{A1}+F_{A2}+F_{A3}-F_{A4})\frac{l_3}{2}=(F_{A2}+F_{A3})l_3\end{array}$

In formula, l ₃for the width of magnetic floating mechanism attachment face;

Around the rotation control effort T in z direction _rzfor:

$\begin{array}{c}{T}_{rz}=(F_{B1}+{\mathrm{\ΔF}}_y)\frac{l_3}{2}-(F_{B2}+{\mathrm{\ΔF}}_x)\frac{l_1}{2}-(F_{B3}+{\mathrm{\ΔF}}_y)\frac{l_3}{2}+(F_{B4}+{\mathrm{\ΔF}}_x)\frac{l_1}{2}\\ =(F_{B1}-F_{B3})\frac{l_3}{2}-(F_{B2}-F_{B4})\frac{l_1}{2}=F_{B1}{l}_3+F_{B4}{l}_1\end{array}$

By making F _b2=-F _b4, F _b1=-F _b3, F _a1+ F _a2+ F _a3+ F _a4=0, make the attitude in load cabin and load cabin and platform cabin relative position control effort full decoupled; Now the kinetics equation in load cabin is:

$\left\{\begin{array}{c}{I}_{px}{\stackrel{\·}{\mathrm{\ω}}}_{px}+{\mathrm{\ω}}_{px}\×\left(I_{px}{\mathrm{\ω}}_{px}\right)=(F_{A1}+{\mathrm{\ΔF}}_z)\frac{L_1}{2}+(F_{A2}+{\mathrm{\ΔF}}_z)\frac{L_1}{2}-(F_{A3}+{\mathrm{\ΔF}}_z)\frac{L_1}{2}-(F_{A4}+{\mathrm{\ΔF}}_z)\frac{L_1}{2}=2F_x{L}_1\\ I_{py}{\stackrel{\·}{\mathrm{\ω}}}_{py}+{\mathrm{\ω}}_{py}\×\left(I_{py}{\mathrm{\ω}}_{py}\right)=-(F_{A1}+{\mathrm{\ΔF}}_z)\frac{L_2}{2}+(F_{A2}+{\mathrm{\ΔF}}_z)\frac{L_2}{2}+(F_{A3}+{\mathrm{\ΔF}}_z)\frac{L_3}{2}-(F_{A4}+{\mathrm{\ΔF}}_z)\frac{L_3}{2}=2F_y{L}_3\\ I_{pz}{\stackrel{\·}{\mathrm{\ω}}}_{pz}+{\mathrm{\ω}}_{pz}\×\left(I_{pz}{\mathrm{\ω}}_{pz}\right)=(F_{B1}+{\mathrm{\ΔF}}_y)\frac{L_3}{2}-(F_{B2}+{\mathrm{\ΔF}}_x)\frac{L_1}{2}-(F_{B3}+{\mathrm{\ΔF}}_y)\frac{L_3}{2}+(F_{B4}+{\mathrm{\ΔF}}_x)\frac{L_1}{2}=F_z\left(L_1+L_3\right)\end{array}\right.$

$\left\{\begin{array}{c}{M}_p{\stackrel{\·\·}{x}}_p=F_{B2}+{\mathrm{\ΔF}}_x+F_{B4}+{\mathrm{\ΔF}}_x=2{\mathrm{\ΔF}}_x\\ M_p{\stackrel{\·\·}{y}}_p=F_{B1}+{\mathrm{\ΔF}}_y+F_{B3}+{\mathrm{\ΔF}}_y=2{\mathrm{\ΔF}}_y\\ M_p{\stackrel{\·\·}{z}}_p=F_{A1}+{\mathrm{\ΔF}}_z+F_{A2}+{\mathrm{\ΔF}}_z+F_{A3}+{\mathrm{\ΔF}}_z+F_{A4}+{\mathrm{\ΔF}}_z=4{\mathrm{\ΔF}}_z\end{array}\right.$

In formula: I _px, I _py, I _pzbe respectively the rotor inertia of load cabin around x, y, z axle, be respectively the angular acceleration of load cabin around x, y, z axle, ω _px, ω _py, ω _pzbe respectively the cireular frequency of load cabin around x, y, z axle, L ₁, L ₃, L ₂be respectively the distance of the length and width of magnetic floating mechanism attachment face, up and down attachment face, F _x, F _y, F _zbe respectively the application force of single magnetic floating mechanism in x, y, z direction, be respectively the acceleration/accel of load cabin along x, y, z axle.

Two super satellite eight bar six degree of freedom satellite platform provided by the invention and decoupling control method thereof, load cabin attitude is regulated by appearance control power, load cabin and platform freight space are put and are regulated by relative position control effort, by following principle: i.e. load cabin gesture stability power equal and opposite in direction, direction is contrary, does not produce load cabin and platform cabin relative position control effort; Load cabin and platform cabin relative position control effort equal and opposite in direction, direction is identical, do not produce the gesture stability moment to load cabin, therefore, achieve the full decoupled of load cabin attitude and load cabin and platform cabin relative position control effort, namely achieve the uneoupled control of load cabin attitude and load cabin and platform cabin relative position, can not control to have an impact to load cabin " superfinishing is super steady "; Meanwhile, eight degrees of freedom magnetic floating mechanism system easily realize, redundancy, highly reliable.

Compared with prior art, the present invention has following beneficial effect:

1) install simply, eight magnetic floating mechanism symmetries are installed;

2) simple, by reasonable disposition magnetic floating mechanism quantity and layout, and the output of real-time dynamic assignment power just can realize measuring with or without, size and Orientation, control decoupling zero;

3) this decoupling control method can pass through algorithm realization completely;

4) Redundancy Design of eight magnetic floating mechanisms, highly reliable.

Accompanying drawing explanation

By reading the detailed description done non-limiting example with reference to the following drawings, other features, objects and advantages of the present invention will become more obvious:

Fig. 1 is sound isolation, the two super satellite platform composition schematic diagram of principal and subordinate's Collaborative Control;

Fig. 2 is platform magnetic floating mechanism schematic layout pattern of the present invention;

Fig. 3 is magnetic floating mechanism element schematic.

Detailed description of the invention

Below embodiments of the invention are elaborated: the present embodiment is implemented under premised on technical solution of the present invention, give detailed embodiment and concrete operating process.It should be pointed out that to those skilled in the art, without departing from the inventive concept of the premise, can also make some distortion and improvement, these all belong to protection scope of the present invention.

Embodiment

Present embodiments provide a kind of two super satellite eight bar six degree of freedom satellite platform, comprise load cabin, platform cabin and levitation device, described levitation device is arranged between load cabin and platform cabin, and described load cabin and platform cabin are arranged by levitation device noncontact.

Further, described levitation device comprises multiple magnetic floating mechanism, wherein each magnetic floating mechanism includes: coil 31, magnet steel 32, yoke 33 and support 34, wherein, described coil 31 is connected to platform cabin by support 34, described magnet steel 32 is connected with load cabin, and without physical connection between described support 34 and yoke 33, thus the noncontact achieved between load cabin and platform cabin is arranged.Arranged by noncontact, the vibration in platform cabin 2 and interference can not transfer to load cabin 1, reach capacity weight 14 dynamic in get quiet, the effect that load cabin and platform cabin sound are isolated.

Further, described coil 31 is equal everywhere to the distance of magnet steel 32 radial direction, forms the balance position of coil 31.

Further, described magnetic floating mechanism also comprises relative position sensor 35, described relative position sensor and magnetic floating mechanism are 8, and integrated design, 8 relative position sensors (edd current transducer) measure the displacement of 8 magnetic floating mechanisms respectively.

Further, described magnetic floating mechanism is eight, be respectively magnetic floating mechanism A1, A2, A3, A4, B1, B2, B3, B4, eight magnetic floating mechanism A1, A2, A3, A4, B1, B2, B3, B4 symmetric configurations are on platform cabin, wherein, magnetic floating mechanism A1, A2, A3, A4 are positioned at four corner locations in platform cabin, and direction is along Z-direction; Magnetic floating mechanism B1, B2, B3, B4 are positioned at four limit point midways of satellite platform, and wherein, magnetic floating mechanism B1, B3 direction is along Y direction, and magnetic floating mechanism B2, B4 direction is along X-direction.

The two super satellite eight bar six degree of freedom satellite platform that the present embodiment provides, its decoupling control method, comprises the steps:

A () sets up load cabin attitude dynamic equations:

$I_p{\stackrel{\·}{\mathrm{\ω}}}_p+{\mathrm{\ω}}_p\×\left(I_p{\mathrm{\ω}}_p\right)=\underset{i=1}{\overset{8}{\Σ}}{l}_i\×F_i+T_{d1}$

Wherein, F _ifor the appearance control power that magnetic floating mechanism produces, T _d1for extraneous long periodic noise, can be eliminated by the effect of magnetic floating mechanism; I _pfor the inertia matrix in load cabin, for load cabin angular acceleration, ω _pfor load cabin cireular frequency, l _ifor the arm of force of each magnetic floating mechanism;

B () sets up platform cabin attitude dynamic equations:

$I_s\stackrel{\·}{\mathrm{\ω}}+\mathrm{\ω}\×\left(I_s\mathrm{\ω}\right)+C_{af1}{\stackrel{\·\·}{q}}_{f1}+C_{af1}{\stackrel{\·\·}{q}}_{f2}=T_c-\underset{i=1}{\overset{8}{\Σ}}{l}_i^{\′}\×F_i+T_{d2}$

${\stackrel{\·\·}{q}}_{f1}+2{\mathrm{\ζ}}_f{\mathrm{\Λ}}_f{\stackrel{\·}{q}}_{f1}+{\mathrm{\Λ}}_f^2{q}_{f1}+C_{af1}^T\stackrel{\·}{\mathrm{\ω}}=0$

${\stackrel{\·\·}{q}}_{f2}+2{\mathrm{\ζ}}_f{\mathrm{\Λ}}_f{\stackrel{\·}{q}}_{f2}+{\mathrm{\Λ}}_f^2{q}_{f2}+C_{af2}^T\stackrel{\·}{\mathrm{\ω}}=0$

In formula, I _sfor platform cabin inertia matrix, ω is platform cabin cireular frequency, C _af1for the coefficient of coupling battle array that the vibration of+Y-direction solar array is rotated satellite hub body, C _af2for the coefficient of coupling battle array that the vibration of-Y-direction solar array is rotated satellite hub body, q _f1for+Y-direction solar array modal coordinate, q _f2for-Y-direction solar array modal coordinate, T _cfor flywheel control torque, T _d2for windsurfing rotates disturbance torque, Λ _ffor solar array model frequency diagonal matrix, ζ _ffor solar array modal damping coefficient; for platform cabin angular acceleration, for the second derivative of+Y-direction solar array modal coordinate, for the second derivative of-Y-direction solar array modal coordinate, for the first derivative of+Y-direction solar array modal coordinate, for the first derivative of-Y-direction solar array modal coordinate, l ' is the arm of force of each magnetic floating mechanism, for the vibration of+Y-direction solar array is to the transposition of the coefficient of coupling battle array that satellite hub body rotates, for the vibration of-Y-direction solar array is to the transposition of the coefficient of coupling battle array that satellite hub body rotates;

C () is set up load freight space and is put governing equation:

$M_p{a}_p=\underset{i=1}{\overset{8}{\Σ}}{F}_i$

In formula, M _pfor load cabin quality, α _pfor load cabin acceleration/accel;

(d) load cabin in the x-direction translation time, magnetic floating mechanism B2, B4 produce relative position control effort be respectively Δ F _x; In the y-direction during translation, the relative position control effort that magnetic floating mechanism B1, B3 produce is respectively Δ F _y; In the z-direction during translation, the relative position control effort that magnetic floating mechanism A1, A2, A3, A4 produce is respectively Δ F _z; In like manner, the appearance control power produced when magnetic floating mechanism A1, A2, A3, A4, B1, B2, B3, B4 makes load rotate is respectively F _a1, F _a2, F _a3, F _a4, F _b1, F _b2, F _b3, F _b4;

Translation control effort F in the x-direction _sxfor:

F _sx＝F _B2+ΔF _x+F _B4+ΔF _x＝F _B2+F _B4+2ΔF _x；

Now for translation control effort F _sxconstraint condition be: produce the moment around y-axis by magnetic floating mechanism A1, A2, A3, A4, offset by Δ F _xthe moment produced;

Translation control effort F in the y-direction _syfor:

F _sy＝F _B1+ΔF _y+F _B3+ΔF _y＝F _B1+F _B3+2ΔF _y；

Now to translation control effort F _syconstraint condition be: produce the moment around x-axis by magnetic floating mechanism A1, A2, A3, A4, offset by Δ F _ythe moment produced;

Translation control effort F in the z-direction _szfor:

F _sz＝F _A1+ΔF _z+F _A2+ΔF _z+F _A3+ΔF _z+F _A4+ΔF _z＝F _A1+F _A2+F _A3+F _A4+4ΔF _z；

By making F _b2=-F _b4, F _b1=-F _b3, F _a1+ F _a2+ F _a3+ F _a4=0, guarantee appearance control power to the translation in load cabin without any impact;

Around the rotation control effort T in x direction _rxfor:

$\begin{array}{c}{T}_{rx}=(F_{A1}+{\mathrm{\ΔF}}_z)\frac{l_1}{2}+(F_{A2}+{\mathrm{\ΔF}}_z)\frac{l_1}{2}-(F_{A3}+{\mathrm{\ΔF}}_z)\frac{l_1}{2}-(F_{A4}+{\mathrm{\ΔF}}_z)\frac{l_1}{2}\\ =(F_{A1}+F_{A2}-F_{A3}-F_{A4})\frac{l_1}{2}=(F_{A1}+F_{A2})l_1\end{array}$

In formula, l ₁for the length for magnetic floating mechanism attachment face;

Around the rotation control effort T in y direction _ryfor:

$\begin{array}{c}{T}_{ry}=-(F_{A1}+{\mathrm{\ΔF}}_z)\frac{l_3}{2}+(F_{A2}+{\mathrm{\ΔF}}_z)\frac{l_3}{2}+(F_{A3}+{\mathrm{\ΔF}}_z)\frac{l_3}{2}-(F_{A4}+{\mathrm{\ΔF}}_z)\frac{l_3}{2}\\ =(-F_{A1}+F_{A2}+F_{A3}-F_{A4})\frac{l_3}{2}=(F_{A2}+F_{A3})l_3\end{array}$

In formula, l ₃for the width for magnetic floating mechanism attachment face;

Around the rotation control effort T in z direction _rzfor:

$\begin{array}{c}{T}_{rz}=(F_{B1}+{\mathrm{\ΔF}}_y)\frac{l_3}{2}-(F_{B2}+{\mathrm{\ΔF}}_x)\frac{l_1}{2}-(F_{B3}+{\mathrm{\ΔF}}_y)\frac{l_3}{2}+(F_{B4}+{\mathrm{\ΔF}}_x)\frac{l_1}{2}\\ =(F_{B1}-F_{B3})\frac{l_3}{2}-(F_{B2}-F_{B4})\frac{l_1}{2}=F_{B1}{l}_3+F_{B4}{l}_1\end{array}$

By making F _b2=-F _b4, F _b1=-F _b3, F _a1+ F _a2+ F _a3+ F _a4=0, make the attitude in load cabin and load cabin and platform cabin relative position control effort full decoupled; Now the kinetics equation in load cabin is:

$\left\{\begin{array}{c}{I}_{px}{\stackrel{\·}{\mathrm{\ω}}}_{px}+{\mathrm{\ω}}_{px}\×\left(I_{px}{\mathrm{\ω}}_{px}\right)=(F_{A1}+{\mathrm{\ΔF}}_z)\frac{L_1}{2}+(F_{A2}+{\mathrm{\ΔF}}_z)\frac{L_1}{2}-(F_{A3}+{\mathrm{\ΔF}}_z)\frac{L_1}{2}-(F_{A4}+{\mathrm{\ΔF}}_z)\frac{L_1}{2}=2F_x{L}_1\\ I_{py}{\stackrel{\·}{\mathrm{\ω}}}_{py}+{\mathrm{\ω}}_{py}\×\left(I_{py}{\mathrm{\ω}}_{py}\right)=-(F_{A1}+{\mathrm{\ΔF}}_z)\frac{L_2}{2}+(F_{A2}+{\mathrm{\ΔF}}_z)\frac{L_2}{2}+(F_{A3}+{\mathrm{\ΔF}}_z)\frac{L_3}{2}-(F_{A4}+{\mathrm{\ΔF}}_z)\frac{L_3}{2}=2F_y{L}_3\\ I_{pz}{\stackrel{\·}{\mathrm{\ω}}}_{pz}+{\mathrm{\ω}}_{pz}\×\left(I_{pz}{\mathrm{\ω}}_{pz}\right)=(F_{B1}+{\mathrm{\ΔF}}_y)\frac{L_3}{2}-(F_{B2}+{\mathrm{\ΔF}}_x)\frac{L_1}{2}-(F_{B3}+{\mathrm{\ΔF}}_y)\frac{L_3}{2}+(F_{B4}+{\mathrm{\ΔF}}_x)\frac{L_1}{2}=F_z\left(L_1+L_3\right)\end{array}\right.$

$\left\{\begin{array}{c}{M}_p{\stackrel{\·\·}{x}}_p=F_{B2}+{\mathrm{\ΔF}}_x+F_{B4}+{\mathrm{\ΔF}}_x=2{\mathrm{\ΔF}}_x\\ M_p{\stackrel{\·\·}{y}}_p=F_{B1}+{\mathrm{\ΔF}}_y+F_{B3}+{\mathrm{\ΔF}}_y=2{\mathrm{\ΔF}}_y\\ M_p{\stackrel{\·\·}{z}}_p=F_{A1}+{\mathrm{\ΔF}}_z+F_{A2}+{\mathrm{\ΔF}}_z+F_{A3}+{\mathrm{\ΔF}}_z+F_{A4}+{\mathrm{\ΔF}}_z=4{\mathrm{\ΔF}}_z\end{array}\right.$

In formula: I _px, I _py, I _pzbe respectively the rotor inertia of load cabin around x, y, z axle, be respectively the angular acceleration of load cabin around x, y, z axle, ω _px, ω _py, ω _pzbe respectively the cireular frequency of load cabin around x, y, z axle, L ₁, L ₃, L ₂be respectively the distance of the length and width of magnetic floating mechanism attachment face, up and down attachment face, F _x, F _y, F _zbe respectively the application force of single magnetic floating mechanism in x, y, z direction, be respectively the acceleration/accel of load cabin along x, y, z axle.

Below in conjunction with accompanying drawing, the present embodiment is further described.

As shown in Figure 1, the two super satellite eight bar six degree of freedom satellite platform that the present embodiment provides and decoupling control method thereof, mainly for sound isolation, the two super satellite platform of principal and subordinate's Collaborative Control.This platform is made up of load cabin 1, platform cabin 2 and non-contacting magnetic floating mechanism 3.Load cabin 1 includes but not limited to that capacity weight 14, attitude sensor are as quiet parts such as star sensor 12, fiber optic gyros 11.Platform cabin 2 is made up of general satellite modules, includes but not limited to flexible appendage and the relative Attitude Control for Spacecraft unit 25 such as the various movable part such as windsurfing driver train 23, momentum wheel 22, solar cell array 24.Magnetic floating mechanism 3 mainly comprises coil 31, magnet steel 32, yoke 33, support 34 and relative position sensor 35 etc., and the balance position of definition coil 31 is that coil 31 is equal everywhere to the distance of magnet steel 32 radial direction.Coil 31 is connected to platform cabin 2 by support 34, magnet steel 32 and load cabin 1 are connected, without physical connection between support 34 and yoke 33, thus achieve the noncontact in two cabins, platform cabin 2 vibrates and disturbs and can not transfer to load cabin 1, reach capacity weight 14 dynamic in get quiet, the effect of two cabin sound isolation.

As shown in Figure 3, eight magnetic floating mechanisms A1, A2, A3, A4, B1, B2, B3, B4 are arranged symmetrically with.Completed the motion of load cabin six-freedom degree by this eight degrees of freedom magnetic floating mechanism, the direction hypothesis of its power as shown by the arrows in Figure 2.

The force and moment of eight magnetic floating mechanism generations is respectively:

Each power

Magnetic floating mechanism	X-direction	Y direction	Z direction
				A1	0	0	F A1
A2	0	0	F A2
				A3	0	0	F A3
A4	0	0	F A4
				B1	0	F B1	0
B2	F B2	0	0
				B3	0	F B3	0
B4	F B4	0	0

Each moment

Magnetic floating mechanism	X-direction	Y direction	Z direction
				A1	F A1L 1/2	-F A1L 3/2	0
A2	F A2L 1/2	F A2L 3/2	0
				A3	-F A3L 1/2	F A3L 3/2	0
A4	-F A4L 1/2	-F A4L 3/2	0
				B1	F B1L	0	F B1L 3/2
B2	0	-F B2L	-F B2L 1/2
				B3	F B3L	0	-F B3L 3/2

B4

0

-F B4L

F B4L 1/2

In formula, L is that load cabin barycenter is to magnetic floating mechanism center of symmetry O _adistance.

Being write as matrix form is:

$\left[\begin{array}{cccccccc}0& 0& 0& 0& 0& 1& 0& 1\\ 0& 0& 0& 0& 1& 0& 1& 0\\ 1& 1& 1& 1& 0& 0& 0& 0\\ \frac{L_1}{2}& \frac{L_1}{2}& -\frac{L_1}{2}& -\frac{L_1}{2}& L& 0& L& 0\\ -\frac{L_3}{2}& \frac{L_3}{2}& \frac{L_3}{2}& -\frac{L_3}{2}& 0& -L& 0& -L\\ 0& 0& 0& 0& \frac{L_3}{2}& -\frac{L_1}{2}& -\frac{L_3}{2}& \frac{L_1}{2}\end{array}\right]\left[\begin{array}{c}{F}_{A1}\\ F_{A2}\\ F_{A3}\\ F_{A4}\\ F_{B1}\\ F_{B2}\\ F_{B3}\\ F_{B4}\end{array}\right]=\left[\begin{array}{c}{F}_x\\ F_y\\ F_z\\ T_x\\ T_y\\ T_z\end{array}\right]$

Can by [F according to above formula _xf _yf _zt _xt _yt _z] ^tunique, the control effort [F calculating each magnetic floating mechanism that determines of situation _a1f _a2f _a3f _a4f _b1f _b2f _b3f _b4] ^t, there is not strangeness.Realize the full decoupled control of load cabin attitude and two cabin relative positions in system, load cabin attitude is regulated by appearance control power, and two cabin relative positions are regulated by relative position control effort.And the decoupling zero of satellite platform control effort is easy, control simple.

As for redundant reliability energy, as can be seen from Figure 3:

Load cabin is made along the magnetic floating mechanism of three coordinate axle straight-line motions to be:

Translation in the x-direction: B2, B4, A1, A2, A3, A4

Translation in the y-direction: B1, B3, A1, A2, A3, A4

Translation in the z-direction: A1, A2, A3, A4

The magnetic floating mechanism moved around three X-axis rotate in load cabin is:

Rotation around x direction: A1, A2, A3, A4

Rotation around y direction: A1, A2, A3, A4

Rotation around z direction: B1, B2, B3, B4

Below the situation of a magnetic floating mechanism fault and any two magnetic floating mechanism faults is considered respectively: (wherein "×" represents fault, and " √ " represents normal)

A1

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Upper table explanation is when only there being a magnetic floating mechanism fault, do not affect the motion of load cabin six-freedom degree, two magnetic floating mechanism faults have 28 kinds of modes, wherein 16 kinds of modes do not affect the motion of load cabin six-freedom degree, can find out that eight bar magnetic floating mechanism configurations achieve the redundancy backup of magnetic floating mechanism, substantially increase reliability.

The present embodiment has following beneficial effect:

The decoupling control method of two super satellite eight bar six degree of freedom satellite platform, be suitable for and be not limited to have the isolated two super satellite platform of the sound of the super steady requirement of superfinishing, by reasonable disposition magnetic floating mechanism quantity and layout, and the output of real-time dynamic assignment power realizes six degree of freedom uneoupled control with or without, size and Orientation, it is characterized in that: load cabin attitude is regulated by appearance control power, two freight spaces are put and are regulated by relative position control effort, load cabin gesture stability power equal and opposite in direction, direction is contrary, does not produce two cabin relative position control effortes; Two cabin relative position control effort equal and opposite in directions, direction is identical, does not produce the gesture stability moment to load cabin.

Eight magnetic floating mechanism symmetric configurations, A1, A2, A3, A4 are positioned at four corner locations, and direction is along Z-direction; B1, B2, B3, B4 are positioned at four limit point midways, and wherein B1, B3 are along Y direction, and B2, B4 are along X-direction.

The present embodiment is installed simple, and eight magnetic floating mechanism symmetries are installed; Simple, by reasonable disposition magnetic floating mechanism quantity and layout, and the output of real-time dynamic assignment power just can realize measuring with or without, size and Orientation, control decoupling zero.

The present embodiment easily can write out load cabin exactly along x, y, z direction translational and the power prosecutor journey around the rotation of x, y, z direction.

The decoupling control method of the present embodiment can pass through algorithm realization completely, even if load cabin gesture stability power equal and opposite in direction, direction is contrary; Two cabin relative position control effort equal and opposite in directions, direction is identical.

Appearance control power and the relative position control effort of the present embodiment can not influence each other, and mutually disturb.

By [F _xf _yf _zt _xt _yt _z] ^tsituation, can uniquely, the control effort [F calculating each magnetic floating mechanism that determines _a1f _a2f _a3f _a4f _b1f _b2f _b3f _b4] ^t, there is not strangeness.

When only having a magnetic floating mechanism fault, no matter be which in eight, do not affect the motion of load cabin six-freedom degree.

Two magnetic floating mechanism faults have 28 kinds of modes, and wherein 16 kinds of modes do not affect the motion of load cabin six-freedom degree, and namely eight bar magnetic floating mechanism configurations achieve the redundancy backup of magnetic floating mechanism, substantially increase reliability.

Regularly arranged form levitation device by one or more groups magnetic floating mechanism by certain, often organize magnetic floating mechanism main body and be made up of the mast of free-running fit and sleeve, the mast often organizing magnetic floating mechanism is affixed on a flanged plate, and sleeve is affixed on another flanged plate.

Levitation device is between load cabin and platform cabin, and its upper flange plate and load cabin are connected, and lower flange plate and platform cabin are connected.

Levitation device several pin to mechanical engagement-cellular type guide and limit structure is installed up and down, for the relative position relation in limit load cabin and platform cabin between flanged plate.

Magnetic floating mechanism utilizes but is not limited to electromagnetic force or electrostatic force mode, regulates the gap between mast and sleeve by control curent change, prevents both collisions.

Magnetic floating mechanism, except the mast cooperatively interacted and sleeve, is also integrated with position transduser, measures the relative position relation between mast and sleeve in real time.

The present embodiment is by reasonable disposition magnetic floating mechanism quantity and layout, and the output of dynamic assignment power in real time realizes six degree of freedom uneoupled control with or without, size and Orientation, and the method can pass through algorithm realization completely.Load cabin attitude is regulated by appearance control power, and two freight spaces are put and regulated by relative position control effort, load cabin gesture stability power equal and opposite in direction, and direction is contrary, does not produce two cabin relative position control effortes; Two cabin relative position control effort equal and opposite in directions, direction is identical, do not produce the gesture stability moment to load cabin, reasonably configure the size of magnetic floating mechanism and the power of generation thereof, relative position control effort between load cabin attitude and two cabins is decoupling zero, can not control to have an impact to load cabin " superfinishing is super steady ".Meanwhile, eight degrees of freedom magnetic floating mechanism system easily realize, redundancy, highly reliable.During this invention can be applied to following high score remote sensing, high precision is formed into columns, High-performance lasers communication and Space Attack etc. have the satellite platform of the requirement of high pointing accuracy, degree of stability to control to load.

Above specific embodiments of the invention are described.It is to be appreciated that the present invention is not limited to above-mentioned particular implementation, those skilled in the art can make various distortion or amendment within the scope of the claims, and this does not affect flesh and blood of the present invention.

Claims (6)

1. a two super satellite eight bar six degree of freedom satellite platform, it is characterized in that, comprise load cabin, platform cabin and levitation device, described levitation device is arranged between load cabin and platform cabin, and described load cabin and platform cabin are arranged by levitation device noncontact.

2. two super satellite eight bar six degree of freedom satellite platform according to claim 1, it is characterized in that, described levitation device comprises multiple magnetic floating mechanism, wherein each magnetic floating mechanism includes: coil, magnet steel, yoke and support, wherein, described coil is connected to platform cabin by support, and described magnet steel and load cabin are connected, without physical connection between described support and yoke, thus the noncontact achieved between load cabin and platform cabin is arranged.

3. two super satellite eight bar six degree of freedom satellite platform according to claim 2, it is characterized in that, described coil is equal everywhere to the distance of magnet steel radial direction, forms the balance position of coil.

4. two super satellite eight bar six degree of freedom satellite platform according to claim 2, it is characterized in that, described magnetic floating mechanism also comprises relative position sensor, and described relative position sensor and magnetic floating mechanism integrated design, relative position sensor measures the displacement of magnetic floating mechanism respectively.

5. two super satellite eight bar six degree of freedom satellite platform according to any one of claim 1 to 4, it is characterized in that, described levitation device comprises eight magnetic floating mechanisms, be respectively magnetic floating mechanism A1, A2, A3, A4, B1, B2, B3, B4, eight magnetic floating mechanism A1, A2, A3, A4, B1, B2, B3, B4 symmetric configurations are on platform cabin, wherein, magnetic floating mechanism A1, A2, A3, A4 are positioned at four corner locations in platform cabin, and direction is along Z-direction; Magnetic floating mechanism B1, B2, B3, B4 are positioned at four limit point midways of satellite platform, and wherein, magnetic floating mechanism B1, B3 direction is along Y direction, and magnetic floating mechanism B2, B4 direction is along X-direction.

6. a decoupling control method for the two super satellite eight bar six degree of freedom satellite platform according to any one of claim 1 to 5, is characterized in that, comprise the steps:

A () sets up load cabin attitude dynamic equations:

$I_p{\stackrel{\·}{\mathrm{\ω}}}_p+{\mathrm{\ω}}_p\×\left(I_p{\mathrm{\ω}}_p\right)=\underset{i=1}{\overset{8}{\Σ}}{l}_i\×F_i+T_{d1}$

Wherein, F _ifor the appearance control power that magnetic floating mechanism produces, T _d1for extraneous long periodic noise, can be eliminated by the effect of magnetic floating mechanism; I _pfor the inertia matrix in load cabin, for load cabin angular acceleration, ω _pfor load cabin cireular frequency, l _ifor the arm of force of each magnetic floating mechanism;

B () sets up platform cabin attitude dynamic equations:

$I_s\stackrel{\·}{\mathrm{\ω}}+\mathrm{\ω}\×\left(I_s\mathrm{\ω}\right)+C_{af1}{\stackrel{\·\·}{q}}_{f1}+C_{af1}{\stackrel{\·\·}{q}}_{f2}=T_c-\underset{i=1}{\overset{8}{\Σ}}{l}_i^{\′}\×F_i+T_{d2}$

${\stackrel{\·\·}{q}}_{f1}+2{\mathrm{\ζ}}_f{\mathrm{\Λ}}_f{\stackrel{\·}{q}}_{f1}+{\mathrm{\Λ}}_f^2{q}_{f1}+C_{af1}^T\stackrel{\·}{\mathrm{\ω}}=0$

${\stackrel{\·\·}{q}}_{f2}+2{\mathrm{\ζ}}_f{\mathrm{\Λ}}_f{\stackrel{\·}{q}}_{f2}+{\mathrm{\Λ}}_f^2{q}_{f2}+C_{af2}^T\stackrel{\·}{\mathrm{\ω}}=0$

In formula, I _sfor platform cabin inertia matrix, ω is platform cabin cireular frequency, C _af1for the coefficient of coupling battle array that the vibration of+Y-direction solar array is rotated satellite hub body, C _af2for the coefficient of coupling battle array that the vibration of-Y-direction solar array is rotated satellite hub body, q _f1for+Y-direction solar array modal coordinate, q _f2for-Y-direction solar array modal coordinate, T _cfor flywheel control torque, T _d2for windsurfing rotates disturbance torque, Λ _ffor solar array model frequency diagonal matrix, ζ _ffor solar array modal damping coefficient; for platform cabin angular acceleration, for the second derivative of+Y-direction solar array modal coordinate, for the second derivative of-Y-direction solar array modal coordinate, for the first derivative of+Y-direction solar array modal coordinate, for the first derivative of-Y-direction solar array modal coordinate, l ' is the arm of force of each magnetic floating mechanism, for the vibration of+Y-direction solar array is to the transposition of the coefficient of coupling battle array that satellite hub body rotates, for the vibration of-Y-direction solar array is to the transposition of the coefficient of coupling battle array that satellite hub body rotates;

C () is set up load freight space and is put governing equation:

$M_p{a}_p=\underset{i=1}{\overset{8}{\Σ}}{F}_i$

In formula, M _pfor load cabin quality, a _pfor load cabin acceleration/accel;

(d) load cabin in the x-direction translation time, magnetic floating mechanism B2, B4 produce relative position control effort be respectively Δ F _x; In the y-direction during translation, the relative position control effort that magnetic floating mechanism B1, B3 produce is respectively Δ F _y; In the z-direction during translation, the relative position control effort that magnetic floating mechanism A1, A2, A3, A4 produce is respectively Δ F _z; In like manner, the appearance control power produced when magnetic floating mechanism A1, A2, A3, A4, B1, B2, B3, B4 makes load rotate is respectively F _a1, F _a2, F _a3, F _a4, F _b1, F _b2, F _b3, F _b4;

Translation control effort F in the x-direction _sxfor:

F _sx＝F _B2+ΔF _x+F _B4+ΔF _x＝F _B2+F _B4+2ΔF _x；

Now for translation control effort F _sxconstraint condition be: produce the moment around y-axis by magnetic floating mechanism A1, A2, A3, A4, offset by Δ F _xthe moment produced;

Translation control effort F in the y-direction _syfor:

F _sy＝F _B1+ΔF _y+F _B3+ΔF _y＝F _B1+F _B3+2ΔF _y；

Now to translation control effort F _syconstraint condition be: produce the moment around x-axis by magnetic floating mechanism A1, A2, A3, A4, offset by Δ F _ythe moment produced;

Translation control effort F in the z-direction _szfor:

F _sz＝F _A1+ΔF _z+F _A2+ΔF _z+F _A3+ΔF _z+F _A4+ΔF _z＝F _A1+F _As+F _A3+F _A4+4ΔF _z；

By making F _b2=-F _b4, F _b1=-F _b3, F _a1+ F _a2+ F _a3+ F _a4=0, guarantee appearance control power to the translation in load cabin without any impact;

Around the rotation control effort T in x direction _rxfor:

$\begin{array}{c}{T}_{rx}=(F_{A1}+{\mathrm{\ΔF}}_z)\frac{l_1}{2}+(F_{A2}+{\mathrm{\ΔF}}_z)\frac{l_1}{2}-(F_{A3}+{\mathrm{\ΔF}}_z)\frac{l_1}{2}-(F_{A4}+{\mathrm{\ΔF}}_z)\frac{l_1}{2}\\ =(F_{A1}+F_{A2}-F_{A3}-F_{A4})\frac{l_1}{2}=(F_{A1}+F_{A2})l_1\end{array}$

In formula, l ₁for the length of magnetic floating mechanism attachment face;

Around the rotation control effort T in y direction _ryfor:

$\begin{array}{c}{T}_{ry}=-(F_{A1}+{\mathrm{\ΔF}}_z)\frac{l_3}{2}+(F_{A2}+{\mathrm{\ΔF}}_z)\frac{l_3}{2}+(F_{A3}+{\mathrm{\ΔF}}_z)\frac{l_3}{2}-(F_{A4}+{\mathrm{\ΔF}}_z)\frac{l_3}{2}\\ =(-F_{A1}+F_{A2}+F_{A3}-F_{A4})\frac{l_3}{2}=(F_{A2}+F_{A3})l_3\end{array}$

In formula, l ₃for the width of magnetic floating mechanism attachment face;

Around the rotation control effort T in z direction _rzfor:

$\begin{array}{c}{T}_{rz}=(F_{B1}+{\mathrm{\ΔF}}_y)\frac{l_3}{2}-(F_{B2}+{\mathrm{\ΔF}}_x)\frac{l_1}{2}-(F_{B3}+{\mathrm{\ΔF}}_y)\frac{l_3}{2}+(F_{B4}+{\mathrm{\ΔF}}_x)\frac{l_1}{2}\\ =(F_{B1}-F_{B3})\frac{l_3}{2}-\left(F_{B2}-F_{B4}\right)\frac{l_1}{2}=F_{B1}{l}_3+F_{B4}{l}_1\end{array}$

By making F _b2=-F _b4, F _b1=-F _b3, F _a1+ F _a2+ F _a3+ F _a4=0, make the attitude in load cabin and load cabin and platform cabin relative position control effort full decoupled; Now the kinetics equation in load cabin is:

$\left\{\begin{array}{c}{I}_{px}{\stackrel{\·}{\mathrm{\ω}}}_{px}+{\mathrm{\ω}}_{px}\×\left(I_{px}{\mathrm{\ω}}_{px}\right)=(F_{A1}+{\mathrm{\ΔF}}_z)\frac{L_1}{2}+(F_{A2}+{\mathrm{\ΔF}}_z)\frac{L_1}{2}-(F_{A3}+{\mathrm{\ΔF}}_z)\frac{L_1}{2}-(F_{A4}+{\mathrm{\ΔF}}_z)\frac{L_1}{2}=2F_x{L}_1\\ I_{py}{\stackrel{\·}{\mathrm{\ω}}}_{py}+{\mathrm{\ω}}_{py}\×\left(I_{py}{\mathrm{\ω}}_{py}\right)=-(F_{A1}+{\mathrm{\ΔF}}_z)\frac{L_2}{2}+(F_{A2}+{\mathrm{\ΔF}}_z)\frac{L_2}{2}+(F_{A3}+{\mathrm{\ΔF}}_z)\frac{L_3}{2}-(F_{A4}+{\mathrm{\ΔF}}_z)\frac{L_3}{2}=2F_y{L}_3\\ I_{pz}{\stackrel{\·}{\mathrm{\ω}}}_{pz}+{\mathrm{\ω}}_{pz}\×\left(I_{pz}{\mathrm{\ω}}_{pz}\right)=(F_{B1}+{\mathrm{\ΔF}}_y)\frac{L_3}{2}-(F_{B2}+{\mathrm{\ΔF}}_x)\frac{L_1}{2}-(F_{B3}+{\mathrm{\ΔF}}_y)\frac{L_3}{2}+(F_{B4}+{\mathrm{\ΔF}}_x)\frac{L_1}{2}=F_z\left(L_1+L_3\right)\end{array}\right.$

$\left\{\begin{array}{c}{M}_p{\stackrel{\·\·}{x}}_p=F_{B2}+{\mathrm{\ΔF}}_x+F_{B4}+{\mathrm{\ΔF}}_x=2{\mathrm{\ΔF}}_x\\ M_p{\stackrel{\·\·}{y}}_p=F_{B1}+{\mathrm{\ΔF}}_y+F_{B3}+{\mathrm{\ΔF}}_y=2{\mathrm{\ΔF}}_y\\ M_p{\stackrel{\·\·}{z}}_p=F_{A1}+{\mathrm{\ΔF}}_z+F_{A2}+{\mathrm{\ΔF}}_z+F_{A3}+{\mathrm{\ΔF}}_z+F_{A4}+{\mathrm{\ΔF}}_z=4{\mathrm{\ΔF}}_z\end{array}\right.$

In formula: I _px, I _py, I _pzbe respectively the rotor inertia of load cabin around x, y, z axle, be respectively the angular acceleration of load cabin around x, y, z axle, ω _px, ω _py, ω _pzbe respectively the cireular frequency of load cabin around x, y, z axle, L ₁, L ₃, L ₂be respectively the distance of the length and width of magnetic floating mechanism attachment face, up and down attachment face, F _x, F _y, F _zbe respectively the application force of single magnetic floating mechanism in x, y, z direction, be respectively the acceleration/accel of load cabin along x, y, z axle.