CN104022704A - Torque control strategy for three degree-of-freedom permanent magnet spherical motor - Google Patents

Abstract

The invention relates to a torque control strategy for a three degree-of-freedom permanent magnet spherical motor. The control strategy is characterized by, to begin with, decomposing a control torque into autoroatation torques and incline torques; and on this basis, allocating the autoroatation torques to different stator phase windings; with the difference of autoroatation torques of the different stator phase windings when the spherical motor rotor inclines being taken into consideration, obtaining a two-dimension torque distribution function; and finally, obtaining control current of antorotation motion directly according to the torque characteristics of the permanent magnet spherical motor. For the incline torques, according to the relative position of the incline torques and each winding torque vector, and through comparing ratio power consumption of different combination modes, incline control windings can be determined; a dimension-reduced incline torque control matrix is obtained; and the control current of incline motion can be obtained through calculating an inverse matrix of the dimension-reduced incline torque control matrix. The control strategy can improve response speed and control precision of a permanent magnet spherical motor control system, reduce torque pulsation in antorotation motion, and prevent increasing stator control current excessively.

Description

A kind of Three Degree Of Freedom permanent magnetism spherical motor torque control strategy

Affiliated technical field

The invention belongs to electric machines control technology field, relate to a kind of control method of multiple degrees of freedom permanent magnetism spherical motor.

Background technology

Along with development complicated, high-precision control system, people are also more and more higher to the requirement of the levels of precision of drive unit and stability.Permanent magnetism spherical motor is as a kind of New-type electric machine, have simple in structure, volume is little, lightweight, torque density is compared with advantages of higher, can realize the motion of rotor three degree of freedom, has improved the integrated level of system, simplified transmission device, be with a wide range of applications.

Yet due to special structure and motion mode, the control strategy of permanent magnetism spherical motor is also more complicated.In existing control program, no matter be open loop control program, or close-loop control scheme, all need to obtain stator current, and in research approach before, in order to obtain the control electric current of each stator winding, generally adopt the method that solves torque Generalized Inverse Matrix matrix, and the torque matrix of globular motor is relevant with rotor position angle, its dimension depends on stator winding number.Obviously, the time variation of torque matrix and high dimensional feature have increased the computation burden of control system, have reduced the real-time of system.There is document analyzing on the basis of permanent magnetism spherical motor torque feature, select different stator winding to control respectively tilt torque and rotating torques, obtain the torque gating matrix of 2 dimensionality reductions.Although this method has reduced the dimension of gating matrix, gating matrix increases to 2, can not reduce total operation time.

Summary of the invention

In order to overcome the above-mentioned deficiency of prior art, improve response speed, the control precision of permanent magnetism spherical electric machine control system, torque pulsation while reducing spinning motion, and avoided increasing greatly stator and control electric current, the present invention proposes a kind of control control program based on Torque-sharing strategy.Technical scheme of the present invention is as follows:

A kind of Three Degree Of Freedom permanent magnetism spherical motor torque control strategy, applicable motor is three degree of freedom spherical motor, comprise base, spherical stator wall, stator coil and rotor, rotor is positioned at stator wall, and its output shaft stretches out from the opening part of stator wall top, it is characterized in that, stator coil is cylindricality non iron-core structure, along being uniformly distributed 3 layers on the parallel parallel in the Ji Yu equator, equator of spherical stator wall, being radial and being fixed on spherical stator wall; Rotor surface is embedded with permanent magnet pole, magnetic pole is along being divided into two-layerly up and down with equator, and the N utmost point and the S utmost point of every layer are alternately distributed, and this control strategy is: first controlling torque is decomposed into rotation torque and tilt torque, on this basis, rotation torque distribution is arrived to different stator phase windings; While considering globular motor rotor tilt, the difference of different stator winding rotation torques, obtains two-dimentional torque distribution function, finally according to permanent magnetism spherical motor torque characteristic, can directly obtain the control electric current of spinning motion.For tilt torque, according to the relative position between tilt torque and each winding torque vector, by comparing the ratio power consumption of various combination mode, determine inclination control winding, obtain the tilt torque gating matrix of dimensionality reduction, by solving the control electric current of the torque gating matrix inverse matrix acquisition banking motion after dimensionality reduction.

Specifically comprise following step:

(1) utilize the numerical algorithms such as Finite Element or analytic method to obtain rotation torque and the tilt torque characteristic of motor, with form or formula form, store;

(2) adopt rotary encoder and angular transducer detection rotor position signalling, and carry out Eulerian angles conversion, obtain the Eulerian angles (α, β, γ) of describing rotor position information;

(3) given trace of establishing permanent magnetism spherical motor is (α _d, β _d, γ _d), by given trace and actual angle, adopt calculating torque method, determine the needed target control torque tau of motor ^*=[τ _α ^*τ _β ^*τ _γ ^*];

(4) target torque is decomposed into the rotation torque reference value τ under rotor coordinate _p ^*with tilt torque reference value τ _dq ^*;

(5) stator winding is numbered, if two stator winding are positioned at the two ends of a diameter of stator spheroid, be referred to as one group of winding, set bulbec face and number and be followed successively by 1,2,3,4 along the stator winding in equator, and upper and lower two-layer winding be divided into A, B, C, D tetra-phases, A+ representative is when this stator winding is given as forward current, this attracts S polarity rotor magnetic pole mutually, repels N polarity rotor magnetic pole, when A is conducted, the current polarity that A+, A-give is contrary, to synthesize rotation torque;

A, the B, C, D tetra-phases that for the upper and lower two-layer winding of stator, form, application of torque is distributed thought, determines the one dimension partition function of each phase subscript i represents stator phase, for the coordinate of stator phase winding in rotor coordinate converted a longitude angle under rotor magnetic pole, consider the difference of two groups of stator winding torque characteristics of each phase when rotor of output shaft axle tilts, each phase rotation torque is carried out to secondary distribution between two windings, and the partition function of winding is respectively subscript i+, i-represent two groups of stator winding of i phase, θ _i+, θ _i-for the coordinate of two windings of i phase in rotor coordinate converted an angle of latitude under rotor magnetic pole;

(6), for intermediate layer stator winding 1,2,3,4 phases, according to motor tilt torque characteristic and stator winding coordinate, can obtain the tilt torque T that 1-4 phase winding produces ₁ ^θ, T ₂ ^θ, T ₂ ^θ, T ₃ ^θ,, T ₄ ^θ.Utilize 4 tilt torque vectors that rotor equatorial plane is divided into I, II, III, four sectors of IV;

(7) select synthetic target tilt torque τ _dq ^*torque component:

(a) if τ _dqbe positioned at sector I, alternative torque vector is (T _{3 θ}, T _{4 θ}), (T _{3 θ}, T _{1 θ}), (T _{2 θ}, T _{4 θ}), (T _{2 θ}, T _{1 θ}); Calculate that each group produces than power consumption p ₃₄ ^*, p ₃₁ ^*, p ₂₄ ^*, p ₂₁ ^*, the stator winding pair of selection power consumption minimum;

(b) if τ _dqbe positioned at sector II, alternative torque vector is (T _{1 θ}, T _{4 θ}), (T _{1 θ}, T _{3 θ}), (T _{2 θ}, T _{4 θ}), (T _{2 θ}, T _{3 θ}); Calculate that each group produces than power consumption p ₁₄ ^*, p ₁₃ ^*, p ₂₄ ^*, p ₂₃ ^*, subscript represents different combinations, selects the stator winding pair of power consumption minimum;

(c) if τ _dqbe positioned at sector III, alternative torque vector is (T _{2 θ}, T _{4 θ}), (T _{2 θ}, T _{1 θ}), (T _{3 θ}, T _{4 θ}), (T _{3 θ}, T _{1 θ}); Calculate that each group produces than power consumption p ₂₄ ^*, p ₂₁ ^*, p ₃₄ ^*, p ₃₁ ^*, the stator winding pair of selection power consumption minimum;

(d) if τ _dqbe positioned at sector IV, alternative torque vector is (T _{1 θ}, T _{4 θ}), (T _{2 θ}, T _{3 θ}), (T _{1 θ}, T _{3 θ}), (T _{2 θ}, T _{4 θ}); Calculating each group produces

Than power consumption p ₁₄ ^*, p ₂₃ ^*, p ₁₃ ^*, p ₂₄ ^*, the stator winding pair of selection power consumption minimum;

(8) on above-mentioned two groups of winding bases selecting, choose A, B, C, D tetra-mutually in the winding of two groups of inclination windings on same stator meridian, totally six groups of stator winding are as inclination control winding;

(9) the torque distribution function in (5) with rotation torque reference value τ _p ^*obtain the torque set-point of each phase winding of stator, according to globular motor rotation torque characteristics, try to achieve each winding of stator of spinning motion and control electric current;

(10), according to globular motor tilt torque characteristic, obtain the torque matrix T of (8) medium dip winding _n2, solve its inverse matrix according to tilt torque reference value τ _dq ^*try to achieve each winding of stator of banking motion and control electric current;

(11) by (9), (10), obtain the total control electric current of each winding of stator;

(12) utilize Hysteresis Current Control Strategy, control in real time the size and Orientation of the electric current of each winding, make the torque of rotor output expection, follow the tracks of desired trajectory.

Beneficial effect of the present invention is as follows:

1, the multifreedom motion of permanent magnetism spherical motor on can implementation space, can be applied to the high accuracy control fields such as joint of robot, panoramic shooting instrument, simplifies the structure of mechanical system.

2, in permanent magnetism spherical motor, application of torque is distributed thought, can control respectively spinning motion and the banking motion of motor, increases the flexibility of controlling.

Each stator winding torque reference value while 3, utilizing torque distribution function to obtain spinning motion, the stator that has reduced spinning motion is controlled the Current calculation time, and the torque pulsation problem can reduce spinning motion time.

4, the position at the rotor equatorial plane according to the set-point of tilt torque vector, select the control winding of banking motion, both reduced the dimension of inclination control torque, the stator that has reduced banking motion is controlled the Current calculation time, can avoid again increasing greatly stator current.

Accompanying drawing explanation

Fig. 1 (a) Three Degree Of Freedom permanent magnetism spherical electric machine structure figure; Fig. 1 (b) rotor ball body structure figure.Number in the figure name is called: 1 stator wall; 2 stator coils; 3 coil bolts; 4 ball rotors; 5 output shafts; 6 bases; 41 permanent magnet poles.

Fig. 2 control system block diagram.

Fig. 3 PD controller block diagram.

Torque decomposing schematic representation in Fig. 4 rotor coordinate.

Fig. 5 stator winding distribution schematic diagram.

Fig. 6 cosine torque distribution function.

Fig. 7 A+ winding two dimension torque distribution function.

Fig. 8 tilt torque control method, (a) (b) torque composition principle is divided in rotor equatorial plane sector.

Fig. 9 permanent magnetism spherical motor torque characteristic, (a) rotation torque (b) tilt torque.

Figure 10 nutation movement track following situation, (a) α axle response (b) β axle response (c) γ axle response.

Figure 11 nutation movement output shaft movement locus.

Figure 12 nutation movement tracking error situation, (a) α axis error (b) β axis error (c) γ axis error.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in further details.

The present invention be directed to a kind of new torque distribution control strategy that novel permanent magnetic globular motor proposes, can, when realizing spinning motion and the banking motion decoupling zero control of motor, reducing torque pulsation, improve the computing time that stator is controlled electric current.

Motor basic structure as shown in Figure 1.The applicable Three Degree Of Freedom permanent magnetism spherical motor of the present invention comprises support section, stator and spherical spinner transducer four parts, wherein, support section comprises stator wall 1, base 6, stator comprises air core coil 2, coil bolt (3), fixing output shaft 5 on spherical spinner 4, and rotor 4 is positioned at stator wall 1, rotor of output shaft axle 5 is stretched out from the opening part of stator wall top, and motor basic structure is as shown in Fig. 1 (a).Rotor surface is pasted permanent magnet pole 41, and magnetic pole is divided into two-layer up and down along equator, every layer of 6 utmost point, and alternately, upper and lower two-layer magnetic pole N, the S utmost point are alternately for every one deck magnetic pole N, the S utmost point.As shown in Fig. 1 (b).

As shown in Figure 2, outer shroud is position and speed ring to control block diagram, and interior ring is electric current loop.Rotary encoder and angular transducer detect rotor-position, obtain Eulerian angles θ=(α, β, the γ) that stator coordinate lower rotor part turns over, and PD controller is according to the given position angle θ of input _d=(α _d, β _d, γ _d) and value of feedback θ, the error signal e of calculating location and speed and output torque control signal τ ^*=[τ _α ^*τ _β ^*τ _γ ^*], controller is decomposed into the rotation torque reference value τ under rotor coordinate by target torque _p ^*with tilt torque reference value τ _dq ^*, to realize decoupling zero, control.Torque distribution unit is according to given rotational component τ _p ^*, tilt component τ _dq ^*and rotor-position Eulerian angles (α, β, γ) select different energising windings, and calculate each winding current reference value.Interior circular current ring adopts stagnant ring comparison strategy, according to the switching signal of current reference value and current feedback signal output winding.

Below will be described further from controller design, Torque-sharing strategy, three aspects of simulation analysis.

1, controller design

Permanent magnetism spherical motor is input more than, many output, the nonlinear system of close coupling.This Non-linear coupling directly affect permanent magnet spherical motor servo system dynamic property and control precision.Adopt a kind of feedforward PD control algolithm--computing power moments method, the coupling terms of reconstruction model, realizes decoupling zero and controls.

Consider continuous path motion, position deviation is defined as

$\left\{\begin{array}{c}e={\mathrm{\θ}}_d-\mathrm{\θ}\\ \stackrel{\·}{e}={\stackrel{\·}{\mathrm{\θ}}}_d-\stackrel{\·}{\mathrm{\θ}}\end{array}\right.---\left(1\right)$

In formula, θ _dfor given angle amount, θ _d=(α _dβ _dγ _d), for θ _dfirst derivative to the time, θ is feedback angle amount, θ=(α β γ), $\stackrel{\·}{\mathrm{\θ}}=\left(\begin{array}{ccc}\stackrel{\·}{\mathrm{\α}}& \stackrel{\·}{\mathrm{\β}}& \stackrel{\·}{\mathrm{\γ}}\end{array}\right),$ for θ _dfirst derivative to the time, $\stackrel{\·}{\mathrm{\θ}}=\left(\begin{array}{ccc}\stackrel{\·}{\mathrm{\α}}& \stackrel{\·}{\mathrm{\β}}& \stackrel{\·}{\mathrm{\γ}}\end{array}\right),$

Definition

$u={\stackrel{\·\·}{\mathrm{\θ}}}_d+K_d\stackrel{\·}{e}+K_{p}e---\left(2\right)$

In formula, Kp is proportionality coefficient matrix, and Kd is differential coefficient matrix, and the two is all positive definite diagonal matrix; for θ _dsecond dervative to the time.

The control rate of computing power moments method is:

$\mathrm{\τ}=M\left(\mathrm{\θ}\right)u+C(\mathrm{\θ},\stackrel{\·}{\mathrm{\θ}})\stackrel{\·}{\mathrm{\θ}}---\left(3\right)$

$C=\left(\begin{array}{ccc}(J_p-J_q)\stackrel{\·}{\mathrm{\β}}\mathrm{c\βs\β}& (J_p-J_q)\stackrel{\·}{\mathrm{\α}}\mathrm{c\βs\β}& J_p\stackrel{\·}{\mathrm{\α}}\mathrm{c\βs\β}\\ -(J_p-J_q)\stackrel{\·}{\mathrm{\α}}\mathrm{c\βs\β}& 0& -J_p\stackrel{\·}{\mathrm{\α}}\mathrm{c\β}\\ 0& J_p\stackrel{\·}{\mathrm{\α}}\mathrm{c\β}& 0\end{array}\right)---\left(4\right)$

$M=\left(\begin{array}{ccc}{J}_q{c}^2\mathrm{\β}+J_p{s}^2\mathrm{\β}& 0& J_p\mathrm{s\β}\\ 0& J_q& 0\\ J_p\mathrm{s\β}& 0& J_p\end{array}\right)---\left(5\right)$

In formula, τ is control moment vector, comprises τ _α, τ _β, τ _γthree components.M (θ) is inertial matrix, for coriolis force matrix.J _d, J _q, J _pbe respectively three of the motor rotor coordinate systems moment of inertia on axially, J _d=J _q≠ J _p, c and s are respectively the abbreviations of cos and sin, τ _ffor each axial friction of Eulerian angles and load torque vector.

In real system, consider the uncertain factors such as the accuracy of manufacture, be difficult to obtain accurate motor model, therefore to inertial matrix M (θ) and coriolis force matrix compensate

$\left\{\begin{array}{c}M\left(\mathrm{\θ}\right)=M_0\left(\mathrm{\θ}\right)+\mathrm{\ΔM}\left(\mathrm{\θ}\right)\\ C(\mathrm{\θ},\stackrel{\·}{\mathrm{\θ}})=C_0(\mathrm{\θ},\stackrel{\·}{\mathrm{\θ}})+\mathrm{\ΔC}(\mathrm{\θ},\stackrel{\·}{\mathrm{\θ}})\end{array}\right.---\left(6\right)$

In formula, M ₀(θ), for actual inertial matrix and the coriolis force matrix of definition, Δ M (θ), uncertain error for matrix.

Use M ₀(θ), replacement M (θ), formula (3) can be changed into

$\mathrm{\τ}=M_0\left(\mathrm{\θ}\right)u+C_0(\mathrm{\θ},\stackrel{\·}{\mathrm{\θ}})\stackrel{\·}{\mathrm{\θ}}---\left(7\right)$

In formula, τ, for controlling the output valve of controller, is torque reference value.Controller block diagram as shown in Figure 3.

In rotor d-q-p coordinate system, the torque of permanent magnetism spherical Electric Machine Control can be decomposed into the component τ of d, q, p axle _d, τ _q, τ _p, can be expressed as

$\left[\begin{array}{c}{\mathrm{\τ}}_d\\ {\mathrm{\τ}}_q\\ {\mathrm{\τ}}_p\end{array}\right]=\left[\begin{array}{ccc}-\mathrm{c\γ}/\mathrm{s\β}& \mathrm{s\γ}& \mathrm{c\γ}\\ \mathrm{s\γ}/\mathrm{s\β}& \mathrm{c\γ}& -\mathrm{s\γ}\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}{\mathrm{\τ}}_{\mathrm{\α}}\\ {\mathrm{\τ}}_{\mathrm{\β}}\\ {\mathrm{\τ}}_{\mathrm{\γ}}\end{array}\right]---\left(8\right)$

In formula, τ _pfor rotation controlling torque, and τ _d, τ _qtilt component τ in synthetic d-q plane _dq, as shown in Figure 4.

2, Torque-sharing strategy

For expressing conveniently, stator winding is numbered.If two stator winding are positioned at the two ends of a diameter of stator spheroid, be referred to as one group of winding, so the present invention is divided into 12 groups of windings, stator winding distribution schematic diagram is as shown in Figure 5.Set bulbec face and be followed successively by 1,2,3,4 along the stator winding numbering in equator, and upper and lower two-layer winding is divided into A, B, C, D tetra-phases, A+ represent when this stator winding is given as forward current, and this attracts S polarity rotor magnetic pole mutually, repulsion N polarity rotor magnetic pole.When A is conducted, the current polarity that A+, A-give is contrary, to synthesize rotation torque.

(1) rotation torque is controlled

Adopt one dimension torque distribution function that rotation torque distribution is arrived to A, B, C, D tetra-phases, torque distribution function is not unique, can be linear function, nonlinear function (as cosine function, exponential function etc.), and Fig. 6 is cosine partition function, and its expression formula is

I=A in formula, D, C, B, for the longitude angle under stator winding reduction to rotor magnetic pole of i phase, in corresponding diagram 6, the angle of flow of i phase,, the pass angle of rupture of the angle of flow of i+1 phase, i phase differs 15 ° of mechanical angles successively, can guarantee to seamlessly transit in each phase torque of commutation period so respectively.

When globular motor rotor tilt, under same current excitation, two windings of same phase are because the change of coordinate produces different static rotation torques, so rotation torque need to carry out secondary distribution between two windings, and function expression is as follows:

In formula refer to respectively the partition function of i phase " ± " winding, θ _i+, θ _i-for the angle of latitude under a rotor magnetic pole of the coordinate conversion of two windings of i phase in rotor coordinate, τ _{γ (i+)}, τ _{γ (i-)}be respectively the static rotation torque of i phase stator winding " ± " winding unit.As shown in Figure 7, other each winding similarly for the two-dimentional torque distribution function of A+ winding.

Therefore, each phase winding rotation torque reference value can be expressed as

Position by stator winding under rotor coordinate, can obtain the static rotation torque component of unit of each stator winding current i is controlled in winding rotation _p,ifor

By each winding current combination, can obtain rotation and control current vector I ₁.

(2) tilt torque is controlled

Compare levels stator winding, intermediate layer stator winding is large to the contribution of tilt torque.In rotor d-q face (equatorial plane), the space phase relation of the tilt torque vector that intermediate layer stator winding produces as shown in Figure 8 (a), the torque vector of 4 phase windings is divided into four sector I, II, III, IV by plane, but amplitude and the phase place of four vectors change with rotor motion, can by coordinate transform, be obtained according to permanent magnetism spherical motor tilt torque characteristic.

From Fig. 8 (b), can find out, as utilize the target tilt torque τ in the I of the synthetic sector of two phase windings _dq, can have 4 kinds of different schemes, i.e. (T _{3 θ}, T _{4 θ}), (T _{3 θ}, T _{1 θ}), (T _{2 θ}, T _{4 θ}), (T _{2 θ}, T _{1 θ}), but required winding current and the power consumption of different schemes is different.When stator winding is positioned at rotor magnetic pole boundary vicinity, the tilt torque of generation is approximately 0, even if this winding produces a less tilt torque component, its current amplitude is also larger.For fear of choosing this unfavorable scheme, need comprehensive relatively 4 kinds of schemes.

With (T _{3 θ}, T _{4 θ}) be example, Fig. 8 (b) has described the composition principle of torque vector, and the relation between target torque and phase winding torque component can be expressed as

τ _dq＝T _3θi ₃+T _4θi ₄ (13)

I in formula ₃, i ₄it is respectively phase winding electric current.

Winding current can be expressed as

ⁱ ₃＝τ _dq·T ⁽³⁾

(14)

ⁱ ₄＝τ _dq·T ⁽⁴⁾

Wherein

$\begin{array}{c}{T}^{\left(3\right)}=\frac{j{T}_{4\mathrm{\θ}}}{T_{3\mathrm{\θ}}\·j{T}_{4\mathrm{\θ}}}\\ T^{\left(4\right)}=\frac{j{T}_{3\mathrm{\θ}}}{T_{4\mathrm{\θ}}\·j{T}_{3\mathrm{\θ}}}\end{array}---\left(15\right)$

For each winding of more different synthesis modes produces than power consumption, definition than power consumption is

${p_{34}}^{*}=\frac{{i_3}^2+{i_4}^2}{{{\mathrm{\τ}}_{\mathrm{dq}}}^2}{T}^{{\left(3\right)}^2}+T^{{\left(4\right)}^2}---\left(16\right)$

In like manner, calculate other combination results than power consumption p ₃₁ ^*, p ₂₄ ^*, p ₂₁ ^*, two groups of windings of selection power consumption minimum.On this basis, also need to add other winding ability synthesis type torque reference value, the winding newly adding should avoid producing extra tilt torque as far as possible, and offsets the rotating torques that inclination winding produces.The present invention directly chooses and the levels of two groups of inclination windings on same stator meridian 4 windings totally.Therefore have 6 groups of inclination control windings, according to permanent magnetism spherical motor tilt torque characteristic, by coordinate transform, obtain corresponding static torque matrix T _n2∈ R ^{3 * 6}.

It will be noted that after rotation winding energising except producing rotation torque, also produce additional tilt torque,

τ ₁＝[τ _α1 τ _β1] ^T＝T _n1I ₁ (17)

In formula, subscript T represents transposition computing, T _n1∈ R ^{2 * 4}for the corresponding static tilt torque of conducting stator winding matrix, I ₁2 current vectors of totally 4 windings mutually for conducting.

Therefore the torque that the winding that tilts produces can be expressed as

τ ₂＝τ ^*-τ ₁＝[τ _α ^*-τ _α1 τ _β ^*-τ _β1 0] (18)

The control current vector I of banking motion ₂can try to achieve according to following formula

$I_2=T_{n2}^{-1}{\mathrm{\τ}}_2---\left(19\right)$

In formula, for T _n2generalized inverse matrix.

By I ₁with I ₂merge, can obtain overall control current vector.

I＝[I ₁ I ₂] (20)

In formula, symbol [] represents union operation, on the basis merging at common vector, by the current summation of identical winding.

The coil current I being obtained by formula (20) is as being input in hysteresis comparator with reference to electric current, the switching signal drawing is controlled opening and turn-offing of main circuit power tube, make the given reference current of current tracking of stator coil, finally realize the Three Degree Of Freedom stable operation of permanent magnetism spherical motor.

3, simulation analysis.

For verifying the validity of control strategy proposed by the invention, utilize Matlab/Simulink emulation platform to study the permanent magnetism spherical motor control strategy based on torque distribution.In emulation, DC bus-bar voltage is 10V, and the parameter of permanent magnetism spherical motor is as shown in table 1, and its torque characteristics as shown in Figure 9.

The structure and material parameter of table 1 motor

PD parameter is set to K _p=diag[140 140 140], K _d=diag[35 35 35]; Interior ring is electric current loop, considers hysteresis band ε=0.1.Δ M (θ)=-0.1M (θ), in order better to check the performance of permanent magnetism spherical motor, make rotor do nutation movement, desired trajectory θ is set _d=[0.2sin2t 0.4cos2t 2t].

Figure 10 is for adopting the control strategy based on torque distribution proposed by the invention, and permanent magnetism spherical motor is for the tracking situation of given trace, the movement locus of Figure 11 output shaft on stator sphere, and Figure 12 is that the error in motor operation course is followed the tracks of situation.From simulation result, can find out, owing to there is certain coupling situation in each axial motion of permanent magnetism spherical motor, and the uncertainty of electric machine structure makes track following occur a little bias, but still in permissible range, within error is controlled at 0.1rad substantially, embodied under model structure uncertainty, control strategy proposed by the invention is tracing preset track well, and control system has good robustness and dynamic property.In order further to reduce tracking error, can adopt the Advanced Control Strategies such as neural net, decoupling zero control to replace, optimize PD controller.

When actual control system designs, must consider the realizability of algorithm.In globular motor control system, the computing time of generalized inverse matrix, the increase along with dimension was how much multiples growths, inverting of higher dimensional matrix taken the ample resources of digital processing unit, increased the computation burden of digital processing unit, had a strong impact on the control effect of system.Table 2 has compared the computing time of the Generalized Inverse Matrix matrix of different dimensions, digital signal processor model is TMS320F2812, its clock cycle is 150MHz, and the Torque-sharing strategy that visible the present invention proposes can effectively reduce matrix dimension, has higher arithmetic speed.

The contrast of table 2 computation complexity

Claims (2)

1. a Three Degree Of Freedom permanent magnetism spherical motor torque control strategy, applicable motor is three degree of freedom spherical motor, comprise base, spherical stator wall, stator coil and rotor, rotor is positioned at stator wall, and its output shaft stretches out from the opening part of stator wall top, it is characterized in that, stator coil is cylindricality non iron-core structure, along being uniformly distributed 3 layers on the parallel parallel in the Ji Yu equator, equator of spherical stator wall, being radial and being fixed on spherical stator wall; Rotor surface is embedded with permanent magnet pole, magnetic pole is along being divided into two-layerly up and down with equator, and the N utmost point and the S utmost point of every layer are alternately distributed, and this control strategy is: first controlling torque is decomposed into rotation torque and tilt torque, on this basis, rotation torque distribution is arrived to different stator phase windings; While considering globular motor rotor tilt, the difference of different stator winding rotation torques, obtains two-dimentional torque distribution function, finally according to permanent magnetism spherical motor torque characteristic, can directly obtain the control electric current of spinning motion.For tilt torque, according to the relative position between tilt torque and each winding torque vector, by comparing the ratio power consumption of various combination mode, determine inclination control winding, obtain the tilt torque gating matrix of dimensionality reduction, by solving the control electric current of the torque gating matrix inverse matrix acquisition banking motion after dimensionality reduction.

2. control strategy according to claim 1, is characterized by, and specifically comprises following step:

(1) utilize the numerical algorithms such as Finite Element or analytic method to obtain rotation torque and the tilt torque characteristic of motor, with form or formula form, store;

(2) adopt rotary encoder and angular transducer detection rotor position signalling, and carry out Eulerian angles conversion, obtain the Eulerian angles (α, β, γ) of describing rotor position information;

(3) given trace of establishing permanent magnetism spherical motor is (α _d, β _d, γ _d), by given trace and actual angle, adopt calculating torque method, determine the needed target control torque tau of motor ^*=[τ _α ^*τ _β ^*τ _γ ^*];

(4) target torque is decomposed into the rotation torque reference value τ under rotor coordinate _p ^*with tilt torque reference value τ _dq ^*;

(5) stator winding is numbered, if two stator winding are positioned at the two ends of a diameter of stator spheroid, be referred to as one group of winding, set bulbec face and number and be followed successively by 1,2,3,4 along the stator winding in equator, and upper and lower two-layer winding be divided into A, B, C, D tetra-phases, A+ representative is when this stator winding is given as forward current, this attracts S polarity rotor magnetic pole mutually, repels N polarity rotor magnetic pole, when A is conducted, the current polarity that A+, A-give is contrary, to synthesize rotation torque;

A, the B, C, D tetra-phases that for the upper and lower two-layer winding of stator, form, application of torque is distributed thought, determines the one dimension partition function of each phase subscript i represents stator phase, for the coordinate of stator phase winding in rotor coordinate converted a longitude angle under rotor magnetic pole, consider the difference of two groups of stator winding torque characteristics of each phase when rotor of output shaft axle tilts, each phase rotation torque is carried out to secondary distribution between two windings, and the partition function of winding is respectively subscript i+, i-represent two groups of stator winding of i phase, θ _i+, θ _i-for the coordinate of two windings of i phase in rotor coordinate converted an angle of latitude under rotor magnetic pole;

(6), for intermediate layer stator winding 1,2,3,4 phases, according to motor tilt torque characteristic and stator winding coordinate, can obtain the tilt torque T that 1-4 phase winding produces ₁ ^θ, T ₂ ^θ, T ₂ ^θ, T ₃ ^θ,, T ₄ ^θ.Utilize 4 tilt torque vectors that rotor equatorial plane is divided into I, II, III, four sectors of IV;

(7) select synthetic target tilt torque τ _dq ^*torque component:

(a) if τ _dqbe positioned at sector I, alternative torque vector is (T _{3 θ}, T _{4 θ}), (T _{3 θ}, T _{1 θ}), (T _{2 θ}, T _{4 θ}), (T _{2 θ}, T _{1 θ}); Calculate that each group produces than power consumption p ₃₄ ^*, p ₃₁ ^*, p ₂₄ ^*, p ₂₁ ^*, the stator winding pair of selection power consumption minimum;

(b) if τ _dqbe positioned at sector II, alternative torque vector is (T _{1 θ}, T _{4 θ}), (T _{1 θ}, T _{3 θ}), (T _{2 θ}, T _{4 θ}), (T _{2 θ}, T _{3 θ}); Calculate that each group produces than power consumption p ₁₄ ^*, p ₁₃ ^*, p ₂₄ ^*, p ₂₃ ^*, subscript represents different combinations, selects the stator winding pair of power consumption minimum;

(c) if τ _dqbe positioned at sector III, alternative torque vector is (T _{2 θ}, T _{4 θ}), (T _{2 θ}, T _{1 θ}), (T _{3 θ}, T _{4 θ}), (T _{3 θ}, T _{1 θ}); Calculate that each group produces than power consumption p ₂₄ ^*, p ₂₁ ^*, p ₃₄ ^*, p ₃₁ ^*, the stator winding pair of selection power consumption minimum;

(d) if τ _dqbe positioned at sector IV, alternative torque vector is (T _{1 θ}, T _{4 θ}), (T _{2 θ}, T _{3 θ}), (T _{1 θ}, T _{3 θ}), (T _{2 θ}, T _{4 θ}); Calculate that each group produces than power consumption p ₁₄ ^*, p ₂₃ ^*, p ₁₃ ^*, p ₂₄ ^*, the stator winding pair of selection power consumption minimum;

(8) on above-mentioned two groups of winding bases selecting, choose A, B, C, D tetra-mutually in the winding of two groups of inclination windings on same stator meridian, totally six groups of stator winding are as inclination control winding;

(9) the torque distribution function in (5) with rotation torque reference value τ _p ^*obtain the torque set-point of each phase winding of stator, according to globular motor rotation torque characteristics, try to achieve each winding of stator of spinning motion and control electric current;

(10), according to globular motor tilt torque characteristic, obtain the torque matrix T of (8) medium dip winding _n2, solve its inverse matrix according to tilt torque reference value τ _dq ^*try to achieve each winding of stator of banking motion and control electric current;

(11) by (9), (10), obtain the total control electric current of each winding of stator;

(12) utilize Hysteresis Current Control Strategy, control in real time the size and Orientation of the electric current of each winding, make the torque of rotor output expection, follow the tracks of desired trajectory.