CN104022704B - 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

Art

The invention belongs to motor control technology field, it is related to a kind of control method of multiple degrees of freedom permanent magnetism spherical motor.

Background technology

With complicated, high-precision control system continuous development, people are to the levels of precision of driving means and stability Requirement also more and more higher.Permanent magnetism spherical motor as a kind of New-type electric machine, have that structure is simple, small volume, lightweight, torque The advantages of density is higher, it is possible to achieve the motion of rotor three degree of freedom, improves the integrated level of system, simplifies transmission dress Put, be with a wide range of applications.

However, due to special structure and motion mode, the control strategy of permanent magnetism spherical motor is also more complicated.Existing Control program in, either opened loop control scheme, or close-loop control scheme, be required for obtaining stator current, and before In research approach, in order to obtain the control electric current of each stator winding, the method for commonly used solution 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, torque matrix Time variation and high dimensional feature increase the computation burden of control system, reduce the real-time of system.There is document in analysis permanent magnetism On the basis of globular motor torque characteristic, select different stator winding to control tilt torque and rotating torques respectively, obtain 2 The direct torque matrix of dimensionality reduction.Although this method reduces the dimension controlling matrix, matrix is controlled to increase to 2, and Total operation time can not be reduced.

Content of the invention

In order to overcome the above-mentioned deficiency of prior art, improve the response speed of permanent magnetism spherical electric machine control system, control essence Degree, reduces torque pulsation during spinning motion, and avoids too greatly increasing stator control electric current, and the present invention proposes a kind of being based on and turns The control control program of square allocation strategy.Technical scheme is as follows:

A kind of Three Degree Of Freedom permanent magnetism spherical motor torque control strategy, the motor being suitable for is three degree of freedom spherical motor, Including base, spherical stator wall, stator coil and rotor, rotor is located in stator wall, its output shaft opening above stator wall Stretch out at mouthful it is characterised in that stator coil is cylindricality iron-free core structure, along the equator of spherical stator wall and parallel with equator It is uniformly distributed 3 layers on parallel, radial be fixed on spherical stator wall；Rotor surface is embedded with permanent magnet pole, magnetic pole along with Equator is divided into upper and lower two-layer, and every layer of n pole and s pole are alternately distributed, and this control strategy is: torque will be controlled to be decomposed into rotation first Torque and tilt torque, on this basis, rotation torque are assigned to different stator phase windings；Incline in view of globular motor rotor When tiltedly, the difference of different stator winding rotation torques, obtain two-dimentional torque partition function, finally according to permanent magnetism spherical motor torque Characteristic can directly obtain the control electric current of spinning motion.For tilt torque, according between tilt torque and each winding torque vector Relative position, by comparing the ratio power consumption of various combination mode, determine inclination control winding, obtain the tilt torque of dimensionality reduction Control matrix, the direct torque matrix inverse matrix after solving dimensionality reduction obtains the control electric current of banking motion.

Specifically include following step:

(1) numerical algorithms such as FInite Element or analytic method is utilized to obtain rotation torque and the tilt torque characteristic of motor, with Form or formula form storage；

(2) adopt rotary encoder and angular transducer to detect rotor-position signal, and carry out Eulerian angles conversion, acquisition is retouched State the Eulerian angles (α, β, γ) of rotor position information；

(3) set the given trace of permanent magnetism spherical motor as (α_d、β_d、γ_d), by given trace and actual angle, using calculating Torque method, determines target control torque τ required for 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, positioned at the two ends of one diameter of stator spheroid, claim Be one group of winding, the stator winding numbering setting bulbec face along equator is followed successively by 1,2,3,4, and upper and lower two-layer winding be divided into a, B, c, d tetra- phase, a+ represents when this stator winding is given as forward current, and this mutually attracts s polarity rotor magnetic pole, repels n polarity Rotor magnetic pole, when a is conducted, the current polarity that a+, a- are given is contrary, to synthesize rotation torque；

A, b, c, d tetra- phase that the winding of two-layer up and down of stator is constituted, application torque distribution thought, determine the one of each phase Dimension partition functionSubscript i represents stator phase,Convert one for coordinate in rotor coordinate for the stator phase winding to turn Longitude angle under sub- magnetic pole it is contemplated that when rotor of output shaft axle tilts two groups of stator winding torque characteristics of each phase difference, will be each Phase rotation torque carries out secondary distribution between two windings, and the partition function of winding is respectivelyUnder Mark i+, i- represent two groups of stator winding of the i-th phase, θ_i+、θ_i-Convert for coordinate in rotor coordinate for two windings of i phase Angle of latitude under one rotor magnetic pole；

(6) for intermediate layer stator winding 1,2,3,4 phase, according to motor tilt torque characteristic and stator winding coordinate, can Obtain tilt torque t of 1-4 phase winding generation₁ ^θ、t₂ ^θ、t₂ ^θ、t₃ ^θ,、t₄ ^θ.Using 4 tilt torque vectors, rotor equator is put down Face is divided into,, four sectors；

(7) select synthesis target tilt torque tau_dq ^*Torque component:

If (a) τ_dqPositioned at sector, alternative torque vector is (t_3θ,t_4θ)、(t_3θ,t_1θ)、(t_2θ,t_4θ)、(t_2θ,t_1θ)；Meter Calculate the ratio power consumption p of each group generation₃₄ ^*、p₃₁ ^*、p₂₄ ^*、p₂₁ ^*, select the minimum stator winding pair of power consumption；

If (b) τ_dqPositioned at sector, alternative torque vector is (t_1θ,t_4θ)、(t_1θ,t_3θ)、(t_2θ,t_4θ)、(t_2θ,t_3θ)；Meter Calculate the ratio power consumption p of each group generation₁₄ ^*、p₁₃ ^*、p₂₄ ^*、p₂₃ ^*, subscript represents different combinations, selects the minimum stator winding of power consumption Right；

If (c) τ_dqPositioned at sector, alternative torque vector is (t_2θ,t_4θ)、(t_2θ,t_1θ)、(t_3θ,t_4θ)、(t_3θ,t_1θ)；Meter Calculate the ratio power consumption p of each group generation₂₄ ^*、p₂₁ ^*、p₃₄ ^*、p₃₁ ^*, select the minimum stator winding pair of power consumption；

If (d) τ_dqPositioned at sector, alternative torque vector is (t_1θ,t_4θ)、(t_2θ,t_3θ)、(t_1θ,t_3θ)、(t_2θ,t_4θ)；Meter Calculate the ratio power consumption p of each group generation₁₄ ^*、p₂₃ ^*、p₁₃ ^*、p₂₄ ^*, select the minimum stator winding pair of power consumption；

(8) on the basis of the above-mentioned two groups of windings selected, it is in same in selection a, b, c, d tetra- phase with two groups of inclination windings Winding on one stator meridian, totally six groups of stator winding are as inclination control winding；

(9) by the torque partition function in (5)With rotation torque reference value τ_p ^*Obtain stator each The torque reference value of phase winding, according to globular motor rotation torque characteristics, tries to achieve stator each winding control electric current of spinning motion；

(10) according to globular motor tilt torque characteristic, obtain the torque matrix t tilting winding in (8)_n2, solve it against square Battle arrayAccording to tilt torque reference value τ_dq ^*Try to achieve stator each winding control electric current of banking motion；

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

(12) utilize Hysteresis Current Control Strategy, the size and Orientation of the electric current of each winding of real-time control, so that rotor is exported Expected torque, follows the tracks of desired trajectory.

Beneficial effects of the present invention are as follows:

1st, permanent magnetism spherical motor can achieve multifreedom motion spatially, can be applied to joint of robot, panorama is taken the photograph As high accuracy control fields such as instrument, simplify the structure of mechanical system.

2nd, application torque distribution thought in permanent magnetism spherical motor, can distinguish the spinning motion of controlled motor and tilt fortune Dynamic, increase the flexibility controlling.

Each stator winding torque reference value when the 3rd, utilizing torque partition function to obtain spinning motion, reduces spinning motion Stator control electric current calculates the time, and can reduce torque pulsation problem during spinning motion.

4th, the set-point according to tilt torque vector, in the position of the rotor equatorial plane, selects the controling winding of banking motion, Both reduced the dimension of tilt control torque, the stator control electric current reducing banking motion calculates the time, is avoided that excessive again Ground increases stator current.

Brief description

Fig. 1 (a) Three Degree Of Freedom permanent magnetism spherical electric machine structure figure；Fig. 1 (b) rotor spheroid structure chart.In figure label is entitled: 1 stator wall；2 stator coils；3 coil bolts；4 ball rotor；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 partition function.

Fig. 7 a+ winding two dimension torque partition function.

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

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.

Specific embodiment

With reference to the accompanying 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 is proposed, can be in reality When the spinning motion of existing motor and banking motion uneoupled control, reduction torque pulsation, improve the calculating time of stator control electric current.

Motor basic structure is as shown in Figure 1.The Three Degree Of Freedom permanent magnetism spherical motor that the present invention is suitable for includes support section, determines Son and spherical spinner sensor four part, wherein, support section includes stator wall 1, base 6, and stator includes air core coil 2, line Circle bolt (3), spherical spinner 4 is fixed output shaft 5, and rotor 4 is located in stator wall 1, and rotor of output shaft axle 5 is above stator wall Stretch out at opening, shown in motor basic structure such as Fig. 1 (a).Rotor surface pastes permanent magnet pole 41, and magnetic pole is divided into along equator Lower two-layer, every layer of 6 pole, each layer of magnetic pole n, s pole replaces, and upper and lower two-layer magnetic pole n, s pole replaces.As shown in Fig. 1 (b).

As shown in Fig. 2 outer shroud is position and speed ring, inner ring is electric current loop to control block diagram.Rotary encoder and angle pass Sensor detects rotor-position, obtains Eulerian angles θ=(α, β, γ) that stator coordinate lower rotor part turns over, pd controller is according to defeated The given position angle θ entering_d=(α_d、β_d、γ_d) and value of feedback θ, calculate position and speed error signal e andOutput torque control Signal τ processed^*=[τ_α ^*τ_β ^*τ_γ ^*], target torque is decomposed into the rotation torque reference value τ under rotor coordinate by controller_p ^*With Tilt torque reference value τ_dq ^*, to realize uneoupled control.Torque allocation 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, exports the switching signal of winding according to current reference value and current feedback signal.

Hereinafter will be described further in terms of controller design, Torque-sharing strategy, simulation analysis three.

1st, controller design

Permanent magnetism spherical motor is a multi input, multi output, the nonlinear system of close coupling.This Non-linear coupling is direct Impact permanent magnet spherical motor servo-drive system dynamic property and control accuracy.Using a kind of feedforward pd control algolithm -- calculate Moment method, the coupling terms of reconstruction model, realize uneoupled control.

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 angular amount, θ_d=(α_dβ_dγ_d),For θ_dFirst derivative to the time, θ is that feedback is angular to be measured, θ=(α β γ),For θ_dFirst derivative to the time,

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_dTo the time Second dervative.

The control rate of computed-torque approach 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_pIt is respectively the rotary inertia in three axial directions of motor rotor coordinate system, j_d=j_q≠j_p, c and s be respectively The abbreviation of cos and sin, τ_fFor each axial friction of Eulerian angles and load torque vector.

In systems in practice it is contemplated that the uncertain factor such as accuracy of manufacture, hardly result in accurate motor model, therefore right Inertial matrix m (θ) and coriolis force matrixCompensate

$\left\{\begin{array}{c}m\left(\mathrm{\θ}\right)=m_0\left(\mathrm{\θ}\right)+\mathrm{\δm}\left(\mathrm{\θ}\right)\\ c(\mathrm{\θ},\stackrel{.}{\mathrm{\θ}})=c_0(\mathrm{\θ},\stackrel{.}{\mathrm{\θ}})+\mathrm{\δc}(\mathrm{\θ},\stackrel{.}{\mathrm{\θ}})\end{array}\right.---\left(6\right)$

In formula, m₀(θ)、Actual inertial matrix for definition and coriolis force matrix, δ m (θ),For matrix Uncertain error.

Use m₀(θ)、Replacement m (θ),Then 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 is the output valve controlling controller, as torque reference value.Controller block diagram is as shown in Figure 3.

In rotor d-q-p coordinate system, permanent magnetism spherical motor control torque can be analyzed to the component τ of d, q, p axle_d、τ_q、τ_p, It is represented by

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

In formula, τ_pControl torque for rotation, and τ_d、τ_qTilt component τ in synthesis d-q plane_dq, as shown in Figure 4.

2nd, Torque-sharing strategy

Convenient for expression, stator winding is numbered.If two stator winding are located at one diameter of stator spheroid Two ends, then referred to as one group winding, the therefore present invention are divided into 12 groups of windings, and stator winding distribution schematic diagram is as shown in Figure 5.If Stator sphere is 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- phase, a+ generation When this stator winding is given as forward current, this mutually attracts s polarity rotor magnetic pole to table, repels n polarity rotor magnetic pole.When a phase During conducting, the current polarity that a+, a- are given is contrary, to synthesize rotation torque.

(1) rotation direct torque

Rotation torque is assigned to by a, b, c, d tetra- phase using one-dimensional torque partition function, torque partition function is not unique, Can be linear function, nonlinear function (as cosine function, exponential function etc.), Fig. 6 is cosine partition function, its expression formula is

I=a, d, c, b in formula,For the longitude angle under a rotor magnetic pole for the stator winding reduction of i phase, Correspond to the angle of flow of i phase, the angle of flow of i+1 phase, the pass angle of rupture of i phase in Fig. 6 respectively, differ 15 ° of mechanical angles successively, so may be used To ensure that each phase torque seamlessly transits during commutation.

When globular motor rotor tilt, under same current excitation, two windings of same phase are due to the change of coordinate And producing different static rotation torques, therefore rotation torque needs to carry out secondary distribution, function expression between two windings As follows:

In formulaRefer respectively to the i-th phase " ± " partition function of winding, θ_i+、θ_i-For i phase two Angle of latitude under a rotor magnetic pole of the coordinate conversion in rotor coordinate for the winding, τ_γ(i+)、τ_γ(i-)It is respectively i-th mutually fixed Sub- winding " ± " the static state rotation torque of winding unit.The two-dimentional torque partition function of a+ winding as shown in fig. 7, other each winding with This is similar to.

Therefore, each phase winding rotation torque reference value is represented by

By position under rotor coordinate for the stator winding, the unit static state rotation torque that can obtain each stator winding divides AmountThen winding rotation control electric current i_p,iFor

Each winding current is combined, you can obtain rotation control electric current vector i₁.

(2) tilt torque controls

Compare levels stator winding, intermediate layer stator winding is big to the contribution of tilt torque.In rotor d-q face (equator Face) in, shown in the relative spatial phase relation such as Fig. 8 (a) of the tilt torque vector that intermediate layer stator winding produces, 4 phase windings Torque vector by plane be divided into four sectors,, but the amplitude of four vectors and phase place become with rotor motion Change, can be obtained by coordinate transform according to permanent magnetism spherical motor tilt torque characteristic.

As can be seen that such as synthesizing the target tilt torque tau in sectors using two phase windings from Fig. 8 (b)_dq, can have 4 Plant different schemes, i.e. (t_3θ,t_4θ)、(t_3θ,t_1θ)、(t_2θ,t_4θ)、(t_2θ,t_1θ), but the winding current needed for different schemes and Power consumption is different.When stator winding is located near rotor magnetic pole border, the tilt torque of generation is approximately 0, and this winding is Make the less tilt torque component of generation one, its current amplitude is also than larger.In order to avoid choosing this unfavorable side Case, needs 4 kinds of schemes of Integrated comparative.

With (t_3θ,t_4θ) as a example, Fig. 8 (b) describes the composition principle of torque vector, and target torque and phase winding torque divide Relation between amount is represented by

τ_dq=t_3θi₃+t_4θi₄(13)

I in formula₃、i₄It is phase winding electric current respectively.

Winding current is represented by

i₃=τ_dq·t⁽³⁾

(14)

i₄=τ_dq·t⁽⁴⁾

Wherein

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

In order to compare different synthesis modes each winding producing ratio 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 the same manner, calculate the ratio power consumption p that other combinations produce₃₁ ^*、p₂₄ ^*、p₂₁ ^*, select two groups of minimum windings of power consumption.? In addition it is also necessary to add other windings ability synthesis type torque reference values on the basis of this, the new winding adding should avoid producing as far as possible Extra tilt torque, and offset the rotating torques that winding produces.The present invention is directly chosen and is in two groups of inclination windings Levels on same stator meridian totally 4 windings.Therefore have 6 groups of inclination control windings, inclined according to permanent magnetism spherical motor Tiltedly torque characteristics, obtains corresponding static torque matrix t by coordinate transform_n2∈r^3×6.

It will be noted that walking around in addition to square except being produced from after the energising of rotation winding, also produce additional tilt torque, that is,

τ₁=[τ_α1τ_β1]^t=t_n1i₁(17)

In formula, subscript t represents transposition computing, t_n1∈r^2×4Static tilt torque matrix corresponding to conducting stator winding, i₁ Current vector for 2 mutually totally 4 windings of conducting.

The torque therefore tilting winding generation is represented by

τ₂=τ^*-τ₁=[τ_α ^*-τ_α1τ_β ^*-τ_β10] (18)

The then control electric current vector i of banking motion₂Can be tried 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 i₁With i₂Merge, you can obtain overall control current vector.

I=[i₁i₂] (20)

In formula, symbol [] represents union operation, that is, on the basis of general vector merging, the electric current of identical winding is added.

It is input in hysteresis comparator as reference current by the coil current i that formula (20) obtains, the switching signal drawing Control opening and turning off of main circuit power tube, the reference current making the current tracking of stator coil give, finally realize permanent magnetism The Three Degree Of Freedom stable operation of globular motor.

3rd, simulation analysis.

For verifying the validity of control strategy proposed by the invention, using matlab/simulink emulation platform to base Permanent magnetism spherical motor control strategy in torque distribution is studied.In emulation, DC bus-bar voltage is 10v, permanent magnetism spherical motor Parameter as shown in table 1, its torque characteristics is as shown in Figure 9.

The structure and material parameter of table 1 motor

Pd parameter is set to k_p=diag [140140140], k_d=diag [353535]；Inner ring is electric current loop it is considered to stagnant ring Width ε=0.1.δ m (θ)=- 0.1m (θ),In order to preferably check the performance of permanent magnetism spherical motor, Make rotor do nutation movement, desired trajectory θ is set_d=[0.2sin 2t 0.4cos2t 2t].

Figure 10 is that permanent magnetism spherical motor is for given trace using the control strategy based on torque distribution proposed by the invention Tracking situation, movement locus on stator sphere for Figure 11 output shaft, Figure 12 be motor operation course in error follow the tracks of feelings Condition.Can be seen that from simulation result and certain coupling condition is had due to each axially-movable of permanent magnetism spherical motor, and motor knot The uncertainty of structure makes track following a little bias, but still in permissible range, error substantially controls Within 0.1rad, embody model structure uncertainty under, control strategy proposed by the invention can follow the tracks of well to Fixed track, control system has good robustness and dynamic property.In order to reduce tracking error further, can be using nerve The Advanced Control Strategies such as network, uneoupled control replace, optimize pd controller.

When actual control system designs it is necessary to consider the realizability of algorithm.In globular motor control system, broad sense The time that calculates of inverse matrix is in that geometry multiple increases with the increase of dimension, and inverting of higher dimensional matrix occupies digital processing unit Ample resources, increases the computation burden of digital processing unit, has had a strong impact on the control effect of system.Table 2 compares different dimensional The calculating time of the Generalized Inverse Matrix matrix of number, digital signal processor model tms320f2812, its clock cycle is 150mhz, it is seen that Torque-sharing strategy proposed by the present invention can effectively reduce matrix dimension, has higher arithmetic speed.

Table 2 computation complexity contrasts

Claims (1)

1. a kind of Three Degree Of Freedom permanent magnetism spherical motor torque control strategy, the motor being suitable for is three degree of freedom spherical motor, bag Include base, spherical stator wall, stator coil and rotor, rotor is located in stator wall, opening above stator wall for its output shaft Place stretches out it is characterised in that stator coil is cylindricality iron-free core structure, along equator and the latitude parallel with equator of spherical stator wall It is uniformly distributed 3 layers on line, radial be fixed on spherical stator wall；Rotor surface is embedded with permanent magnet pole, magnetic pole along with red Road is divided into upper and lower two-layer, and every layer of n pole and s pole are alternately distributed, and this control strategy is: certainly walks around controlling torque to be decomposed into first Square and tilt torque, on this basis, rotation torque are assigned to different stator phase windings；In view of globular motor rotor tilt When, the difference of different stator winding rotation torques, obtain two-dimentional torque partition function, finally according to permanent magnetism spherical motor torque Characteristic can directly obtain the control electric current of spinning motion；For tilt torque, according between tilt torque and each winding torque vector Relative position, by comparing the ratio power consumption of various combination mode, determine inclination control winding, obtain the tilt torque of dimensionality reduction Control matrix, the direct torque matrix inverse matrix after solving dimensionality reduction obtains the control electric current of banking motion, specifically includes down The step of row:

(1) utilize FInite Element numerical algorithm or analytic method to obtain rotation torque and the tilt torque characteristic of motor, with form or Formula form stores；

(2) adopt rotary encoder and angular transducer to detect rotor-position signal, and carry out Eulerian angles conversion, obtain description and turn The Eulerian angles (α, β, γ) of sub- positional information；

(3) set the given trace of permanent magnetism spherical motor as (α_d、β_d、γ_d), by given trace and actual angle, using calculating torque Method, determines the target control torque required for motor

(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, positioned at the two ends of one diameter of stator spheroid, are referred to as One group of winding, the stator winding numbering setting bulbec face along equator is followed successively by 1,2,3,4, and upper and lower two-layer winding be respectively a, b, C, d tetra- phase, a+ represents when this stator winding is given as forward current, and this mutually attracts s polarity rotor magnetic pole, repels n polarity and turns Sub- magnetic pole, when a is conducted, the current polarity that a+, a- are given is contrary, to synthesize rotation torque；

A, b, c, d tetra- phase that the winding of two-layer up and down of stator is constituted, application torque distribution thought, determine one-dimensional point of each phase Join functionSubscript i represents stator phase,Convert a rotor for coordinate in rotor coordinate for the stator phase winding Longitude angle under magnetic pole it is contemplated that when rotor of output shaft axle tilts two groups of stator winding torque characteristics of each phase difference, Jiang Gexiang Rotation torque carries out secondary distribution between two windings, and the partition function of winding is respectivelySubscript i +, i- represent two groups of stator winding of the i-th phase, θ_i+、θ_i-Convert one for coordinate in rotor coordinate for two windings of i phase Angle of latitude under rotor magnetic pole；

(6) for intermediate layer stator winding be 1,2,3,4 phases, according to motor tilt torque characteristic and stator winding coordinate, can obtain Tilt torque t producing to 1-4 phase winding₁ ^θ、t₂ ^θ、t₃ ^θ、t₄ ^θ, using 4 tilt torque vectors, rotor equatorial plane is divided into ,, four sectors；

(7) select synthesis target tilt torque tau_dq ^*Torque component:

If (a) τ_dqPositioned at sector, alternative torque vector is (t_3θ,t_4θ)、(t_3θ,t_1θ)、(t_2θ,t_4θ)、(t_2θ,t_1θ)；Calculate The ratio power consumption p that each group produces₃₄ ^*、p₃₁ ^*、p₂₄ ^*、p₂₁ ^*, select the minimum stator winding pair of power consumption；

If (b) τ_dqPositioned at sector, alternative torque vector is (t_1θ,t_4θ)、(t_1θ,t_3θ)、(t_2θ,t_4θ)、(t_2θ,t_3θ)；Calculate The ratio power consumption p that each group produces₁₄ ^*、p₁₃ ^*、p₂₄ ^*、p₂₃ ^*, subscript represents different combinations, selects the minimum stator winding pair of power consumption；

If (c) τ_dqPositioned at sector, alternative torque vector is (t_2θ,t_4θ)、(t_2θ,t_1θ)、(t_3θ,t_4θ)、(t_3θ,t_1θ)；Calculate The ratio power consumption p that each group produces₂₄ ^*、p₂₁ ^*、p₃₄ ^*、p₃₁ ^*, select the minimum stator winding pair of power consumption；

If (d) τ_dqPositioned at sector, alternative torque vector is (t_1θ,t_4θ)、(t_2θ,t_3θ)、(t_1θ,t_3θ)、(t_2θ,t_4θ)；Calculate The ratio power consumption p that each group produces₁₄ ^*、p₂₃ ^*、p₁₃ ^*、p₂₄ ^*, select the minimum stator winding pair of power consumption；

(8) on the basis of the above-mentioned two groups of windings selected, choose in a, b, c, d tetra- phase and be in certain with two groups of inclination windings Winding on sub- meridian, totally six groups of stator winding are as inclination control winding；

(9) by the torque partition function in (5)With rotation torque reference value τ_p ^*Obtain each phase of stator The torque reference value of winding, according to globular motor rotation torque characteristics, tries to achieve stator each winding control electric current of spinning motion；

(10) according to globular motor tilt torque characteristic, obtain the torque matrix t tilting winding in (8)_n2, solve its inverse matrix t_n2 ^-1, according to tilt torque reference value τ_dq ^*Try to achieve stator each winding control electric current of banking motion；

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

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