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

Abstract

The present invention relates to a three-degree-of-freedom permanent magnet spherical motor torque control strategy: first, the control torque is decomposed into rotation torque and tilt torque, and on this basis, the rotation torque is distributed to different stator phase windings; considering When the rotor of the spherical motor is tilted, the difference in the rotation torque of different stator windings can obtain the two-dimensional torque distribution function, and finally the control current of the rotation motion can be directly obtained according to the torque characteristics of the permanent magnet spherical motor. For the tilting torque, according to the relative position between the tilting torque and the torque vector of each winding, the tilting control winding is determined by comparing the specific power consumption of different combinations, and the dimensionality-reduced tilting torque control matrix is obtained. By solving the dimensionality reduction The inverse matrix of the torque control matrix after that obtains the control current of the tilting motion. The invention can improve the response speed and control precision of the permanent magnet spherical motor control system, reduce the torque ripple during self-rotating motion, and avoid excessively increasing the stator control current.

Description

A torque control strategy for a three-degree-of-freedom permanent magnet spherical motor

Technical field

The invention belongs to the technical field of motor control, and relates to a control method of a multi-degree-of-freedom permanent magnet spherical motor. the

Background technique

With the continuous development of complex and high-precision control systems, people have higher and higher requirements for the accuracy and stability of the driving device. As a new type of motor, the permanent magnet spherical motor has the advantages of simple structure, small size, light weight, and high torque density. It can realize the movement of the rotor with three degrees of freedom, improve the integration of the system, simplify the transmission device, and have Wide application prospects. the

However, due to the special structure and motion mode, the control strategy of the permanent magnet spherical motor is also more complicated. In the existing control scheme, whether it is an open-loop control scheme or a closed-loop control scheme, it is necessary to obtain the stator current. In the previous research scheme, in order to obtain the control current of each stator winding, it is generally used to solve the generalized inverse of the torque matrix The matrix method, while the torque matrix of the spherical motor is related to the rotor position angle, and its dimension depends on the number of stator windings. Obviously, the time-varying and high-dimensional characteristics of the torque matrix increase the computational burden of the control system and reduce the real-time performance of the system. In some literatures, based on the analysis of the torque characteristics of permanent magnet spherical motors, different stator windings are selected to control the tilt torque and rotation torque respectively, and two torque control matrices with reduced dimensionality are obtained. Although this method reduces the dimension of the control matrix, the number of control matrices is increased to two, which cannot reduce the total operation time. the

Contents of the invention

In order to overcome the above-mentioned deficiencies in the prior art, improve the response speed and control accuracy of the permanent magnet spherical motor control system, reduce the torque ripple during the rotation movement, and avoid excessively increasing the stator control current, the present invention proposes a torque-based Allocation strategy control control scheme. Technical scheme of the present invention is as follows:

A three-degree-of-freedom permanent magnet spherical motor torque control strategy, the applicable motor is a three-degree-of-freedom spherical motor, including a base, a spherical stator wall, stator coils and a rotor, the rotor is located inside the stator wall, and its output shaft is from above the stator wall It is characterized in that the stator coil is a cylindrical coreless structure, and 3 layers are evenly distributed along the equator of the spherical stator wall and the parallel parallel to the equator, and are radially fixed on the spherical stator wall; the surface of the rotor is embedded with The magnetic poles of permanent magnets are divided into upper and lower layers along the equator, and the N poles and S poles of each layer are alternately distributed. The control strategy is: firstly, the control torque is decomposed into rotation torque and tilt torque. On this basis, Distribute the rotation torque to different stator phase windings; consider the difference in the rotation torque of different stator windings when the rotor of the spherical motor is tilted, obtain a two-dimensional torque distribution function, and finally obtain the rotation motion directly according to the torque characteristics of the permanent magnet spherical motor the control current. For the tilting torque, according to the relative position between the tilting torque and the torque vector of each winding, the tilting control winding is determined by comparing the specific power consumption of different combinations, and the dimensionality-reduced tilting torque control matrix is obtained. By solving the dimensionality reduction The inverse matrix of the torque control matrix after that obtains the control current of the tilting motion. the

Specifically include the following steps:

(1) Use numerical algorithms such as finite element method or analytical methods to obtain the characteristics of the motor's rotation torque and tilt torque, and store them in the form of tables or formulas;

(2) Use the rotary encoder and angle sensor to detect the rotor position signal, and perform Euler angle transformation to obtain the Euler angle (α, β, γ) describing the rotor position information;

(3) Set the given trajectory of the permanent magnet spherical motor as (α _d , β _d , γ _d ), and use the calculation torque method to determine the target control torque τ ^* = [ _τα ^* _τβ ^* _τγ ^* ];

(4) Decompose the target torque into the reference value τ _p ^* of the rotation torque and the reference value τ _dq ^* of the tilting torque in the rotor coordinate system;

(5) Number the stator windings. If two stator windings are located at both ends of a diameter of the stator sphere, it is called a set of windings. Set the stator winding numbers of the stator sphere along the equator as 1, 2, 3, 4 , while the upper and lower layers of windings are divided into four phases A, B, C, and D. A+ means that when the stator winding is given a forward current, this phase attracts the S polarity rotor magnetic pole and repels the N polarity rotor magnetic pole. When A When the phase is turned on, the polarity of the current given by A+ and A- is opposite to synthesize the rotation torque;

For the four phases A, B, C, and D composed of the upper and lower winding layers of the stator, apply the idea of torque distribution to determine the one-dimensional distribution function of each phase The subscript i indicates the stator phase, is the longitude angle converted from the coordinates of the stator phase windings in the rotor coordinate system to a rotor magnetic pole. Considering the difference in the torque characteristics of the two groups of stator windings of each phase when the rotor output shaft is tilted, the rotation torque of each phase is divided into two Secondary distribution is carried out between the windings, and the distribution functions of the windings are respectively The subscripts i+ and i- represent the two sets of stator windings of the i-th phase, and θ _i+ and θ _i- are the latitude angles converted from the coordinates of the two windings of the i phase in the rotor coordinate system to one rotor magnetic pole;

(6) For phases 1, 2, 3, and 4 of the intermediate stator windings, according to the characteristics of the motor’s tilting torque and the coordinates of the stator windings, the tilting torques T ₁ ^θ , T ₂ ^θ , and T ₂ generated by the 1-4 phase windings can be obtained ^θ , T ₃ ^θ , and T ₄ ^θ . The equatorial plane of the rotor is divided into four sectors Ⅰ, Ⅱ, Ⅲ and Ⅳ by using 4 tilting torque vectors;

(7) Select the torque component of the synthetic target tilt torque _τdq ^* :

(a) If τ _dq is located in sector I, the alternative torque vectors are (T _3θ ,T _4θ ), (T _3θ ,T _1θ ), (T _2θ ,T _4θ ), (T _2θ ,T _1θ ); calculate Find out the specific power consumption p ₃₄ ^* , p ₃₁ ^* , p ₂₄ ^* , p ₂₁ ^* generated by each group, and select the stator winding pair with the smallest power consumption;

(b) If τ _dq is located in sector II, the alternative torque vectors are (T _1θ ,T _4θ ), (T _1θ ,T _3θ ), (T _2θ ,T _4θ ), (T _2θ ,T _3θ ); calculate Find out the specific power consumption p ₁₄ ^* , p ₁₃ ^* , p ₂₄ ^* , p ₂₃ ^* generated by each group, the subscript indicates different combinations, and select the stator winding pair with the smallest power consumption;

(c) If τ _dq is located in sector III, the alternative torque vectors are (T _2θ ,T _4θ ), (T _2θ ,T _1θ ), (T _3θ ,T _4θ ), (T _3θ ,T _1θ ); calculate Calculate the specific power consumption p ₂₄ ^* , p ₂₁ ^* , p ₃₄ ^* , p ₃₁ ^* generated by each group, and select the stator winding pair with the smallest power consumption;

(d) If τ _dq is located in sector IV, the alternative torque vectors are (T _1θ ,T _4θ ), (T _2θ ,T _3θ ), (T _1θ ,T _3θ ), (T _2θ ,T _4θ ); calculate out of each group to produce

specific power consumption p ₁₄ ^* , p ₂₃ ^* , p ₁₃ ^* , p ₂₄ ^* , select the stator winding pair with the smallest power consumption;

(8) On the basis of the two sets of windings selected above, select the windings in the four phases A, B, C, and D that are on the same stator longitude line as the two sets of inclined windings, and a total of six sets of stator windings are used as the inclined control windings;

(9) by the torque distribution function in (5) and the self-rotation torque reference value τ _p ^* to obtain the torque given value of each phase winding of the stator, and according to the self-rotation torque characteristic of the spherical motor, obtain the control current of each winding of the stator in the self-rotation motion;

(10) According to the tilting torque characteristics of the spherical motor, obtain the torque matrix T _n2 of the tilting winding in (8), and solve its inverse matrix Calculate the control current of each winding of the stator in tilting motion according to the tilting torque reference value τ _dq ^* ;

(11) Obtain the total control current of each winding of the stator from (9) and (10);

(12) Use the current hysteresis control strategy to control the magnitude and direction of the current of each winding in real time, so that the rotor can output the expected torque and track the expected trajectory. the

The beneficial effects of the present invention are as follows:

1. The permanent magnet spherical motor can realize multi-degree-of-freedom movement in space, and can be applied to high-precision control fields such as robot joints and panoramic cameras, simplifying the structure of the mechanical system. the

2. Applying the idea of torque distribution in the permanent magnet spherical motor can control the rotation and tilting motion of the motor separately, increasing the flexibility of control. the

3. Using the torque distribution function to obtain the torque reference value of each stator winding during autorotation, which reduces the calculation time of the stator control current for autorotation, and can reduce the torque ripple problem during autorotation. the

4. According to the position of the given value of the tilting torque vector on the equatorial plane of the rotor, the control winding for the tilting motion is selected, which not only reduces the dimension of the tilting control torque, reduces the calculation time of the stator control current for the tilting motion, but also avoids Excessive increase in stator current. the

Description of drawings

Fig. 1(a) Structural diagram of three-degree-of-freedom permanent magnet spherical motor; Fig. 1(b) Structural diagram of rotor sphere. The label names in the figure are: 1 stator wall; 2 stator coil; 3 coil bolt; 4 ball rotor; 5 output shaft; 6 base; 41 permanent magnet pole. the

Figure 2 Control system block diagram. the

Figure 3 PD controller block diagram. the

Fig. 4 Schematic diagram of torque decomposition in the rotor coordinate system. the

Figure 5. Schematic diagram of stator winding distribution. the

Fig. 6. Cosine torque distribution function. the

Figure 7A + Winding two-dimensional torque distribution function. the

Fig. 8 Tilting torque control method, (a) division of rotor equatorial plane sector (b) principle of torque synthesis. the

Figure 9 Torque characteristics of permanent magnet spherical motor, (a) self-rotation torque (b) tilting torque. the

Figure 10 Tracking of nutating motion trajectory, (a) α-axis response (b) β-axis response (c) γ-axis response. the

Fig. 11 Motion trajectory of nutating motion output shaft. the

Figure 12 Nutating motion tracking error situation, (a) α-axis error (b) β-axis error (c) γ-axis error. the

Detailed ways

The present invention will be described in further detail below in conjunction with the accompanying drawings and embodiments. the

The invention is a new torque distribution control strategy proposed for a new type of permanent magnet spherical motor, which can improve the calculation time of the stator control current when realizing the decoupling control of the motor's self-rotating motion and tilting motion and reducing torque ripple. the

The basic structure of the motor is shown in Figure 1. The three-degree-of-freedom permanent magnet spherical motor applicable to the present invention includes four parts: a support part, a stator and a spherical rotor sensor, wherein the support part includes a stator wall 1, a base 6, and the stator includes a hollow coil 2, coil bolts (3), and a spherical rotor 4 The output shaft 5 is fixed on the top, the rotor 4 is located in the stator wall 1, and the rotor output shaft 5 protrudes from the opening above the stator wall. The basic structure of the motor is shown in Figure 1(a). Permanent magnet poles 41 are pasted on the surface of the rotor. The poles are divided into upper and lower layers along the equator. Each layer has 6 poles. The N and S poles of each layer alternate, and the N and S poles of the upper and lower layers alternate. As shown in Figure 1(b). the

The control block diagram is shown in Figure 2, the outer ring is the position and speed loop, and the inner ring is the current loop. The rotary encoder and angle sensor detect the rotor position, and obtain the Euler angle θ=(α, β, γ) that the rotor rotates in the stator coordinate system, and the PD controller inputs the given position angle θ _d = (α _d , β _d , γ _d ) and feedback value θ, calculate the error signal e of position and speed and The output torque control signal τ ^* = [τ _α ^* τ _β ^* τ _γ ^* ], the controller decomposes the target torque into the reference value τ _p ^* of the rotation torque and the reference value τ _dq ^* of the tilting torque in the rotor coordinate system , to achieve decoupled control. The torque distribution unit selects different energized windings according to the given rotation component τ _p ^* , tilt component τ _dq ^* and rotor position Euler angles (α, β, γ), and calculates the current reference value of each winding. The inner loop current loop adopts the hysteresis loop comparison strategy, and outputs the switch signal of the winding according to the current reference value and the current feedback signal.

The following will further explain from the three aspects of controller design, torque distribution strategy, and simulation analysis. the

1. Controller design

The permanent magnet spherical motor is a multi-input, multi-output, strongly coupled nonlinear system. This nonlinear coupling directly affects the dynamic performance and control accuracy of the permanent magnet spherical motor servo system. A feed-forward PD control algorithm, the calculated moment method, is used to reconstruct the coupling items of the model to realize decoupling control. the

Considering continuous trajectory motion, the position deviation is defined as

$\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}\\ \stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In the formula, θ _d is a given angle vector, θ _d ＝(α _d β _d γ _d ), is the first derivative of θ _d with respect to time, θ is the feedback angle vector, θ=(α β γ), $\stackrel{\&CenterDot;}{\mathrm{\&theta;}}=\left(\begin{array}{ccc}\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}& \stackrel{\&CenterDot;}{\mathrm{\&beta;}}& \stackrel{\&CenterDot;}{\mathrm{\&gamma;}}\end{array}\right),$ is the first derivative of θ _d with respect to time, $\stackrel{\&CenterDot;}{\mathrm{\&theta;}}=\left(\begin{array}{ccc}\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}& \stackrel{\&CenterDot;}{\mathrm{\&beta;}}& \stackrel{\&Center\; Dot;}{\mathrm{\&gamma;}}\end{array}\right),$

definition

$\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

In the formula, Kp is the proportional coefficient matrix, and Kd is the differential coefficient matrix, both of which are positive definite diagonal matrices; is the second derivative of θ _d with respect to time.

The control rate of the calculated moment method is:

$\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; =</span>\left(\begin{array}{ccc}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\mathrm{<span\; class="notranslate">\; c\&beta;s\&beta;</span>}& <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\mathrm{<span\; class="notranslate">\; c\&beta;s\&beta;</span>}& {\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\mathrm{<span\; class="notranslate">\; c\&beta;s\&beta;</span>}\\ <span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\mathrm{<span\; class="notranslate">\; c\&beta;s\&beta;</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\mathrm{<span\; class="notranslate">\; c\&beta;</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\mathrm{<span\; class="notranslate">\; c\&beta;</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right)<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\left(\begin{array}{ccc}{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&beta;</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\mathrm{<span\; class="notranslate">\; s\&beta;</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ {\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\mathrm{<span\; class="notranslate">\; s\&beta;</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\end{array}\right)<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

In the formula, τ is the control torque vector, including three components of τ _α , τ _β , τ _γ . M(θ) is the inertia matrix, is the Coriolis force matrix. J _d , J _q , J _p are the moments of inertia of the three axes of the motor rotor coordinate system, J _d ＝J _q ≠J _p , c and s are the abbreviations of cos and sin respectively, τ _f is the Euler angle Axial friction and load torque vectors.

In an actual system, considering uncertain factors such as manufacturing accuracy, it is difficult to obtain an accurate motor model, so the inertia matrix M(θ) and Coriolis force matrix make compensation

$\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;M</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;C</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; )</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

In the formula, M ₀ (θ), is the defined actual inertia matrix and Coriolis force matrix, ΔM(θ), is the uncertain error of the matrix.

With M ₀ (θ), Instead of M(θ), Then formula (3) can be changed to

$\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

In the formula, τ is the output value of the control controller, which is the torque reference value. The block diagram of the controller is shown in Figure 3. the

In the rotor dqp coordinate system, the control torque of permanent magnet spherical motor can be decomposed into d, q, p axis components τ _d , τ _q , τ _p , which can be expressed as

$\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; c\&gamma;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; s\&beta;</span>}& \mathrm{<span\; class="notranslate">\; s\&gamma;</span>}& \mathrm{<span\; class="notranslate">\; c\&gamma;</span>}\\ \mathrm{<span\; class="notranslate">\; s\&gamma;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; s\&beta;</span>}& \mathrm{<span\; class="notranslate">\; c\&gamma;</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; s\&gamma;</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

In the formula, τ _p is the rotation control torque, and τ _d and τ _q synthesize the tilt component τ _dq on the dq plane, as shown in Fig. 4 .

2. Torque distribution strategy

For the convenience of expression, the stator windings are numbered. If two stator windings are located at both ends of a diameter of the stator sphere, it is called a set of windings. Therefore, the present invention is divided into 12 sets of windings. The distribution diagram of the stator windings is shown in FIG. 5 . Set the number of stator windings along the equator of the subsphere to be 1, 2, 3, 4 in sequence, and the upper and lower layers of windings are divided into four phases of A, B, C, and D. A+ means that when the stator winding is given a forward current , the phase attracts the S-polarity rotor pole and repels the N-polarity rotor pole. When the A phase is turned on, the polarity of the current given by A+ and A- is opposite to synthesize the rotation torque. the

(1) Autorotation torque control

The self-rotation torque is distributed to the four phases A, B, C, and D by using a one-dimensional torque distribution function. The torque distribution function is not unique and can be a linear function or a nonlinear function (such as a cosine function, an exponential function, etc.), as shown in Fig. 6 is the cosine distribution function, its expression is

Where i=A,D,C,B, is the longitude angle of the i-phase stator winding reduced to one rotor magnetic pole, Corresponding to the conduction angle of i-phase, the conduction angle of i+1 phase, and the turn-off angle of i-phase in Fig. 6, respectively, the difference is 15° mechanical angle, which can ensure the smooth transition of the torque of each phase during the commutation period.

When the spherical motor rotor is tilted, under the same current excitation, the two windings of the same phase will produce different static rotation torques due to the change of coordinates, so the rotation torque needs to be redistributed between the two windings, the function expression as follows:

In the formula Respectively refer to the distribution function of the i-th phase "±" winding, θ _i+ , θ _i- are the latitude angles under one rotor magnetic pole converted from the coordinates of the two windings of phase i in the rotor coordinate system, τ _γ(i+) , τ _γ(i-) is respectively the unit static rotation torque of the i-th stator winding “±” winding. The two-dimensional torque distribution function of the A+ winding is shown in Figure 7, and the other windings are similar.

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

From the position of the stator winding in the rotor coordinate system, the unit static rotation torque component of each stator winding can be obtained Then the winding rotation control current _ip,i is

The rotation control current vector I ₁ can be obtained by combining the winding currents.

(2) Tilt torque control

Compared with the upper and lower stator windings, the middle stator winding contributes more to the tilting torque. In the d-q plane of the rotor (equatorial plane), the relative spatial phase relationship of the tilted torque vector generated by the stator winding in the middle layer is shown in Fig. 8(a), and the torque vector of the 4-phase winding divides the plane into four sectors I , Ⅱ, Ⅲ, Ⅳ, but the magnitude and phase of the four vectors change with the movement of the rotor, which can be obtained by coordinate transformation according to the tilt torque characteristics of the permanent magnet spherical motor. the

It can be seen from Fig. 8(b) that if two-phase winding is used to form the target tilt torque τ _dq in sector I, there are four different schemes, namely (T _3θ ,T _4θ ), (T _3θ , T _1θ ), (T _2θ , T _4θ ), (T _2θ , T _1θ ), but the winding current and power consumption required by different schemes are different. When the stator winding is located near the rotor magnetic pole boundary, the generated tilt torque is approximately 0. Even if this winding generates a small tilt torque component, its current amplitude is relatively large. In order to avoid choosing such an unfavorable plan, it is necessary to comprehensively compare the four plans.

Taking (T _3θ ,T _4θ ) as an example, Figure 8(b) describes the synthesis principle of the torque vector, and the relationship between the target torque and the torque component of the phase winding can be expressed as

τ _dq =T _3θ i ₃ +T _4θ i ₄ (13)

Where i ₃ and i ₄ are the phase winding currents respectively.

The winding current can be expressed as

ⁱ ₃ =τ _dq T ⁽³⁾

(14)

ⁱ ₄ =τ _dq T ⁽⁴⁾

in

$\begin{array}{c}{\mathrm{<span\; class="notranslate">\; T</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; j</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; j</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}\\ {\mathrm{<span\; class="notranslate">\; T</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; j</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; j</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

In order to compare the specific power consumption of each winding in different synthesis methods, the specific power consumption is defined as

${{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 34</span>}}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>\frac{{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; dq</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; T</span>}}^{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; T</span>}}^{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

Similarly, calculate the specific power consumption p ₃₁ ^* , p ₂₄ ^* , p ₂₁ ^* generated by other combinations, and select the two groups of windings with the smallest power consumption. On this basis, it is necessary to add other windings to synthesize the torque reference value. The newly added winding should avoid generating additional tilting torque as much as possible, and offset the rotation torque generated by the tilting winding. The present invention directly selects 4 windings in the upper and lower layers on the same stator longitude line as the two sets of inclined windings. Therefore, there are 6 sets of tilt control windings. According to the tilt torque characteristics of the permanent magnet spherical motor, the corresponding static torque matrix T _n2 ∈ R ^3×6 is obtained by coordinate transformation.

It should be noted that after the rotation winding is energized, in addition to the rotation torque, an additional tilting torque is generated, namely

τ ₁ ＝[τ _α1 τ _β1 ] ^T ＝T _n1 I ₁ (17)

In the formula, the superscript T represents the transpose operation, T _n1 ∈ ^{R 2×4} is the static tilting torque matrix corresponding to the conduction of the stator windings, and I ₁ is the current vector of the 2-phase 4 windings that are conducted.

Therefore, the torque generated by the tilted winding can be expressed as

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

Then the control current vector _I2 of the tilting motion can be obtained according to the following formula

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 19</span>}<span\; class="notranslate">\; )</span>$

In the formula, is the generalized inverse matrix of T _n2 .

Combining I ₁ and I ₂ , the overall control current vector can be obtained.

I=[I ₁ I ₂ ] (20)

In the formula, the symbol [] represents the merge operation, that is, the current of the same winding is added on the basis of the common vector merge. the

The coil current I obtained by formula (20) is input into the hysteresis comparator as a reference current, and the switching signal obtained controls the opening and closing of the power tube of the main circuit, so that the current of the stator coil tracks the given reference current, and finally The three-degree-of-freedom stable operation of the permanent magnet spherical motor is realized. the

3. Simulation analysis. the

In order to verify the effectiveness of the control strategy proposed by the present invention, the control strategy of the permanent magnet spherical motor based on torque distribution is studied by using the Matlab/Simulink simulation platform. In the simulation, the DC bus voltage is 10V, the parameters of the permanent magnet spherical motor are shown in Table 1, and its torque characteristics are shown in Figure 9. the

Table 1 Structure and material parameters of the motor

The PD parameters are set as K _p =diag[140 140 140], K _d =diag[35 35 35]; the inner loop is a current loop, considering the hysteresis width ε=0.1. ΔM(θ)=-0.1M(θ), In order to better test the performance of the permanent magnet spherical motor, let the motor rotor perform nutating motion, and set the expected trajectory θ _d = [0.2sin2t 0.4cos2t 2t].

Fig. 10 is the tracking situation of the permanent magnet spherical motor for a given trajectory using the control strategy based on torque distribution proposed by the present invention, Fig. 11 is the motion trajectory of the output shaft on the stator spherical surface, and Fig. 12 is the error tracking during the operation of the motor Condition. It can be seen from the simulation results that due to the certain coupling of the axial movements of the permanent magnet spherical motor and the uncertainty of the motor structure, there is a slight deviation in trajectory tracking, but it is still within the allowable range, and the error is basically controlled at 0.1 Within rad, it shows that under the uncertainty of the model structure, the control strategy proposed by the present invention can track the given trajectory well, and the control system has good robustness and dynamic performance. In order to further reduce the tracking error, advanced control strategies such as neural network and decoupling control can be used to replace and optimize the PD controller. the

In the actual control system design, the realizability of the algorithm must be considered. In the spherical motor control system, the calculation time of the generalized inverse matrix increases geometrically with the increase of the dimension. The inversion of the high-dimensional matrix takes up a lot of resources of the digital processor and increases the calculation burden of the digital processor. Seriously affected the control effect of the system. Table 2 compares the calculation time of the matrix generalized inverse matrix of different dimensions, and the model of digital signal processor is TMS320F2812, and its clock cycle is 150MHz, as seen the torque distribution strategy that the present invention proposes can reduce matrix dimension effectively, has higher operating speed. the

Table 2 Computational Complexity Comparison

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.