CN109730625B

CN109730625B - Three-dimensional space voltage vector control method of space universal rotating magnetic field

Info

Publication number: CN109730625B
Application number: CN201910173796.3A
Authority: CN
Inventors: 张永顺; 李辉; 王殿龙
Original assignee: Dalian University of Technology
Current assignee: Dalian University of Technology
Priority date: 2019-03-08
Filing date: 2019-03-08
Publication date: 2021-08-10
Anticipated expiration: 2039-03-08
Also published as: CN109730625A

Abstract

The invention belongs to the technical field of automation engineering, and relates to a three-dimensional space voltage vector control method for a space universal rotating magnetic field for driving a capsule robot. According to the invention, the space universal rotating magnetic field is generated by controlling the tail end track of the three-dimensional voltage space vector on the triaxial orthogonal Helmholtz coil, and the control of the rotating magnetic fields with different frequencies, amplitudes and axial directions can be conveniently realized by adjusting parameters. In each control period which rotates for one circle and is equally divided, the instantaneous voltage vectors are taken to be synthesized, the approach of the magnetic field change synthesized in each control period to the target track is ensured, the precision of the rotating magnetic field is improved, and a solid foundation is laid for the clinical application of the space universal rotating magnetic field control capsule robot in the future.

Description

Three-dimensional space voltage vector control method of space universal rotating magnetic field

Technical Field

The invention belongs to the technical field of automation engineering, and relates to a three-dimensional space voltage vector control method for a space universal rotating magnetic field for driving a capsule robot.

Background

In modern society, more and more people live in a sub-health state, and are easy to breed a plurality of chronic diseases, wherein the diseases belong to gastrointestinal diseases most commonly. Most gastrointestinal diseases if diagnosed and cured in time at an early stage to prevent further deterioration or even carcinogenesis. Therefore, diagnosis and treatment of gastrointestinal diseases are important in the medical field. Most medical facilities currently employ electronic endoscopes as the primary means for diagnosing gastrointestinal disorders. However, the length of the guide tube limits the scope of the endoscope and does not allow the endoscope to traverse the entire gastrointestinal tract.

In order to solve the problems, researches find that the cableless driving mode can obviously improve the trafficability of the capsule robot in a complex gastrointestinal tract environment, and in the cableless driving mode, the magnetic control type capsule robot has the advantages of high reliability, good safety and the like in a non-contact control mode, so that the magnetic control type capsule robot is called as a research hotspot of domestic and foreign scholars.

Sehyuk Yim et al, usa, uses an external permanent magnet to generate a gradient magnetic field to control a soft capsule robot. The head and the tail of the capsule robot are respectively provided with two permanent magnets which can axially stretch and retract under the action of an external magnetic field to release the medicine loaded in the capsule robot, so that targeted medicine application is realized. The movement of the capsule robot is controlled by generating a rotating magnetic field through controlling the external permanent magnet. Because the magnetic field of the external permanent magnet has gradient, the magnetic force of the external permanent magnet cannot be accurately controlled, so that the method has the defects of complex operation, poor flexibility, poor robot position control stability and low precision, and has the risk of damaging the surface of the gastrointestinal tract due to overlarge magnetic force.

Ishiyama et al in Japan use triaxial Helmholtz coils to generate a spatial rotating magnetic field, the capsule robot embedded with radially magnetized NdFeB permanent magnets rotates under the control of the rotating magnetic field, and screw threads on the surface of the robot are used for generating precession motion, but the method for arbitrarily adjusting the axis of the rotating magnetic field is not provided, and the driving in the intestinal bending environment cannot be realized.

In order to realize free walking of the capsule robot in the bent intestinal environment, the subject group provides a space universal rotating magnetic field control method with adjustable rotation axis in an authorized national invention patent 'universal rotating magnetic field driving control method of in-vivo medical micro-robot' (patent authorization number: ZL 200810011110.2), and provides a basic current superposition formula of a rotating magnetic field suitable for a first quadrant of space.

In the granted national invention patent 'control method of rotation axis direction and rotation direction of space universal superposition rotating magnetic field' (patent grant number: ZL 201210039753.4), the combined driving mode of anti-phase current of three-phase sinusoidal current signals in the basic current superposition formula taking three direction angles of a certain fixed axis in space as input variables and the change rule of the rotation axis direction and the rotation direction of the space universal uniform rotating magnetic field superposed in a triaxial orthogonal nested Helmholtz coil device are taken as the basis, so that the uniqueness control of the rotation axis direction and the rotation direction of the space universal rotating magnetic field in each quadrant of a space coordinate system is realized, and the problems of realization of space universal rotating magnetic vector direction, rotation direction, strength, magnetic flux density and the like through digital control are theoretically solved, The problem of arbitrary adjustment of the rotating speed lays a foundation for realizing the posture adjustment and the directional driving walking of the robot. As shown in fig. 1, by inputting the intensity amplitude, the axis direction, the rotation speed, and the like of the rotating magnetic field into the computer control platform 2, the computer control platform calculates the current amplitude and the phase parameter introduced into the triaxial helmholtz coil through a basic current superposition formula, and transmits the current amplitude and the phase parameter into the DSP control system 1, and the control system drives the triaxial orthogonal square helmholtz coil 4 to generate the rotating magnetic field to realize the control of the capsule robot 3.

In order to solve the problem that two motion modes of posture adjustment and walking of a capsule robot are separated from each other when the capsule robot is examined in the gastrointestinal tract, the invention discloses an active and passive double-hemispherical capsule robot and a posture adjustment and turning drive control method thereof in an authorized national patent (patent authorization No. ZL 201510262778.4), the flexibility and the universality of a spherical structure are utilized, the rolling motion of the spherical robot is avoided when the posture is adjusted, the free posture adjustment and turning walking of the active and passive double-hemispherical capsule robot in the body can be realized by combining the control of a space universal rotating magnetic field, and researches show that the control precision of the robot is directly influenced by the position of the space universal rotating magnetic field and the circular track error at the tail end.

In an authorized national invention patent 'a space universal rotating magnetic field man-machine interaction control method' (patent authorization No. ZL 201610009285.4), a space universal rotating magnetic field superposition formula in a current form with two attitude angles of a yaw angle and a pitch angle as input variables in a longitude and latitude coordinate system is provided for realizing space universal rotating magnetic field man-machine interaction control,

wherein

Wherein θ and δ are the yaw angle and the pitch angle of the axis of the robot, I0 is the amplitude of the sinusoidal current in the three sets of orthogonal helmholtz coils, ω is the angular frequency of the applied sinusoidal signal current, and f is 2 pi/ω. The three-dimensional superposition problem of the space universal rotating magnetic field is converted into a two-dimensional superposition problem in a plane, and the pendulums and the pitching angles are separately controlled through two control rods, so that low-dimensionality separable variable interactive control is realized.

The driving of triaxial orthogonal Helmholtz coils is a key technology for generating a space universal rotating magnetic field to control the capsule robot, and the rotating magnetic field is generated in the coil space by driving the Helmholtz coils to generate three groups of sine current waveforms with certain amplitudes and phases. At present general Helmholtz coil drive technique regards single-axis Helmholtz coil as resistance-inductance load to on the basis of inverter technique, adopt inverter circuit to connect load coil, through the control to switch unit among the inverter circuit, exert sinusoidal pulse width modulation voltage waveform on resistance-inductance load coil, drive Helmholtz coil and produce sinusoidal current waveform. Corresponding currents are independently applied to three shafts of the Helmholtz coil respectively, and finally, a space rotating magnetic field is superposed by three-shaft magnetic field components according to the BioSaval law. The current in the load coil is bound to have a certain harmonic component except the ideal fundamental wave sinusoidal current, the corresponding sinusoidal alternating magnetic field generated by the shaft coil also has a certain harmonic component, and the harmonic component can be regarded as an error superposed on the ideal sinusoidal component, so that finally a space universal rotating magnetic field superposed by three shafts has a certain error. Three inverter circuits are adopted to independently drive the three-axis load coils respectively, only sine fundamental wave components are taken as modulation targets, and the effect of three-axis synthesis is not directly considered.

In order to reduce errors caused by harmonic components, the application patent proposes a three-dimensional space voltage vector control method, and at present, no method has been proposed for carrying out three-axis comprehensive control on a three-axis helmholtz coil through retrieval, deducing a three-dimensional voltage space vector tail end track loaded by the three-axis helmholtz coil by directly aiming at synthesizing a space circular rotating magnetic field, equally dividing one rotating period of the magnetic field into a plurality of control periods, and controlling a switching unit in a power driving structure in each control period to synthesize the three-dimensional voltage space vector tail end track so as to finally generate a space rotating magnetic field. Compared with the method that the three-axis load coil is independently driven, the three-axis Helmholtz coil is comprehensively controlled, and the ideal rotating magnetic field and the corresponding ideal voltage vector tail end track are used as targets for controlling in each control period, so that the error of the finally generated space rotating magnetic field can be reduced. The method adopts a brand-new control idea, ensures the approach of the synthesized magnetic field and the target track in each control period, improves the precision of the rotating magnetic field, and lays a solid foundation for the clinical application of the space universal rotating magnetic field control capsule robot in the future.

Disclosure of Invention

The invention provides a brand-new three-phase six-bridge-arm power driving structure diagram for driving a Helmholtz coil to generate a space universal rotating magnetic field and a corresponding three-dimensional space voltage vector control method. Compared with a method for independently driving the three-axis coil by using three groups of sinusoidal pulse width modulation, the method can improve the precision of the rotating magnetic field under the condition of the same parameters.

The technical scheme of the invention is as follows:

a three-dimensional space voltage vector control method of a space universal rotating magnetic field comprises the following steps:

firstly, three groups of sinusoidal voltage formulas applied to Helmholtz coils are deduced according to the axial direction and the magnetic field intensity of a space universal rotating magnetic field and by combining the space structure and the load characteristic of the triaxial Helmholtz coil. The voltage terminal trajectory parameter curve is proved to be a generalized ellipse by taking the voltage terminal trajectory parameter curve as a three-dimensional space vector through a differential geometric method. In order to synthesize the elliptical voltage tracks, one rotation period is equally divided, and an end track vector corresponding to the middle point time of each equally divided interval is taken as an instantaneous voltage vector for synthesizing the whole rotation period.

And secondly, enumerating the switch state combinations of all the bridge arms, wherein each switch state combination corresponds to a voltage state loaded on the triaxial Helmholtz coil, and the voltage state can be regarded as a space voltage vector which is called a basic voltage vector by combining the orthogonal space structure of the coil.

Thirdly, constructing a plurality of segmentation planes to segment the three-dimensional space according to the spatial distribution characteristics of the basic voltage vector to form a plurality of space segmentation areas, providing a mode of equally dividing the track of the tail end of the generalized elliptic voltage by one circle and taking the value of the instantaneous voltage vector in each equally-divided interval, and providing a method for judging the space segmentation area where the current instantaneous voltage vector is located;

and fourthly, after the space division area where the current instantaneous voltage vector is located is judged, the basic voltage vector corresponding to the space division area is determined. And deriving a duty ratio formula of each basic voltage vector action in the control period based on a volt-second balance principle.

And fifthly, providing a design method for the arrangement mode of each basic voltage vector in a control period.

And sixthly, after the control of one control cycle is finished, continuing to calculate the instantaneous voltage vector of the next control cycle, calculating the space partition region, determining the basic voltage vector, calculating the corresponding duty ratio, and switching the states of the bridge arms according to a cycle time sequence design method to drive the Helmholtz coil. And when all control periods which are equally divided into one rotation period are controlled, the universal rotating magnetic field generated by the triaxial Helmholtz coil also rotates for one circle.

In the first step, the principle of deriving three sets of sinusoidal voltage equations applied to the helmholtz coil is as follows:

combining the formula (1) with the BioSaval law, set K_x，K_y，K_zThree sets of orthogonal Helmholtz coils with structural parameters B_i＝K_i*I₀(i ═ x, y, z). And because the triaxial Helmholtz coil belongs to the resistance-inductance load, R is set_x，R_y，R_zIs the resistance of the Helmholtz coil, L_x，L_y，L_zThe voltage formula loaded on the triaxial Helmholtz coil can be deduced from the voltage and current formula for the inductance of the coil,

B₀is the magnitude of the spatial rotating magnetic field.

The voltage formula can be regarded as a three-dimensional space voltage vector with time t as a variable, and the terminal track characteristics of the three-dimensional space voltage vector are analyzed below. The subject group invented a patent "directional wireless energy transmission method of space linear polarization universal alternating magnetic field" (patent authorization number: ZL 201610997340.5) in the granted country discusses the space parameter curve in the form of the above formula, and according to the theorem of curve theory, it proves that the flexibility of the space curve superimposed by three arbitrary orthogonal sinusoidal magnetic field components is constantly equal to zero and is a plane curve in space. Similarly, it can be proved that the voltage trajectory curve described by the formula (2) is an ellipse in a spatial plane, that is, in order to superimpose the space-universal rotating magnetic field of the circular end trajectory described by the formula (1), the applied spatial voltage trajectory curve of the formula (2) is an ellipse, and the two are different in the rotating plane. Further, it can be deduced that the unit normal vector of the plane where the voltage space curve described in formula (2) is located is,

the unit normal vector corresponds to the attitude angles θ 2 and δ 2. The shape of the end trajectory is discussed by transforming the voltage space curve expression in the fixed coordinate system to the rotating coordinate system, as shown in fig. 3, where oxyz is the fixed coordinate system fixed to the three-axis orthogonal helmholtz coil, and ox2y2z2 is the rotating coordinate system after the rotation transformation. Firstly, the normal vector of the rotation plane of the tail end track rotating in the xoz plane is coincided with the y axis, the tail end track rotates clockwise by theta 2 angle around the z axis, and then rotates anticlockwise by delta 2 angle around the x2 axis, so that a coordinate system ox2y2z2 can be obtained, and the tail end track is deduced to be ox in the x2oz2 plane by utilizing a coordinate transformation formula provided in the granted national invention patent 'a space universal rotation magnetic field man-machine interaction control method' (patent grant No. ZL 201610009285.4)₂y₂z₂The voltage end trajectory in the coordinate system is expressed as,

from the correlation characteristic of the polarization of electromagnetic waves, x is the number in the above formula₂oz₂The same amplitude of frequency in the plane is superposed with two orthogonal sine vectors with random phases, and the tail end track of the voltage vector is a generalized ellipse. The terminal trace of the voltage vector is modulo,

note that when the sine value in the formula is 1, i.e. the

The mode value of the time-end trajectory is the largest, corresponding to half the length of the long axis. The time point is substituted into a voltage space vector formula to obtain the coordinate of the semimajor axis vector of the generalized elliptic tail end track in an oxyz coordinate system in a rotation period,

when the sine value in the formula is-1, i.e.

The module value of the end trajectory is the smallest and corresponds to half the length of the minor axis. The time point is substituted into a voltage space vector formula to obtain the coordinate of the semi-minor axis vector of the generalized elliptic tail end track under an oxyz coordinate system,

in the second step, the proposed three-phase six-arm power driving structure diagram for the three-axis helmholtz coil driving is shown in fig. 2, each group of the three-axis helmholtz coils is driven by two arms, two ends of the load coil are respectively connected to the midpoints of the two arms, the three-axis coils correspond to six arms Ai (i is 1,2,3,4,5,6), and each arm is composed of an upper switching tube, a lower switching tube and a freewheeling diode. When the helmholtz coil is driven, only two states of the two switching tubes of each bridge arm are specified, wherein the bridge arm state is recorded as Ai being 1 when the upper tube is turned on and the lower tube is turned off, the middle point of the bridge arm is communicated with the positive pole of the direct current bus voltage Udc, the potential is the positive pole voltage of the direct current bus, and when the upper tube of each bridge arm is turned off and the lower tube is turned on, the bridge arm middle point is communicated with the negative pole of the direct current bus voltage, and the potential is the negative pole voltage of the direct current bus. All state combinations of the six bridge arms are 64 combination modes, each combination mode corresponds to a six-bridge arm midpoint voltage combination mode, voltages at two ends of each Helmholtz coil group can be obtained by subtracting voltages at two corresponding bridge arm midpoints, and voltages at two ends of x-axis, y-axis and z-axis coils are respectively set to be U_a，U_b，U_cFurther, the voltage state of the three-axis coil is regarded as a voltage vector U ═ U (U)_a，U_b，U_c)^TCalculating all voltage vectors corresponding to 64 six-bridge arm switch state combination modes,referred to as 64 basic voltage vectors, are given below in tabular form,

table 164 basic voltage vectors

Of the 64 basic voltage vectors, the vector (0,0,0) at the origin of the coordinates^TAlso known as zero vector, where U_a U_bU_cThe state that the voltage of each phase is 0 corresponds to two states of 00 or 11 for driving two bridge arms of the Helmholtz coil, and 8 state combinations of six bridge arms corresponding to the zero vector can be calculated by the permutation and combination. The basic voltage vector with directions distributed along the x, y and z axes is characterized by U_a U_b U_cIn the three phases, the voltage of two phases is zero, the voltage of the other phase is not zero, the states of two bridge arms corresponding to the phase with the non-zero voltage are 01 and 10, and 24 kinds of six bridge arm state combinations corresponding to the basic voltage vector distributed according to the rule can be calculated through permutation and combination. The basic voltage vector with the direction in one of the xy, yz and xz planes and the angle of 45 degrees with the coordinate axis has the characteristics that the voltage of one phase in three phases of Ua Ub Uc is zero, the voltage of the other two phases is not zero, and 24 types of six bridge arm state combinations corresponding to the basic voltage vector with the distribution characteristic can be calculated according to the permutation and combination. The rest basic voltage vectors are distributed at the vertex of a three-dimensional space cube, the voltage of three phases of the Ua Ub Uc is not zero, and the distribution characteristic corresponds to 8 middle six-bridge arm state combination according to permutation and combination. In the attached drawings 4(a), 4(b), 4(c) and 4(d), all 64 basic voltage vectors are drawn in the form of three-dimensional space vectors, and all the basic voltage vectors jointly form a side length of 2U which spans 8 quadrants of the three-dimensional space_dcA cube of (a).

In the third step, the principle that the proposed construction plane divides the three-dimensional space to form a plurality of space division areas is as follows:

through the observation of the distribution rule of the basic voltage vectors in fig. 4(a), 4(b), 4(c) and 4(d), it can be found that all the basic voltage vectors are parallel to the coordinate axes or form an angle of 45 degrees with a certain coordinate axis, or the projection of the basic voltage vectors on the xy yz or xz plane forms an angle of 45 degrees with a certain coordinate axis. Therefore, the three-dimensional cubic space is divided into 48 space division areas with the coordinate axis origin as the vertex and the cube surface as the bottom surface by 9 space planes as shown in fig. 5, and the bottom surfaces of the space division areas are all isosceles right triangles.

These space division areas are all given in fig. 6 as well, and it can be seen from the drawing that each quadrant includes six space division areas, three sides of the bottom surface of each space division area, which are induced by the vertex, are three basic voltage vectors, and one of the three voltage vectors is a basic voltage vector along the x, y or z axis, and each voltage vector along the coordinate axis corresponds to four six-leg switch states; the vector direction is in the xy yz or xz plane and forms an angle of 45 degrees with the coordinate axis, and the vector direction corresponds to two basic voltage vectors; the other vector direction points to the vertex of the cube from the origin of the coordinate system and only corresponds to one six-arm switch state. In order to mark the space division areas, each space division area adopts a unique RP value corresponding to the space division area, and the definition method and the numerical significance of the RP value are given later.

Dividing N equally for a rotation period T2 pi/omega of the generalized elliptic voltage space vector tail end track, taking one part as a control period, taking the other part as a target for synthesizing the current control period, and taking the voltage vector corresponding to the midpoint moment of the current control period as an instantaneous voltage vector u_ins. The method specifically takes the instantaneous vector and the number of the equal parts N of one rotation period is even, the control period Tc is T/N is 2 pi/N omega, and the interval time between every two instantaneous vectors is Tc, so that the time taken by the instantaneous vector is taken into (formula 2), and the coordinate u of the instantaneous voltage vector in the three-dimensional space is obtained_ins＝(u_insx，u_insy，u_insz)^T。

In order to synthesize the instantaneous voltage vectors in each control cycle after being equally divided, it is necessary to know the space division region where the instantaneous voltage vector is located, further determine the corresponding basic voltage vector, and synthesize the instantaneous vectors by using the linear-time combination of the basic voltage vectors. Based on the partition plane design boundary conditions shown in fig. 5, a decision formula is proposed,

the voltage vector in each space division region corresponds to k₁k₂k₃k₄k₅k₆k₇k₈k₉There is only one state combination, so that the calculation formula of RP has a unique value corresponding to each space division region, and the RP value obtained by the calculation of the above formula corresponds to the space division region marked with the corresponding RP value in the figure, i.e., corresponds to the basic voltage vector used to synthesize the instantaneous voltage vector.

In the fourth step, based on the volt-second balance principle, the principle of the duty ratio formula of each basic vector in a control period derived in the process of synthesizing the instantaneous voltage vector by using the basic voltage vector is as follows:

taking a certain control cycle as a discussion target, setting the elapsed time period to be T1-T2, where Tc is T2-T1, and because the Tc time length is short, the current in the three sets of helmholtz coil resistors Ri (i is x, y, z) can be regarded as a constant value in this time period, that is, the voltage in the resistors can be regarded as a constant value u_RiTherefore, the change of the inductive current of the Helmholtz coil can be conveniently solved to solve the change of the magnetic field. Combining with the Bio Saval law, a formula of the three-axis magnetic field and the voltage relative to the time t can be obtained,

further converting T₁，T₂And Tc, the variation from T1 to T2B under the action of instantaneous voltage can be obtained,

let u be the corresponding three basic voltage vectors calculated from the instantaneous voltage vector as set forth in the third section_1bv u_2bv u_3bv，u_jbv＝[u_jbvx,u_jbvy,u_jbvz]^T(j ═ 1,2,3) the times at which it acts in the current control period Tc period are t1t2t3, respectively, zero vector u_0bvThe action time of (2) is t0, the sum of the action times of all the basic voltage vectors is equal to the time length of Tc, and t0+ t1+ t2+ t3 is Tc. In a certain small time period t0t1t2t3, assuming that the starting time of the small segment is tsj (j is 0,1,2,3), the amount of change in the magnetic field after the time period tj (j is 0,1,2,3) from this time is set as,

the ultimate goal of the synthesis is to produce an effect equal to the instantaneous vector effect, i.e. to make the total amount of magnetic field change the same over the entire Tc control period, i.e.:

the expression (10) and the expression (11) are brought into the above expression and expanded to obtain the product,

u_0bvit₀+u_1bvit₁+u_2bvit₂+u_3bvit₃＝u_insiT_c(i＝x,y,z) (13)

i.e. the sum of the products of the respective basic voltage vectors and their action times (volt-second product) is equal to the volt-second product of the instantaneous voltage vectors. The two sides of the equation are equally divided by Tc, and the ratio of the acting time of each basic voltage vector to Tc is taken as the duty ratio dj/Tc (j is 0,1,2, 3). Combining the formula with equal action time length, listing the formula in a matrix form,

the matrix is sorted to obtain a duty ratio calculation matrix,

in the formula, the respective parameters are as follows,

during the whole process of rotating the rotating voltage vector by one circle, all instantaneous vectors of the control period after the equal division calculate the duty ratio of the basic voltage vector in the mode.

In the fifth step, the principle of the proposed cycle timing design method is as follows:

the method for calculating the duty cycle of each basic voltage vector for synthesizing the instantaneous voltage vector in one control period Tc is given above, and the sorting mode is provided below. The schematic diagram of the period timing sequence is shown in the attached figure, the action duty ratios of the zero vector are respectively arranged at two ends and the central position of a control period, and in one control period, each bridge arm in six bridge arms is regulated to perform state switching only twice, namely from 0 to 1 to 0. In addition, when the basic voltage vector is switched every time, namely, the state of the voltage vector acting on the three-axis Helmholtz coil is changed, the switching can be realized by only switching the state of one of the six bridge arms. Firstly outputting a zero vector when a control period starts, taking the acting duty ratio time length as d0/4, and sequentially experiencing d according to the condition that one bridge arm state is switched every time₁U of/4_1bv，d₂U of/4_2bv，d₃U of/2_3bv，d₂U of/4_2bv，d₁U of/4_1bvAnd when the zero vector reaches the center, the duty cycle time length of the zero vector at the center is d0/2, and the bridge arm state is 111111. That is, in the first half of the control cycle, the state of one bridge arm is switched from 0 to 1 each time, and the zero vector in the center is reached after six times of switching. After the central zero vector state, the state of one bridge arm is switched from 1 to 0 every time, and the zero vector at the end of one control period is reached after six times of switching. The bridge arm states in the whole control period are symmetrical left and right by taking the midpoint moment as a boundary line.

As can be seen from table 1, the voltage states expressed by u1bv and u2bv do not correspond to only one kind of basic voltage vector in table 1, that is, only one kind of switching state of the arm. In the periodic timing design method, the bridge arm switching states need to be determined, and the correspondence between the zero vector, the specific basic voltage vectors represented by u1bv and u2bv, and the bridge arm switching states is given below. For example, assuming that the RP value of the space division region where the instantaneous voltage vector of the current control period is located is 270, it can be known from fig. 6 that the voltage state expressed by u1bv is [0-Udc 0] T, the voltage state expressed by u2bv is [0-Udc ] T, and the voltage state expressed by u3bv is [ Udc-Udc ] T. At the beginning of a control cycle, a zero vector is output, as can be seen from table 1, the zero vector has 8 numbers, corresponds to 8 kinds of six-arm switching states, wherein 000000 state is selected, corresponds to a basic voltage vector u57, and the zero vector acts on a d0/4 duty cycle length and then is switched to u1bv, as can be seen from table 1, the corresponding basic voltage vectors have u29, u30, u31 and u32, and the six-arm switching states 000111, 000100, 110111 and 110100, and according to the principle that only one arm is operated when the basic voltage vector is switched each time, the u 29000100 state only reverses the a4 arm compared with the 000000 arm state under the zero vector output, so that u1bv is u29 and a d1/4 duty cycle length is applied. Then, the value u2bv is switched, and table 1 shows that the corresponding basic voltage vectors include u35, u36 and six-arm switching states 000110 and 110110 thereof, wherein u35 only reverses the state of the arm a5 compared with the last state u 29000100, so that u2bv is u35 and a d2/4 duty cycle length is applied. Next, switching to u3bv is performed, and it is known from table 1 that the current state corresponds to only one basic voltage vector u40 and its six-arm switching state 100110, and the state can be obtained by merely inverting the state of the a1 arm with respect to the previous state u 35000110, so that u3bv is taken as u40 and d3/2 duty cycle length is applied. Switching next to u2bv, from the above description, its corresponding base voltage vector u36 and its six leg switching state 110110 can be obtained by flipping only the a2 leg state compared to the previous state u 40100110, thus taking u2bv as u36 and applying d2/4 duty cycle length. Switching to u1bv next, it is found from the above description that u32 and its six leg switching state 110111 can be obtained by state inversion of the a6 leg from the last state u 36110110, thus taking u1bv as u32 and applying d1/4 duty cycle length. Then, switching to the zero vector is performed, and from table 1, it can be found that, in 8 basic voltage vectors corresponding to the zero vector, u64 and the six-leg switch state 111111 thereof can be obtained by state-flipping the A3 leg by u 32110111 in the previous state, so that the zero vector is taken as u64 and the duty cycle length of d0/2 is applied. By this step, the whole control cycle goes through more than half, and the output basic voltage vector switching goes through zero vectors (u57) -u1bv (u29) -u2bv (u35) -u3bv (u40) -u2bv (u36) -u1bv (u32) -zero vectors (u64), respectively, and only one arm is actuated per switching (in the order of a4-a5-a1-a2-A6-A3), and six arms are actuated once in the first half of the control cycle. And the subsequent output basic voltage vector, the acting duty ratio length, the bridge arm switching state and the previous half period are in mirror symmetry with respect to the midpoint moment by taking the midpoint moment of the control period as a reference, which is not described herein.

The basic voltage vector of the synthesized instantaneous voltage vector and the determination method of the bridge arm switch state are given by taking the space division region with RP being 270 as an example, and actually, the remaining 47 space division regions are similar to the basic voltage vector, and the rule that one bridge arm is operated each time and the state of each bridge arm is turned over twice in the whole control period can be realized by selecting the basic voltage vector. Two zero vectors are taken as u57 and u64, and basic voltage vectors corresponding to u1bv, u2bv and u3bv in all 48 space division areas are given in a table form. The vector to the left of the two basic voltage vectors in the columns u1bv and u2bv of the table occurs first in one control cycle compared to the vector to the right.

TABLE 2 spatial partitioning of regions and corresponding base voltage vector selection

According to the invention, the space universal rotating magnetic field is generated by controlling the tail end track of the three-dimensional voltage space vector on the triaxial orthogonal Helmholtz coil, and the control of the rotating magnetic fields with different frequencies, amplitudes and axial directions can be conveniently realized by adjusting parameters. In each control period which is equally divided by one circle of rotation, the instantaneous voltage vectors are taken for synthesis, the approach of the synthesized magnetic field change and the target track in each control period is ensured, and the precision of the rotating magnetic field is improved. Lays a solid foundation for the clinical application of the space universal rotating magnetic field control capsule robot in the future.

Drawings

Fig. 1 is a schematic diagram of a space-universal rotating magnetic field overall control system of a capsule robot.

FIG. 2 is a schematic diagram of a power driving configuration for driving a three-axis Helmholtz coil.

Fig. 3 is a schematic view of a rotating coordinate system.

FIG. 4(a) is a schematic diagram of a zero vector;

FIG. 4(b) is a schematic diagram of the basic voltage vectors distributed along the x, y or z axis;

FIG. 4(c) is a schematic diagram of the basic voltage vectors at 45 to the coordinate axes in the xy, yz or xz plane;

fig. 4(d) is a schematic diagram of the basic voltage vectors at the vertices of the cube space.

Fig. 5 is a schematic plan view of a space used for dividing the cuboid space.

FIG. 6 is a diagram of 48 spatially partitioned regions and their corresponding RP values.

FIG. 7 is a schematic diagram of a method for designing cycle timing in a control cycle.

FIG. 8(a) is a schematic diagram of the rotating magnetic field generated inside a three-axis Helmholtz coil using the proposed three-dimensional space voltage vector control method under certain parameters;

fig. 8(b) is a schematic diagram of the rotating magnetic field generated inside the triaxial helmholtz coil using a common sinusoidal pulse width modulation scheme under the same parameters as fig. 8 (a).

FIG. 8(c) is a schematic diagram of the rotating magnetic field generated inside a three-axis Helmholtz coil using the proposed three-dimensional space voltage vector control method under another set of parameters;

fig. 8(d) is a schematic diagram of the rotating magnetic field generated inside the triaxial helmholtz coil using a common sinusoidal pulse width modulation scheme under the same parameters as fig. 8 (c).

In the figure:

1, a DSP control system; 2, a computer control platform; 3 a capsule robot with embedded radial magnetized permanent magnets;

4 a triaxial orthogonal helmholtz coil;

a5 x axis Helmholtz coil;

a6 y-axis Helmholtz coil;

7 z-axis Helmholtz coils;

8, a plane where the tail end track of the three-dimensional space voltage vector is located;

9, the normal direction of the plane where the three-dimensional space voltage vector tail end track is located;

the 10 plane Ua is 0; plane Ub of 11 is 0; 12 plane Uc is 0; 13 plane Ub + Uc is 0;

14 plane Ub-Uc is 0; 15 plane Ua + Uc is 0; the 16 plane Ua-Uc is 0; plane Ua + Ub of 17 is 0;

the 18 plane Ua-Ub is 0;

a Udc dc bus voltage;

a1 and A2 are bridge arms for driving x-axis Helmholtz coils;

a3 and A4 are bridge arms for driving y-axis Helmholtz coils;

a5 and A6 are bridge arms for driving z-axis Helmholtz coils;

s1 and S2 are upper and lower switching tubes of an A1 bridge arm;

s3 and S4 are upper and lower switching tubes of an A2 bridge arm;

s5 and S6 are upper and lower switching tubes of an A3 bridge arm;

s7 and S8 are upper and lower switching tubes of an A4 bridge arm;

s9 and S10 are upper and lower switching tubes of an A5 bridge arm;

s11 and S12 are upper and lower switching tubes of an A6 bridge arm;

a1, A2, A3, A4, A5 and A6 are the switching states of six bridge arms respectively; tc is the control period.

Detailed Description

The following detailed description of the embodiments of the invention refers to the accompanying drawings.

Example 1:

the overall structure of a conventional triaxial orthogonal helmholtz coil of the subject group is shown in fig. 1, and the structure and electrical parameters of a square helmholtz coil for each axis used are shown in table 3.

TABLE 3 Helmholtz coil size parameters for each axis

The process of generating a spatial rotating magnetic field by using a three-dimensional space voltage vector control model will be described in detail by taking as an example that the amplitude of the generated rotating magnetic field is 10mT, the rotating frequency is f 8Hz, that is, the angular frequency is ω 16 π rad/s, the dc bus voltage is Udc 205V, and the axis of the rotating magnetic field is (17 ° or 63 °).

Firstly, with the axial direction information of the rotating magnetic field, namely theta 17 and delta 63 as the rotating magnetic field axis under the fixed coordinate system oxyz, combining the biot savart law and the voltage and current formula, and referring to the three-axis orthogonal Helmholtz coil parameters given in the above table, the parameters Ux 105.16Uy in the voltage space vector end trajectory formula with the time t as the variable on the three-axis coil are calculated-57.74Uz＝14.71

Further obtaining the formula of the tail end track as follows,

obtaining a normal vector of a plane where a terminal locus of the space vector of the characterization voltage is located by the formula (3), obtaining azimuth angles theta 2 and delta 2 of the normal vector under a fixed coordinate system oxyz,

further calculating parameters a 5-62.17, a 6-85.34, a 7-48.06, a 8-33.91, a 9-7352.2, a 10-2256.6,

calculating the time when the sine value in the module value formula is 1 and corresponds to half of the length of the long half shaft

k is taken to be 0 to obtain

The semimajor axis vector of the generalized elliptic voltage terminal locus under the fixed coordinate system oxyz is (104.99, -11.25, -0.33) by substituting the terminal locus formula^T。

And secondly, taking the frequency corresponding to the control period as 2000Hz, and dividing the control period Tc into 1/2000-0.0005 s, namely equally dividing one rotation period into N2000/8-250 parts. And the control of the tail end track of the whole generalized elliptical voltage vector is realized by performing equivalent synthesis on the instantaneous voltage vector in each control period. Firstly, the semimajor axis vector of the generalized elliptic voltage terminal track obtained by the previous step is used as an instantaneous voltage vector,

in order to determine the space-divided region where the instantaneous voltage vector is located, an RP value corresponding to the instantaneous voltage vector is calculated by using a determination formula, where each parameter in the calculation formula is k 1-1, k 2-0, k 3-0, k 4-1, k 5-1, k 6-0, k 7-0, k 8-1, and k 9-1, and the calculation formula is obtained by:

the RP value has only one spatially partitioned area corresponding to it, as shown in fig. 6.

And thirdly, determining a space division region where the instantaneous voltage vector is located in the last step, wherein the space division region is positioned in an eighth quadrant and is led to three sides of the bottom surface of a triangle positioned on the surface of the square space from the origin of a coordinate system, one of the three sides is positioned along the direction of an x axis, and the corresponding basic voltage vector is (Udc,0,0)^TAnd one side forms an angle of 45 degrees with the positive direction of the x axis and the negative direction of the y axis in the xy plane, and the corresponding basic voltage vector is (Udc, -Udc,0)^TThe other side points to the vertex of the lower left corner of the cube, and the corresponding basic voltage vector is (Udc, -Udc)^T。

The three basic voltage vectors used in the duty cycle calculation matrix are respectively,

combining the instantaneous voltage vector u calculated in the first step_insSubstituting the obtained result into a duty ratio matrix formula to obtain the action duty ratios of the basic voltage vectors,

i.e. zero vector function 0.4878Tc time length, base voltage vector (Udc,0,0) in the current control period Tc^TAction 0.4573Tc time duration, base voltage vector (Udc, -Udc,0)^T0.0533Tc duration of action, basic voltage vector (Udc, -Udc)^TThe effect is 0.0016Tc time length.

And fourthly, sequencing the states of the bridge arms in one control period according to the calculated duty ratio of each basic voltage vector. As shown in fig. 7, (1) at the beginning of one control cycle, the basic voltage vector acting on the triaxial helmholtz coil is u57, the six-leg state is 000000, and the acting time length is Tc · d0/4 ═ 0.1220 Tc. (2) Next, according to table 2, the basic voltage vector applied to the triaxial helmholtz coil is u1, the six-arm state is 100000, and the a1 arm state is inverted based on the original state, and the action time length is Tc · d1/4, which is 0.1143 Tc. (3) Next, according to table 2, the basic voltage vector applied to the triaxial helmholtz coil is u47, the six arm state is 100100, and the a4 arm state is inverted based on the original state, and the operating time length Tc · d2/4 is 0.0133 Tc. (4) Next, according to table 2, the basic voltage vector applied to the triaxial helmholtz coil becomes u56, the six arm state 100101 is obtained by inverting the a6 arm state based on the original state, and the operating time length Tc · d3/2 is 0.0008 Tc. (5) Next, according to table 2, the basic voltage vector applied to the triaxial helmholtz coil becomes u48, the six arm state 100111 is obtained by inverting the a5 arm state based on the original state, and the operating time length Tc · d2/4 is 0.0133 Tc. (6) Next, according to table 2, the basic voltage vector applied to the triaxial helmholtz coil becomes u4, the six arm state 101111, and the a5 arm state is inverted based on the original state, and the operating time length Tc · d1/4 is 0.1143 Tc. (7) And switching the basic voltage vector loaded on the triaxial Helmholtz coil to a zero vector, overturning the A2 arm state on the basis of the original arm state, and outputting the 111111 arm state. The action time length is Tc.d 0/2-0.2439 Tc. The time in one control cycle has been half so far, and the a1-a 6 arms are each operated once by switching one arm state from 000000 to 111111 each time the basic voltage vector output is changed. (8) And taking the midpoint moment of the control period as a reference, wherein the subsequent basic voltage vector output, bridge arm switching mode and action time length are symmetrical to the control period of the first half, and are not repeated here, and each bridge arm acts twice during the whole control period.

And fifthly, after finishing one control period, starting the calculation of the next control period. And returning to the first step, taking the next instantaneous voltage vector time at the interval of Tc time length on the basis of the time of the previous instantaneous voltage vector value, substituting the current voltage vector into a terminal track formula (2), calculating the instantaneous voltage vector of the next control period, and sequentially carrying out a new control period according to the first, second, third and fourth steps. Until all N is performed for 250 control cycles, one rotation cycle is controlled, and finally, the rotating magnetic field generated inside the triaxial helmholtz coil space is as shown in fig. 8 (a). For convenience of comparison, it is shown that the effect of the method on improving the accuracy of the rotating magnetic field is achieved, fig. 8(b) shows that under the conditions of the same parameters of the triaxial helmholtz coils, the same amplitude of the rotating magnetic field, the same rotating frequency, the same dc bus voltage, the same axial direction of the rotating magnetic field, and the carrier frequency of 2000Hz, three sets of sinusoidal pulse width modulation are used to respectively drive the triaxial helmholtz coils to generate the rotating magnetic field trajectory superimposed by the sinusoidal current waveforms shown in formula (1), and as can be seen from comparison between fig. 8(a) and fig. 8(b), the method has a good effect on improving the accuracy of the rotating magnetic field compared with the currently general sinusoidal pulse width modulation mode.

Example 2:

the three-axis square orthogonal helmholtz coil structure and electrical parameters used in this example are as shown in table 3, and a process of generating a spatial rotating magnetic field using a three-dimensional spatial voltage vector control model will be described in detail, taking as an example that the amplitude of the generated rotating magnetic field is 8mT, the rotating frequency is f equal to 10Hz, that is, the angular frequency is ω equal to 20 π rad/s, the dc bus voltage is Udc equal to 205V, and the axis of the rotating magnetic field is (247 ° and 41 °).

First, rotating the axial direction of the magnetic fieldThe information theta is 247 DEG, delta is 41 DEG as the axis of the rotating magnetic field under the fixed coordinate system oxyz, the biotival law and the voltage and current formula are combined, and the parameters of the triaxial orthogonal Helmholtz coil given in the above table are referred to, so that each parameter Ux, 73.91Uy, 58.44Uz, 22.95 in the formula of the terminal trajectory of the voltage space vector on the triaxial coil with the time t as the variable is calculated

Further obtaining the formula of the tail end track as follows,

further calculating parameters a 5-54.69, a 6-53.83, a 7-51.66, a 8-29.08, a 9-2882.9, a 10-1915.2,

k is taken to be 0 to obtain

The semi-major axis vector of the generalized elliptic voltage end track under the fixed coordinate system oxyz is (-71.28,34.65, -12.30) by substituting the end track formula into the time point^T。

And secondly, taking the frequency corresponding to the control period as 2000Hz, and then dividing the control period Tc into 1/2000-0.0005 s, namely equally dividing one rotation period into N2000/10-200 parts. And the control of the tail end track of the whole generalized elliptical voltage vector is realized by performing equivalent synthesis on the instantaneous voltage vector in each control period. Firstly, the semimajor axis vector of the generalized elliptic voltage terminal track obtained by the previous step is used as an instantaneous voltage vector,

in order to determine the space-divided region where the instantaneous voltage vector is located, the RP value corresponding to the instantaneous voltage vector is calculated by using a determination formula, where k1 is 0, k2 is 1, k3 is 0, k4 is 0, k5 is 0, k6 is 1, k7 is 1, k8 is 0, and k9 is 0, and the calculation formula is obtained

And thirdly, determining a space division region where the instantaneous voltage vector is located in the last step, wherein the space division region is positioned in the eighth quadrant and is led to three sides of the bottom surface of the triangle positioned on the surface of the square space from the origin of the coordinate system, one of the three sides is in the negative direction of the x axis, and the corresponding basic voltage vector is (-Udc,0,0)^TAnd one side forms an angle of 45 degrees with the negative direction of the x axis and the positive direction of the y axis in the xy plane, and the corresponding basic voltage vector is (-Udc, 0)^TThe other side points to the vertex of the sixth quadrant of the cube, and the corresponding basic voltage vector is (-Udc )^T。

i.e. the zero vector function 0.6523Tc time length, the basic voltage vector (-Udc,0,0) in the current control period Tc^TFunction 0.1787Tc time duration, basic voltage vector (-Udc, 0)^T0.1090Tc duration of action, basic voltage vector (-Udc )^TWith an effect of 0.0600Tc time duration.

And fourthly, sequencing the states of the bridge arms in one control period according to the calculated duty ratio of each basic voltage vector. As shown in fig. 7, (1) at the beginning of one control cycle, the basic voltage vector acting on the triaxial helmholtz coil is u57, the six-leg state is 000000, and the acting time length is Tc · d0/4 ═ 0.1631 Tc. (2) Next, according to table 2, the basic voltage vector applied to the triaxial helmholtz coil is u20, the six arm state is 010000, and the a2 arm state is inverted based on the original state, and the operating time length is Tc · d1/4 — 0.0447 Tc. (3) Next, according to table 2, the basic voltage vector applied to the triaxial helmholtz coil is u24, the six arm state is 011000, and the A3 arm state is inverted based on the original state, and the operating time length is Tc · d2/4 is 0.0273 Tc. (4) Next, according to table 2, the basic voltage vector applied to the triaxial helmholtz coil is u52, the six arm state 011001 is obtained by inverting the a6 arm state based on the original state, and the operating time length Tc · d3/2 is 0.0300 Tc. (5) Next, according to table 2, the basic voltage vector applied to the triaxial helmholtz coil becomes u25, the six arm state 011011 is obtained by inverting the a5 arm state based on the original state, and the operating time length Tc · d2/4 is 0.0273 Tc. (6) Next, according to table 2, the basic voltage vector applied to the triaxial helmholtz coil becomes u23, the six arm state 011111 is obtained by inverting the a4 arm state based on the original state, and the operating time length is Tc · d1/4 — 0.0447 Tc. (7) And switching the basic voltage vector loaded on the triaxial Helmholtz coil to a zero vector, overturning the A1 arm state on the basis of the original arm state, and outputting the 111111 arm state. The action time length is Tc.d 0/2-0.3262 Tc. The time in one control cycle has been half so far, and the a1-a 6 arms are each operated once by switching one arm state from 000000 to 111111 each time the basic voltage vector output is changed. (8) And taking the midpoint moment of the control period as a reference, wherein the subsequent basic voltage vector output, bridge arm switching mode and action time length are symmetrical to the control period of the first half, and are not repeated here, and each bridge arm acts twice during the whole control period.

And fifthly, after finishing one control period, starting the calculation of the next control period. And returning to the first step, taking the next instantaneous voltage vector time at the interval of Tc time length on the basis of the time of the previous instantaneous voltage vector value, substituting the current voltage vector into a terminal track formula, solving the instantaneous voltage vector of the next control period, and sequentially carrying out a new control period according to the first, second, third and fourth steps. Until all N is performed for 200 control cycles, one rotation cycle is controlled, and finally, the rotating magnetic field generated inside the triaxial helmholtz coil space is as shown in fig. 8 (c). For convenience of comparison, it is shown that the effect of the method on improving the accuracy of the rotating magnetic field is achieved, fig. 8(d) shows that under the conditions of the same parameters of the triaxial helmholtz coils, the same amplitude of the rotating magnetic field, the same rotating frequency, the same dc bus voltage, the same axial direction of the rotating magnetic field, and the same carrier frequency of 2000Hz, three sets of sinusoidal pulse width modulation are used to respectively drive the triaxial helmholtz coils to generate the rotating magnetic field trajectory superimposed by the sinusoidal current waveforms shown in formula (1), and as can be seen from comparison between fig. 8(a) and fig. 8(b), the method has a good effect on improving the accuracy of the rotating magnetic field compared with the currently general sinusoidal pulse width modulation mode.

Claims

1. A three-dimensional space voltage vector control method of a space universal rotating magnetic field is characterized by comprising the following steps:

firstly, deducing three groups of sinusoidal voltage formulas applied to Helmholtz coils according to the axial direction and the magnetic field intensity of a space universal rotating magnetic field and by combining the space structure and the load characteristic of a triaxial Helmholtz coil; the three-dimensional space vector is regarded as a three-dimensional space vector, and a differential geometric method is used for proving that a track parameter curve at the tail end of the voltage is a generalized ellipse; in order to synthesize the elliptical voltage track, equally dividing a rotation period and taking a tail end track vector corresponding to the middle point time of each equally divided interval as an instantaneous voltage vector for synthesizing the whole rotation period;

the method for deriving the three groups of sinusoidal voltage formulas applied to the Helmholtz coil comprises the following steps of:

a universal rotating magnetic field superposition formula is adopted,

wherein

Wherein theta and delta are the yaw angle and pitch angle of the axis of the robot, I₀The amplitude of the sinusoidal current in the three sets of orthogonal Helmholtz coils is shown, omega is the angular frequency of the applied sinusoidal signal current, and the frequency of the applied sinusoidal signal current is f-2 pi/omega; the three-dimensional superposition problem of the space universal rotating magnetic field is converted into a two-dimensional superposition problem in a plane, and the lateral swing and the pitching angle are separately controlled through two control rods, so that low-dimensional separable variable interactive control is realized;

combining the formula (1) with the BioSaval law, set K_x，K_y，K_zThree sets of orthogonal Helmholtz coils with structural parameters B_i＝K_i*I₀(i ═ x, y, z); and because the triaxial Helmholtz coil belongs to the resistance-inductance load, R is set_x，R_y，R_zIs the resistance of the Helmholtz coil, L_x，L_y，L_zDeriving the loading for the inductance of the coil from the voltage-current equationThe voltage formula on the triaxial helmholtz coil,

B₀is the amplitude of the spatial rotating magnetic field;

secondly, enumerating the switch state combinations of all bridge arms, wherein each switch state combination corresponds to a voltage state loaded on the triaxial Helmholtz coil, and considering the voltage state as a space voltage vector called a basic voltage vector by combining the orthogonal space structure of the coil; the method specifically comprises the following steps:

each group of the three-axis Helmholtz coils is driven by two bridge arms, two ends of the load coil are respectively connected to the midpoints of the two bridge arms, the three-axis coils correspond to six bridge arms Ai (i is 1,2,3,4,5 and 6), and each bridge arm consists of an upper switching tube, a lower switching tube and a freewheeling diode; when the Helmholtz coil is driven, only two states of the two switching tubes of each bridge arm are specified, wherein the state of the bridge arm is recorded as Ai being 1 when the upper tube is switched on and the lower tube is switched off, the midpoint of the bridge arm is communicated with the positive electrode of the direct-current bus voltage Udc in the state, the potential is the positive electrode voltage of the direct-current bus, and the state of the switching tubes of each bridge arm is recorded as Ai being 0 when the lower tube is switched off, the midpoint of the bridge arm is communicated with the negative electrode of the direct-current bus voltage in the state, and the potential is the negative electrode voltage of the direct-current bus; all state combinations of the six bridge arms have 64 combination modes, each combination mode corresponds to a six-bridge arm midpoint voltage combination mode, voltages at two ends of each Helmholtz coil are obtained by subtracting voltages at two corresponding bridge arm midpoints, and voltages at two ends of x-axis, y-axis and z-axis coils are respectively set as U_a，U_b，U_cFurther, the voltage state of the three-axis coil is regarded as a voltage vector U ═ U (U)_a，U_b，U_c)^TAll voltage vectors corresponding to 64 six-bridge arm switch state combination modes are calculated and are called as 64 basic voltage vectors;

table 164 basic voltage vectors

Of the 64 basic voltage vectors, the vector (0,0,0) at the origin of the coordinates^TAlso known as zero vector, where U_a U_b U_cThe voltage of each phase is 0 state corresponding to 00 or 11 states of two bridge arms driving the Helmholtz coil, and 8 six bridge arm state combinations corresponding to zero vectors can be calculated by permutation and combination; the basic voltage vector with directions distributed along the x, y and z axes is characterized by U_a U_b U_cTwo phases in the three phases have zero voltage, the other phase voltage is not zero, two bridge arm states corresponding to the phase with non-zero voltage are 01 and 10, and 24 bridge arm state combinations corresponding to the basic voltage vector distributed according to the rule can be calculated by permutation and combination; the basic voltage vector oriented in one of the xy, yz, xz planes and forming an angle of 45 degrees with the coordinate axis is characterized by U_a U_b U_cThe voltage of one phase in the three phases is zero, the voltage of the other two phases is not zero, and 24 types of six-bridge arm state combinations corresponding to the basic voltage vector with the distribution characteristics can be calculated according to the permutation and combination; the rest basic voltage vectors are distributed at the vertex of a cube in a three-dimensional space, U_a U_b U_cThe voltage of three phases is not zero, and the distribution characteristics correspond to 8-middle six-bridge arm state combination according to permutation and combination;

the method for forming the space division areas by dividing the three-dimensional space by the construction plane comprises the following specific steps:

all basic voltage vectors are parallel to a coordinate axis or form an angle of 45 degrees with the coordinate axis in the projection of the basic voltage vectors on an xy yz or xz plane; the three-dimensional cubic space is divided into 48 space division areas by 9 space planes, wherein the coordinate axis origin is used as a vertex, and the cube surface is used as a bottom surface, and the bottom surfaces of the space division areas are isosceles right triangles; each quadrant comprises six space division areas, three sides of each space division area, which are led to the bottom surface from the top point, are three basic voltage vectors, one of the three voltage vectors is a basic voltage vector along an x axis, a y axis or a z axis, and each voltage vector along a coordinate axis corresponds to four six-bridge arm switch states; the vector direction is in the xy yz or xz plane and forms an angle of 45 degrees with the coordinate axis, and the vector direction corresponds to two basic voltage vectors; the other vector direction points to the top point of the cube from the origin of the coordinate system and only corresponds to the switch state of one six-bridge arm; in order to mark the space division areas, each space division area adopts a unique RP value corresponding to the space division area, and the definition method and the numerical significance of the RP value are given later;

dividing N equally for a rotation period T2 pi/omega of the generalized elliptic voltage space vector tail end track, taking one part as a control period, taking the other part as a target for synthesizing the current control period, and taking the voltage vector corresponding to the midpoint moment of the current control period as an instantaneous voltage vector u_ins(ii) a Concrete method for taking instantaneous vector: the number of the equal parts N in one rotation period is even, and the period T is controlled_cT/N2 pi/N omega, and the interval time between every two instantaneous vectors is T_cThus, the time of the value of the instantaneous vector is brought into the formula (2), and the instantaneous voltage vector is obtained in the three-dimensional spaceCoordinate u of_ins＝(u_insx，u_insy，u_insz)^T；

In order to synthesize the instantaneous voltage vectors in each equally divided control period, it is necessary to know the space division region where the instantaneous voltage vector is located and further determine the corresponding basic voltage vector, and synthesize the instantaneous vectors by using the linear time combination of the basic voltage vectors; according to the boundary condition of the partition plane design, a judgment formula is provided,

the voltage vector in each space division region corresponds to k₁ k₂ k₃ k₄ k₅ k₆ k₇ k₈ k₉Only one state combination is needed, so that the calculation formula of the RP has a unique value corresponding to each space division area, and the RP value obtained by the calculation of the formula corresponds to the space division area of the corresponding RP value and also corresponds to a basic voltage vector used for synthesizing the instantaneous voltage vector;

fourthly, after the space division area where the current instantaneous voltage vector is located is judged, the basic voltage vector corresponding to the space division area is determined; deriving a duty ratio formula of each basic voltage vector action in the control period based on a volt-second balance principle; the method comprises the following specific steps:

setting the time interval of a certain control cycle as T₁～T₂Having a value of T_c＝T₂-T₁During this time, the current in the three sets of helmholtz coil resistances Ri (i ═ x, y, z) is regarded as a constant value, i.e. the voltage across the resistances is regarded as a constant value u_RiTherefore, the change of the inductive current of the Helmholtz coil can be conveniently solved to solve the change of the magnetic field; combining with the Bio Saval law to obtain a formula of the triaxial magnetic field and the voltage relative to the time t,

further converting T₁，T₂And T_cCarry in, get the voltage from T under the action of transient voltage₁To T₂The amount of change at the time point B,

let u be the corresponding three basic voltage vectors calculated from the instantaneous voltage vector as set forth in the third step_1bv u_2bv u_3bv，u_jbv＝[u_jbvx,u_jbvy,u_jbvz]^T(j ═ 1,2,3) during the current control period T_cThe time of action in the time period is t₁ t₂ t₃Zero vector u_0bvHas an action time of t₀Sum of action times of all basic voltage vectors and T_cEqual length of time, t₀+t₁+t₂+t₃＝T_c(ii) a At t₀ t₁ t₂ t₃Within a certain small time period, the starting time of the small segment is set as t_sj(j is 0,1,2,3), t passes by starting at that time_jThe amount of change in the magnetic field after the (j-0, 1,2,3) period is,

the ultimate goal of the synthesis is to produce an effect equal to the instantaneous vector effect, i.e. over the entire T_cThe control period being such that the total amount of change in the magnetic field is the same, i.e.

u_0bvit₀+u_1bvit₁+u_2bvit₂+u_3bvit₃＝u_insiT_c(i＝x,y,z) (13)

that is, the sum (volt-second product) of the products of the respective basic voltage vectors and their action times is equal to the volt-second product of the instantaneous voltage vector; divide both sides of the equation by T_cAnd the action time of each basic voltage vector is compared with T_cAs the duty ratio d_j＝t_j/T_c(j ═ 0,1,2, 3); combining the formula with equal action time length, listing the formula in a matrix form,

the matrix is sorted to obtain a duty ratio calculation matrix,

in the formula, the respective parameters are as follows,

in the whole process that the rotating voltage vector rotates for one circle, all instantaneous vectors of the control period after the equal division calculate the duty ratio of the basic voltage vector in the mode;

fifthly, providing a design method of the arrangement mode of each basic voltage vector in a control period; the method specifically comprises the following steps:

respectively arranging the action duty ratios of the zero vectors at two ends and the central position of a control period, and in the control period, only two-time state switching is specified for each bridge arm in six bridge arms, namely from 0 to 1 to 0; in addition, each time the basic voltage vector is switched, namely the voltage vector state acting on the triaxial Helmholtz coil is changed, the voltage vector is switchedThe switching of the state of only one of the six bridge arms can be realized; firstly outputting a zero vector when a control period starts, and taking the time length of the duty ratio of the zero vector as d₀And 4, sequentially experiencing d according to the condition that one bridge arm is switched every time₁U of/4_1bv，d₂U of/4_2bv，d₃U of/2_3bv，d₂U of/4_2bv，d₁U of/4_1bvReaching a zero vector positioned in the center, wherein the acting duty cycle time length of the zero vector positioned in the center is d0/2, and the state of a bridge arm is 111111; in other words, in the first half of the control period, the state of one bridge arm is switched from 0 to 1 every time, and the zero vector positioned in the center is reached after six times of switching; after passing through the central zero vector state, switching the state of one bridge arm from 1 to 0 every time, and sequentially performing switching for six times to reach a zero vector at the end of one control period; the bridge arm states in the whole control period are bilaterally symmetrical by taking the midpoint moment as a boundary line;

as can be seen from table 1, the voltage states expressed by u1bv and u2bv do not correspond to only one kind of basic voltage vector in table 1, that is, only one kind of switching state of the bridge arm; in the periodic time sequence design method, a clear bridge arm switch state is required; the basic voltage vector of the synthesized instantaneous voltage vector and the determining method of the bridge arm switch state can realize the rule that one bridge arm acts each time and each bridge arm state is turned over twice in the whole control period by selecting the basic voltage vector; taking two zero vectors as u57 and u64 respectively, and giving basic voltage vectors corresponding to u1bv, u2bv and u3bv in all 48 space division areas in a table form; the vector to the left of the two basic voltage vectors in the columns u1bv and u2bv of the table occurs first in one control cycle compared to the vector to the right;

Sixthly, after control of one control cycle is finished, continuing instantaneous voltage vector calculation and calculation of a space partition region in the next control cycle, determining a basic voltage vector, calculating a corresponding duty ratio, and switching the states of bridge arms according to a cycle time sequence design method to drive the Helmholtz coil; and when all control periods which are equally divided into one rotation period are controlled, the universal rotating magnetic field generated by the triaxial Helmholtz coil also rotates for one circle.

2. The method according to claim 1, wherein the first step of deriving three sets of sinusoidal voltage equations for the Helmholtz coils further comprises the steps of:

the voltage formula (2) is regarded as a three-dimensional space voltage vector taking time t as a variable; further deducing that the unit normal vector of the plane where the voltage space curve described by the formula (2) is located is,

the space azimuth angle corresponding to the unit normal vector is theta₂、δ₂(ii) a Transforming the voltage space curve expression under the fixed coordinate system into the rotating coordinate system to discuss the tail end track shape, wherein oxyz is the fixed coordinate system fixed with the three-axis orthogonal Helmholtz coil, and ox₂y₂z₂Is a rotational coordinate system after rotational transformation; the end trajectory, initially rotated in the xoz plane with its normal vector to the plane of rotation coincident with the y-axis, is first rotated clockwise by θ about the z-axis₂Angle, rewind x₂Counter-clockwise rotation of the shaft delta₂Angle, then the coordinate system ox can be obtained₂y₂z₂Then the end locus is at x₂oz₂In-plane, derived as ox₂y₂z₂Voltage terminal trajectory expression under coordinate systemIn order to realize the purpose,

from the correlation characteristic of the polarization of electromagnetic waves, x is the number in the above formula₂oz₂The amplitude with the same frequency in a plane is superposed with two orthogonal sine vectors with random phases, and the tail end track of the voltage vector is a generalized ellipse; the terminal trace of the voltage vector is modulo,

when the sine value in the formula is 1, i.e.

The mode value of the time tail end track is maximum and corresponds to half of the length of the long shaft; the time point is substituted into a voltage space vector formula to obtain the coordinate of the semimajor axis vector of the generalized elliptic tail end track in an oxyz coordinate system in a rotation period,

when the sine value in the formula is-1, i.e.

The module value of the terminal track is minimum and corresponds to half of the length of the short shaft; the time point is substituted into a voltage space vector formula to obtain the coordinate of the semi-minor axis vector of the generalized elliptic tail end track under an oxyz coordinate system,