RU2576493C2 - Method for synthesis of shape of reflecting surface of mirror-type antenna system - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: outer loop is given in the form of a convex polyhedron having N vertices, the plane of which includes an N-dimensional barycentric coordinate system; determining the number and the position of deformation points, establishing the corresponding number of deformation devices, performing the approximation of the reflector, introducing weight coefficients, based on the generated approximation of the reflecting surface and given requirements for the orientation of the principal maximum and the beam shape, generating a nonlinear optimisation problem based on the criterion of the minimum mean-square deviation between the realised beam pattern and the required beam pattern; solving the generated extremal problem using numerical optimisation methods with the variation of the value of the generated target function by varying the value of weight coefficients of the approximation of the reflecting surface; in accordance with the calculated values of the weight coefficients, a switching device performs the deformation of the reflecting surface of the flexible membrane of the reflector.

EFFECT: high efficiency of setting the required shape of the reflecting surface of a mirror-type antenna system.

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Description

The invention relates to the field of radio engineering, and in particular to radio systems (PC) of the microwave / extra-high frequency range, equipped with mirror-type antenna systems and providing beamforming (DV) with a variable orientation of the main maximum and (or) shape, and is intended for use mainly in mobile radio communication systems and radar.

Known devices and technical solutions of antenna systems that provide a change in the orientation and (or) the shape of the DN waves (RU 2130674 05/20/1999; RU No. 2181519 04/20/2002; RU 2461929 09/20/2012; KR 20130122242 11/07/2013).

However, the effectiveness of such antenna systems when changing the orientation and (or) the shape of the beam decreases due to the lack of technical solutions aimed at changing the shape of the reflecting surface.

Of the known solutions, the closest in technical essence (prototype) is a drive system for a reflector antenna with a deformable reflective surface (patent ES 2433007 12/05/2013), which proposes an antenna system equipped with a reflector that includes a chassis and a flexible membrane with a reflector formed applying metal particles to the surface of a flexible membrane fixed at the periphery to the aforementioned chassis. The reflector of the aforementioned antenna system also includes: a housing attached to the chassis under a flexible membrane; switching device; drive device; a set of deformation devices that deform the flexible membrane of the reflector at various points called deformation points. Deformation devices are attached to the housing under the side of the flexible membrane opposite the reflective surface. Each of the aforementioned deformation devices consists of: a fixing structure; rod; pairs of pulleys connected by a drive belt; threaded couplings; bearing. The aforementioned rod is connected to the second of a pair of pulleys of the deformation device and is fixed to the fixing structure through a threaded sleeve. The first of the pair of pulleys of the deformation device is mounted on a locking structure through a bearing to rotate the pulley around its axis. The free end of the rod of the deforming element is designed for contact with a flexible membrane at the point of deformation to change its shape. The switching device is attached by a fixing structure to the reflector housing and comprises a support arm and an electric motor. The switching device is designed to be actuated through the support lever of the drive device with respect to each of the deformation devices so that the drive device through its control part is able to control the rod of the selected deformation device. The rod of the selected deformation device is controlled by rotating the control part of the drive device connected to the first pulley around its axis with the transmission of rotational movement to the system, including the pair of deformation device pulleys connected by the drive belt.

The disadvantage of this invention is the lack of a technical solution aimed at synthesizing the shape of the reflecting surface of a flexible membrane that implements the required orientation of the main maximum and (or) the shape of the MD, with the rational position of the rods of the deforming devices relative to the deformable surface. The latter leads to a complication of the design of the antenna system, as well as to a complication of the control system for the shape of the deformable reflective surface.

The objective of the invention is to provide a method for synthesizing the shape of the reflecting surface of an antenna system of a mirror type, allowing with a minimum number of deforming elements to effectively set the required shape of the reflecting surface of an antenna system of a mirror type that implements the required orientation of the main maximum and (or) the shape of the beam.

This problem is solved in that the method of synthesizing the shape of the reflective surface of a mirror-type antenna system equipped with a reflector including a chassis, a housing, a set of deformation devices, a drive device, a switching device, a switching device control system, a flexible membrane with a reflector formed by the deposition of metal particles on the surface of the flexible membrane, characterized in that in the control system of the switching device, an external circuit bounding the reflective surface of the flexible membrane p reflector, set in the form of a convex polyhedron containing N vertices, an N-dimensional barycentric coordinate system is introduced in the plane of the specified N-dimensional polyhedron [see Alexandrov P.S. Lectures on analytic geometry. - M .: Nauka, 1968. - 912 p., P. 352], based on the representation of the aforementioned polyhedron in a TV-dimensional barycentric coordinate system, the number K and the position ix of the deformation points are determined and the corresponding number of deformation devices is set by setting the approximation order m, for a given approximation order m, approximate the reflecting surface of a flexible membrane by a rational N-coal Bezier surface [see Golovanov, N.N. Geometric modeling. - M .: Publishing house of the phys.-math. lit., 2002. - 472 p., p. 176] with the introduction of ix weight coefficients w _i corresponding to certain i-th deformation points, while the value of the weight coefficient w _i at a particular deformation point in comparison with others determines the degree of proximity of the passage of reflective surface to it, for the values of the introduced weight coefficients w _{i, the} position of the rods in the deformation devices is matched, taking into account the formed approximation of the reflecting surface of the flexible membrane of the reflector and the given requirements for the orientation of the main maximum and (or) the shape of the beam form a nonlinear optimization problem according to the criterion of the minimum standard deviation (RMS) between the beam of the deformable antenna system and the required beam, the formed extremal problem is solved by numerical optimization methods [see Vasiliev F.P. Numerical methods for solving extreme problems. - M .: Nauka, 1980. - 520 p.] With a change in the value of the generated objective function by varying the weight coefficients of approximation of the reflective surface of the flexible membrane of the reflector, in accordance with the calculated values of the weight coefficients, the switching device deforms the reflective surface of the flexible membrane of the reflector.

The listed new set of essential features makes it possible to synthesize the shape of the reflecting surface of a flexible membrane that implements the required orientation of the main maximum and (or) the shape of the MD, with the rational positions of the rods of deforming devices relative to the deformable surface.

The analysis of the prior art made it possible to establish that analogues that are characterized by a combination of features that are identical to all the features of the claimed technical solution are absent, which indicates compliance of the invention with the condition of patentability "novelty".

Search results for known solutions in this and related fields of technology in order to identify features that match the distinctive features of the claimed object from the prototype showed that they do not follow explicitly from the prior art. The prior art also did not reveal the popularity of the impact provided for by the essential features of the claimed invention, the transformations to achieve the specified technical result. Therefore, the claimed invention meets the condition of patentability "inventive step".

The claimed method is illustrated by drawings, which show:

in FIG. 1 is an example of representing an external contour bounding a reflective surface of a flexible reflector membrane in the form of a convex polyhedron containing N vertices;

in FIG. 2 is a graphical interpretation of the translation procedure from rectangular to barycentric coordinates using the example of a hexagon;

in FIG. 3 is an example of defining deformation points for a circular reflective surface of a flexible reflector membrane, represented by a trihedral at m = 2;

in FIG. 4 is a flowchart of a method for controlling the shape of a reflective surface of a mirror-type antenna system;

in FIG. 5 is a radiation pattern in the E and H planes formed by the irradiator of a single-mirror antenna;

in FIG. 6 is a slice for ξ = 0 ° of the radiation pattern formed by the original parabolic single-mirror antenna;

in FIG. 7 is a slice for ξ = 0 ° of the radiation pattern formed by the final single-mirror antenna synthesized by the claimed method;

in FIG. 8 - a change in the shape of the original parabolic single-mirror antenna when it is deformed according to the claimed method.

In the General case, the claimed method of synthesizing the shape of the reflecting surface of the antenna system of the mirror type is to solve the problem of structural synthesis of the antenna system and is reduced to two main stages.

The first stage is the parameterization of the flexible reflective surface of the flexible membrane of the deformable antenna system of the mirror type under consideration. In this case, the first stage involves the sequential implementation of the following actions:

из N точек. Каждая n-я точка представлена двухмерным вектором

, определяющим ее положение в системе координат OXY;1) the outer contour 1 (see Fig. 1), bounding the reflective surface of the flexible membrane 3 (see Fig. 1) of the reflector, is represented in the form of a convex polyhedron 2 (see Fig. 1) containing N vertices. Moreover, the aforementioned external circuit 1 (see FIG. 1) is represented by a plurality $$P=\left\{{\overrightarrow{P}}_{\mathrm{one}},{\overrightarrow{P}}_2,...,{\overrightarrow{P}}_n,...,{\overrightarrow{P}}_N\right\}$$

from N points. Each nth point is represented by a two-dimensional vector

determining its position in the coordinate system OXY;

, определявших вершины N-мерного выпуклого многоугольника в плоскости OXY (см. фиг. 1), ввести N-мерную барицентрическую систему координат ζ₁, ζ₂, …, ζ_N, такую, что 0≤ζ_n≤1; $${\displaystyle \sum _{n=1}^N{\zeta }_n=1}$$

; $$n=\overline{\mathrm{1,}N}$$

. Правило перехода от барицентрической системы координат ζ₁, ζ₂, …, ζ_N в прямоугольную x, y определяется отношением:2) for many points $$P=\left\{{\overrightarrow{P}}_{\mathrm{one}},{\overrightarrow{P}}_2,...,{\overrightarrow{P}}_n,...,{\overrightarrow{P}}_N\right\}$$

defining the vertices of an N-dimensional convex polygon in the OXY plane (see Fig. 1), introduce an N-dimensional barycentric coordinate system ζ ₁ , ζ ₂ , ..., ζ _N , such that 0≤ζ _n ≤1; $${\displaystyle \sum _{n=\mathrm{one}}^N{\zeta }_n=\mathrm{one}}$$

; $$n=\overline{\mathrm{one,}N}$$

. The transition rule from the barycentric coordinate system ζ ₁ , ζ ₂ , ..., ζ _N to the rectangular x, y is determined by the ratio:

в барицентрические

применяется обобщение для N-мерного случая через так называемые Wachspress координаты [см. Wachspress Е.L. A Rational Finite Element Basis. Academic Press, New York, 1975. - 216 p.]:For reverse translation of coordinates of an arbitrary point

to barycentric

a generalization is applied for the N-dimensional case through the so-called Wachspress coordinates [see Wachspress E.L. A Rational Finite Element Basis. Academic Press, New York, 1975. - 216 p.]:

определяет площадь треугольника, вершины которого заданы набором точек $${\overrightarrow{P}}_{n-1},{\overrightarrow{P}}_n,{\overrightarrow{P}}_{n+1}$$

. Графическая интерпретация процедуры перевода из прямоугольных координат в барицентрические на примере шестиугольника представлена на фиг. 2;Where $$S_{\Delta }({\overrightarrow{P}}_{n-\mathrm{one}},{\overrightarrow{P}}_n,{\overrightarrow{P}}_{n+\mathrm{one}})$$

determines the area of a triangle whose vertices are given by a set of points $${\overrightarrow{P}}_{n-\mathrm{one}},{\overrightarrow{P}}_n,{\overrightarrow{P}}_{n+\mathrm{one}}$$

. A graphical interpretation of the translation procedure from rectangular to barycentric coordinates using the example of a hexagon is shown in FIG. 2;

3) determine the approximation order m of the reflecting surface of the flexible membrane of the reflector and, for a given m, generate an ordered set M _{m of} multi-indices i such that

where Z _≥0 is the set of positive integers [see Vygodsky M.Ya. Handbook of Higher Mathematics. - M .: Nauka, 1975. - 871 p.].

в системе координат OXY c учетом соотношений (1) задается по правилуThe total number of generated set of multi-indices determines the number of deformation points K = | M _m | (the operator | · | determines the cardinality of the set), and the position of the ith strain points $${\overrightarrow{P}}_i^d={\left(x_i^d{y}_i^d\right)}^T$$

in the coordinate system OXY taking into account relations (1) is specified by the rule

An example of defining deformation points for a circular reflecting surface of a flexible reflector membrane represented by a thirteen for the approximation order m = 2 is shown in FIG. 3;

задать число и исходные значения положения стержней $$Z_i^{д}$$

в системе координат OXYZ отражающей поверхности гибкой мембраны рефлектора (см. фиг. 1), по сути характеризующих исходную форму отражателя, например, заданную в виде параболоида вращения с фокусным рассеянием f.4) for a specific set of coordinates of strain points $${\overrightarrow{P}}_i^d$$

set the number and initial values of the position of the rods $$Z_i^d$$

in the coordinate system OXYZ of the reflecting surface of the flexible membrane of the reflector (see Fig. 1), which essentially characterize the initial shape of the reflector, for example, specified in the form of a paraboloid of revolution with focal scattering f.

задать аппроксимацию отражающей поверхности рациональной N-угольной поверхностью Безье, по существу определяющее соответствие положение стержней в устройствах деформации:Based on calculated values $$Z_i^d$$

set the approximation of the reflecting surface to a rational N-coal Bezier surface, which essentially determines the correspondence of the position of the rods in the deformation devices:

, при этом величина весового коэффициента w_i в конкретной точке деформации в сравнении с другими определяет степень близости прохождения отражающей поверхности ней; $$B_i^m(x,y)$$

- полином Бернштейна, определяемый отношением [см. Loop, С.Т. A Multisided Generalization of Bezier Surfaces / Charles T. Loop, Tony B. DeRose // ACM Transactions on Graphics. V. 8. 1989. - P. 204-234]:where i is a multi-index (4); w _i - weighting coefficients corresponding to certain i-th deformation points $${\overrightarrow{P}}_i^d$$

while the value of the weight coefficient w _i at a particular point of deformation in comparison with others determines the degree of proximity of the passage of the reflecting surface of it; $$B_i^m(x,y)$$

- Bernstein polynomial defined by the relation [see Loop, S.T. A Multisided Generalization of Bezier Surfaces / Charles T. Loop, Tony B. DeRose // ACM Transactions on Graphics. V. 8. 1989. - P. 204-234]:

и определяемые по правилу (2), (3).In the expression (8), ζ ₁ (x, y), ζ ₂ (x, y), ..., ζ _N (x, y) are the barycentric coordinates corresponding to an arbitrary point $$\overrightarrow{P}={(xy)}^T$$

and determined by rule (2), (3).

. При этом второй этап предполагает последовательное выполнение следующих действий:The second stage is the determination of the shape of the reflecting surface, taking into account the specified requirements for the orientation of the maxima and (or) the shape of the beam by finding the corresponding values of the vector of weight coefficients $$\overrightarrow{W}={(w_i)}_{M_m}$$

. In this case, the second stage involves the sequential implementation of the following actions:

1) taking into account the formed approximation (7) of the reflecting surface of the flexible membrane of the reflector and the given requirements for the orientation of the main maximum and (or) the shape of the beam, form a nonlinear optimization problem by the criterion of the minimum standard deviation of the beam between the implemented deformable antenna system and the required beam:

- формируемая комплексная ДН антенной системы зеркального типа для основного вида поляризации в направлении (θ, ξ); $${\dot{F}}_{E_{тр}}(\theta ,\xi )$$

- требуемая комплексная ДН антенной системы зеркального типа в направлении (θ, ξ); [θ_min; θ_max], [ξ_min, ξ_max] - сектор углов, в которых определяется соответствие формируемой и требуемой ДН. Значение $${\dot{F}}_E(\overrightarrow{W},\theta ,\xi )$$

в заданном направлении (θ, ξ) может определяться токовым методом [см. Айзенберг Г.З. Антенны УКВ. В 2 ч. Ч. 1. - Москва: Связь, 1977. - 381 с.];where R is the set of real numbers; θ and ξ are the zenith and azimuth angles, respectively, of the spherical coordinate system of the reflector in the direction to an arbitrary observation point Q (see Fig. 1); $${\dot{F}}_E(\overrightarrow{W},\theta ,\xi )$$

- the formed integrated pattern of the antenna system of the mirror type for the main type of polarization in the direction (θ, ξ); $${\dot{F}}_{E_{tR}}(\theta ,\xi )$$

- the required integrated MD of the antenna system of the mirror type in the direction (θ, ξ); [θ _min ; θ _max ], [ξ _min , ξ _max ] is the sector of angles in which the correspondence of the formed and required MD is determined. Value $${\dot{F}}_E(\overrightarrow{W},\theta ,\xi )$$

in a given direction (θ, ξ) can be determined by the current method [see Eisenberg G.Z. VHF antennas. At 2 hours, Part 1. - Moscow: Communication, 1977. - 381 p.];

;2) to solve the formed extremal problem (9) by numerical optimization methods [see Vasiliev F.P. Numerical methods for solving extreme problems. - M .: Nauka, 1980. - 520 p.] With a change in the value of the formed objective function by varying the magnitude of the weight coefficients of approximation of the reflecting surface of the flexible membrane of the reflector $$\overrightarrow{W}=\underset{w_i\in R}{\arg \min }\left(f(\overrightarrow{W})\right)$$

;

в точках деформации $${\overrightarrow{P}}_i^{д}$$

задать итоговые положения стержней, используя аппроксимацию (7).3) in accordance with the calculated values of the weights $$\overrightarrow{W}$$

at strain points $${\overrightarrow{P}}_i^d$$

set the final positions of the rods using the approximation (7).

Consider the implementation of the proposed method on a computer using the example of solving the problem of deforming the shape of the reflecting surface of the flexible membrane of the reflector of a single-mirror parabolic antenna when forming the maximum radiation of the antenna in the direction θ = 10 °, ξ = 0 °. The parameters of the synthesized antenna system at a wavelength of λ = 0.05 m: the ratio of the diameter of the reflector to the wavelength D / λ = 20, the ratio of the focal length of the reflector to its diameter f / D = 0.5. The irradiator is placed in the focus of the antenna. The radiation pattern formed by the irradiator of the considered single-mirror antenna in E and H planes is shown in FIG. 5.

As a result of solving the problem under consideration by the claimed method, when specifying the external contour bounding the reflector surface with a thirteen triangle and indicating the approximation order m = 2, a reflecting surface is formed that implements the pattern shown in FIG. 7 in section along the angle ξ = 0 °. The initial MD of a parabolic single-mirror antenna in section along the angle ξ = 0 ° is shown in FIG. 6. In FIG. 8 shows a change in the shape of the original parabolic single-mirror antenna when it is deformed according to the claimed method.

The result of changing the orientation of the main maximum while maintaining the symmetry of the formed deflected pattern during the deformation of its reflector by deforming devices according to the claimed method provides the possibility with the smallest minimum number of deforming elements to effectively set the required shape of the reflecting surface of the mirror-type antenna system that implements the required orientation of the main maximum and (or) shape NAM

Thus, the proposed method for synthesizing the shape of a reflecting surface can be considered as a new method for the structural synthesis of antenna systems of a mirror type, providing a change in the orientation and (or) the shape of the DN waves. It should be understood that not all aspects or advantages of the present invention can be achieved when forming an extreme task of the form (9), since the present method involves the use of various synthesis criteria: maximum surface utilization, maximum directional coefficient, antenna efficiency; gain in a given direction (s), etc., taking into account all sorts of restrictions.

Claims (1)

The method of controlling the shape of the reflective surface of a mirror-type antenna system equipped with a reflector including a chassis, a housing, a set of deformation devices, a drive device, a switching device, a switching device control system, a flexible membrane with a reflector formed by applying metal particles to the surface of a flexible membrane, characterized the fact that in the control system of the switching device, the external circuit limiting the reflective surface of the flexible membrane of the reflector is set in de convex polyhedron containing N vertices, in the plane of a given N- dimensional polyhedron introduce an N- dimensional barycentric coordinate system, based on the representation of the aforementioned polyhedron in an N- dimensional barycentric coordinate system, determine the number K and the position of i- x deformation points and set the corresponding number K deformation devices by setting the approximation order m , for a given approximation order m approximate the reflecting surface of a flexible membrane of a rational N- angled surface Bezier axis with the introduction of i -x weight coefficients w _i corresponding to certain i- th deformation points, while the value of the weight coefficient w _i at a particular strain point in comparison with others determines the degree of proximity of the passage of the reflecting surface to it, for the values of the introduced weight coefficients w _i match the position of the rods in the deformation devices, taking into account the formed approximation of the reflecting surface of the flexible membrane of the reflector and the given requirements for the orientation of the main maximum and (or) The radiation pattern frames (ND) form a nonlinear optimization problem by the criterion of the minimum standard deviation between the realized ND deformable antenna system and the desired ND, solving the formed extremal problem by numerical optimization methods by changing the value of the generated objective function by varying the weight of the approximation weights of the reflective surface of the flexible reflector membrane , in accordance with the calculated values of the weights, switching the device performs the deformation of the reflective surface of the flexible membrane of the reflector.

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