Intelligent display rack remote management and control system based on Internet of Things

Abstract

The invention relates to the technical field of intelligent display rack control, and discloses an intelligent display rack remote management and control system based on the Internet of Things, and the system comprises the steps: firstly obtaining the physical attributes and arrangement information of commodities displayed on an intelligent display rack, and constructing a commodity lattice display topology representing the periodic distribution of a medium space according to the physical attributes and arrangement information; thirdly, an electromagnetic forbidden band is calculated based on the topology, a terminal to be controlled is regarded as a dielectric structure defect in the topology, and a localization defect mode strictly existing in the frequency range of the electromagnetic forbidden band is solved; and in the execution stage, the remote control end accurately tunes the carrier center frequency of the wireless transmission signal to a frequency value corresponding to the localization defect mode, and strictly configures the transmission bandwidth according to the quality factor of the mode. And finally, electromagnetic energy of the control instruction is directionally focused and coupled to the to-be-controlled terminal by using a resonance excitation transmission mechanism of the localized defect mode, so that the communication shielding limitation of a high-density display environment is broken through.

Description

Technical Field

[0001] This invention relates to the field of intelligent display stand control technology, and more specifically, to an intelligent display stand remote management and control system based on the Internet of Things. Background Technology

[0002] With the deep integration of smart retail and IoT technologies, intelligent display rack systems based on wireless communication technology have been widely used in large supermarkets, unmanned convenience stores, and warehousing and logistics centers. These systems typically consist of a cloud management platform, a wireless gateway, and numerous intelligent terminals (such as electronic price tags, inventory sensors, and multimedia displays) deployed on the racks. Their core operating mode utilizes wireless radio frequency signals (such as Zigbee, Wi-Fi, and Bluetooth protocols) to achieve remote control, for example, issuing batch price change commands, synchronizing promotional displays, or reading inventory status. To ensure visual appeal and maximize space utilization, the retail industry generally adopts standardized display specifications, requiring goods (especially bottled beverages, canned goods, and liquid detergents) to be arranged in a high-density, matrix-like neat arrangement on shelf shelves.

[0003] In existing intelligent display stand remote control solutions, communication links are typically established based on free-space propagation models or simple multipath fading models. The control terminal (gateway) is configured to transmit electromagnetic signals on a fixed standard center frequency (e.g., a specific channel in the 2.4 GHz band) using omnidirectional broadcasting or beamforming. Existing designs generally assume that as long as the receiving terminal is within the gateway's signal coverage radius and is not completely enclosed by a metal shield, the signal can reach the terminal via direct transmission, reflection, or diffraction. When signal transmission fails, conventional solutions often involve simple physical layer retransmission, reducing the communication baud rate, or blindly increasing the gateway's transmit power in an attempt to penetrate obstacles by increasing energy density.

[0004] However, in actual operational scenarios, the aforementioned conventional methods often fail, frequently resulting in persistent blind spots where communication is impossible even when the goods are very close. Specifically, the goods displayed on the smart display rack are not random, ordinary obstacles, but rather form a high-dielectric-constant array with strict spatial periodicity. When a large number of identical goods (such as hundreds of neatly arranged bottles of mineral water or metal cans) are arranged closely at specific intervals, this macroscopic periodic structure physically creates a medium environment that strongly repels electromagnetic waves of specific wavelengths. In this environment, the display rack not only blocks signals but also creates a frequency-forbidden effect on electromagnetic waves of specific frequencies. When the standard carrier frequency of the remote control signal happens to fall within the forbidden range determined by this display structure, the electromagnetic wave, after entering the display rack, no longer propagates forward in a wave-like form but transforms into a rapidly attenuating state, preventing energy from penetrating deep into the receiving terminal located in the product array or gaps. At this point, even if the transmission power is increased, most of the energy will be reflected by the structure as a whole or dissipated on the surface, making it impossible to establish an effective communication connection. This results in certain smart display rack nodes remaining out of control for extended periods, unable to respond to remote control commands. Summary of the Invention

[0005] This invention provides an IoT-based intelligent display rack remote management and control system, which solves the technical problem of communication blind spots and unreachable remote control commands caused by the inability of electromagnetic waves to propagate in specific structures in high-density, periodic merchandise display environments.

[0006] This invention provides a remote management and control system for smart display stands based on the Internet of Things, comprising: Based on the physical attributes and arrangement information of the displayed goods on the intelligent display rack, a product lattice display topology representing the periodic distribution of the medium space is constructed. The electromagnetic bandgap is calculated based on the topology of the commodity lattice display, and the terminal to be controlled is regarded as a dielectric structure defect in the topology of the commodity lattice display. The localized defect mode existing in the frequency range of the electromagnetic bandgap is calculated. The remote control terminal tunes the carrier center frequency of the wireless transmission signal to the frequency value corresponding to the localized defect mode, and configures the transmission bandwidth according to the quality factor of the localized defect mode. Through the resonant excitation transmission of the localized defect mode, the electromagnetic energy of the control command is focused and coupled to the terminal to be controlled.

[0007] The beneficial effects of this invention are as follows: by reconstructing the array of displayed goods into a dielectric lattice model and using the calculated localized defect mode for precise resonant excitation transmission, remote control commands can penetrate the physical shielding layer and be directionally focused and coupled to the target terminal in an evanescent wave tunneling manner; thus solving the industry pain point of communication blind spots in dense shelf scenarios, and significantly improving the signal-to-noise ratio and transmission efficiency of the signal through energy focusing, achieving precise control of intelligent display racks with zero packet loss and low power consumption in complex electromagnetic environments. Attached Figure Description

[0008] Figure 1 This is a comparison diagram of the spectrum transmission characteristics in a high-density display environment according to the present invention; Figure 2 This is a comparison diagram of the spatial distribution of electromagnetic energy across the cross-section of the intelligent display stand of this invention; Figure 3 This is a block diagram of a smart display stand remote management and control system based on the Internet of Things according to the present invention. Detailed Implementation

[0009] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, features described in some examples may be combined in other examples.

[0010] like Figure 1 As shown, Figure 1 This demonstrates the core mechanism by which this solution overcomes signal shielding. The red dashed line shows that under normal circumstances, a high-density product display near the center frequency (2.40 GHz) forms a deep and wide electromagnetic bandgap, resulting in severe signal attenuation (below -55 dB). The blue solid line shows that this solution, by calculating and utilizing the defects introduced by the terminal to be controlled, successfully excites an extremely narrow localized defect mode resonant peak at the center of the originally non-communicable bandgap, thereby improving the signal transmission efficiency at a specific frequency by tens of decibels.

[0011] like Figure 2 As shown, Figure 2 The significant differences in spatial energy transfer between conventional methods and the method of this invention were compared using two-dimensional heat maps.

[0012] The left figure (A) shows that when using conventional methods, the transmission frequency falls into the electromagnetic inaccessibility zone. The electromagnetic energy decays rapidly after contacting the high-density merchandise display area, and the terminal to be controlled deep inside is in the energy blind zone (dark blue) and cannot receive commands.

[0013] Figure (B) on the right shows that when using the method of the present invention, by precisely tuning to the defect mode frequency, electromagnetic energy tunnels through the shielding layer and forms a strong energy focusing resonance point (bright red area) at the location of the terminal to be controlled, thereby realizing fixed-point and efficient remote control.

[0014] like Figure 3 As shown, a remote management and control system for smart display stands based on the Internet of Things includes: Based on the physical attributes and arrangement information of the displayed goods on the intelligent display rack, a product lattice display topology representing the periodic distribution of the medium space is constructed. The electromagnetic bandgap is calculated based on the topology of the commodity lattice display, and the terminal to be controlled is regarded as a dielectric structure defect in the topology of the commodity lattice display. The localized defect mode existing in the frequency range of the electromagnetic bandgap is calculated. The remote control terminal tunes the carrier center frequency of the wireless transmission signal to the frequency value corresponding to the localized defect mode, and configures the transmission bandwidth according to the quality factor of the localized defect mode. Through the resonant excitation transmission of the localized defect mode, the electromagnetic energy of the control command is focused and coupled to the terminal to be controlled.

[0015] In one embodiment of the present invention, a product lattice display topology characterizing the periodic distribution of the medium space is constructed based on the physical properties and arrangement information of the displayed products on the smart display rack, including: Based on the spacing of the product display, determine the grid point position vector of each product unit in the display rack coordinate system; Obtain the background dielectric constant of the air environment and the spatial dielectric distribution function of a single commodity; Calculate the dielectric function at any spatial location vector within the area where the smart display stand is located. The value of the dielectric function is equal to the sum of the background dielectric constant and the dielectric contribution. For each grid point position vector, calculate the difference between the spatial position vector and the grid point position vector. Substitute this difference into the spatial dielectric distribution function of the commodity to obtain the function value. Calculate the difference between the function value and the background dielectric constant as the net dielectric contribution of a single commodity. Perform a summation operation on the net dielectric contributions corresponding to all grid point position vectors to obtain the total dielectric contribution.

[0016] The spacing between product displays refers to the distance between the centers of two adjacent products on the display shelf plane. The spacing between product displays includes horizontal spacing and vertical spacing. The spacing between product displays needs to be measured along the horizontal direction of the display shelf. The unit of spacing between product displays is uniformly millimeters. The spacing between product displays is the basic parameter for determining the spatial position of products.

[0017] The grid point position vector of each product unit in the display rack coordinate system is a parameter representing the specific position of the center of a single product in the preset display rack coordinate system. The display rack coordinate system takes the lower left corner of the display rack as the origin, with the horizontal axis pointing to the right and the vertical axis pointing upward. Without considering the height direction, the grid point position vector of each product unit in the display rack coordinate system is a two-dimensional position representation. Specifically, the horizontal position is equal to the horizontal arrangement number minus one, and then multiplied by the horizontal arrangement spacing; the vertical position is equal to the vertical arrangement number minus one, and then multiplied by the vertical arrangement spacing. The grid point position vector of each product unit in the display rack coordinate system is obtained by combining the horizontal and vertical positions.

[0018] The background dielectric constant of the air environment refers to the standard value of the dielectric constant of the air medium in the space where the smart display stand is located. The background dielectric constant of the air environment is fixed at normal temperature and pressure, and it is the benchmark reference value for calculating the dielectric contribution of the product.

[0019] The spatial dielectric distribution function (SDF) of a single product describes the variation of the dielectric constant at different locations within the product. The value of the SDF of a single product varies with the material distribution within the product. The SDF value of a single product in the same material region is constant, while the SDF value of a single product in different material regions is different. The SDF of a single product is obtained by measuring the dielectric constant of different material regions of the product using a dielectric constant tester and fitting it according to the material distribution range. The SDF of a single product in the same material is a constant value function, while the SDF of a single product in different materials is a piecewise function.

[0020] The arbitrary spatial position vector within the area of ​​the intelligent display stand refers to the position representation of any point within the shelf area of ​​the intelligent display stand in the display stand coordinate system. The arbitrary spatial position vector within the area of ​​the intelligent display stand and the grid point position vector of each product unit in the display stand coordinate system use the same coordinate system. The arbitrary spatial position vector within the area of ​​the intelligent display stand is used to traverse and calculate the dielectric properties of the entire display stand area.

[0021] The dielectric function is a parameter that characterizes the overall dielectric properties of any location within the smart display area. The dielectric function reflects the actual value of the dielectric constant at that location after being affected by both air and merchandise. The calculation principle of the dielectric function is that the dielectric properties of a point in space are determined by both air and all merchandise. The actual dielectric constant is obtained by superimposing the dielectric effects of air and merchandise. Specifically, the dielectric function is equal to the background dielectric constant of the air environment plus the sum of the dielectric contributions of all merchandise.

[0022] The net dielectric contribution of a single product is the increment of dielectric influence generated by a single product at a certain spatial location. The net dielectric contribution of a single product is the difference between the dielectric properties of the product itself and the dielectric properties of the air background. The design purpose of the net dielectric contribution of a single product is to eliminate the basic influence of air dielectric and accurately reflect the dielectric effect of the product itself. Specifically, first calculate the difference between the vector of any spatial location in the area where the smart display stand is located and the vector of the grid point location of each product unit in the display stand coordinate system. Substitute this difference into the product spatial dielectric distribution function of the single product to obtain the function value. Then subtract the background dielectric constant of the air environment from the function value. The result is the net dielectric contribution of a single product.

[0023] The total dielectric contribution is the sum of the dielectric effects of all displayed goods on a certain spatial location within the smart display rack area. The total dielectric contribution is the core intermediate parameter for calculating the dielectric function. The total dielectric contribution is obtained by superimposing the net dielectric contributions of all goods. Specifically, iterate through the grid point position vectors of each product unit corresponding to all goods on the display rack in the display rack coordinate system, calculate the net dielectric contribution of each product at any spatial position vector within the current smart display rack area, and add up the net dielectric contributions of all individual products. The result is the total dielectric contribution.

[0024] In one embodiment of the present invention, calculating the electromagnetic bandgap based on the topology of a commodity lattice array includes: The inverse dielectric function is obtained by calculating the reciprocal of the dielectric function, and the Fourier coefficients are obtained by performing a Fourier transform on the inverse dielectric function. The eigenvalue equations for the magnetic field expansion coefficients are constructed as follows: Calculate the vector difference between the target reciprocal lattice vector and the summed reciprocal lattice vector, and obtain the Fourier coefficients corresponding to the vector difference; calculate the vector sum of the wave vector and the summed reciprocal lattice vector, and obtain the squared magnitude of the vector sum; calculate the product of the Fourier coefficients, the squared magnitude, and the magnetic field expansion coefficients corresponding to the summed reciprocal lattice vectors; perform a summation operation on the products corresponding to all summed reciprocal lattice vectors to obtain the left-hand side of the equation; calculate the ratio of the angular frequency to the speed of light, and obtain the square of the ratio; calculate the product of the square and the magnetic field expansion coefficients corresponding to the target reciprocal lattice vector to obtain the right-hand side of the equation; Let the left-hand term of the equation equal the right-hand term of the equation; By traversing the wave vectors and solving the eigenvalue equations within the first Brillouin zone, the set of eigenfrequency is obtained. The frequency range with discontinuous numerical distributions in the intrinsic frequency set is selected and defined as the electromagnetic bandgap.

[0025] The inverse dielectric function is the reciprocal of the dielectric function. It is used to meet the mathematical requirements of Fourier transform, converting dielectric properties into computable parameters in the frequency domain. Specifically, the inverse dielectric function is equal to the numerical value divided by the corresponding dielectric function, and each spatial location of the dielectric function corresponds to a unique inverse dielectric function value.

[0026] Fourier coefficients are the coefficients obtained after Fourier transforming the inverse dielectric function. They characterize the distribution of the inverse dielectric function in the frequency domain; different vector differences correspond to different Fourier coefficients, and they are core parameters for constructing eigenvalue equations. Obtaining Fourier coefficients requires using the Discrete Fourier Transform algorithm, which transforms the inverse dielectric function in the spatial domain into a set of coefficients in the frequency domain. Specifically, the effective range of values ​​for the inverse dielectric function is selected, discrete data points are extracted at equal intervals, and substituted into the Discrete Fourier Transform formula to calculate the coefficient corresponding to each frequency component; this coefficient is the Fourier coefficient.

[0027] The magnetic field expansion coefficient is the coefficient corresponding to each plane wave after the magnetic field is decomposed into a superposition of plane waves. The magnetic field expansion coefficient is divided into the magnetic field expansion coefficient corresponding to the summation reciprocal lattice vector and the magnetic field expansion coefficient corresponding to the target reciprocal lattice vector, which are used to calculate the left-hand and right-hand terms of the eigenvalue equation, respectively. Specifically, based on Bloch's theorem, the magnetic field is expanded into a superposition of plane waves in the first Brillouin zone, and the coefficient corresponding to each plane wave is obtained by solving the orthogonal normalization condition, which is the magnetic field expansion coefficient.

[0028] The eigenvalue equation is a mathematical equation relating the wave vector, angular frequency, and magnetic field expansion coefficient. The solution of the eigenvalue equation is the eigenfrequency corresponding to the magnetic field expansion coefficient. The eigenvalue equation is constructed based on the simplified derivation of Maxwell's equations in periodic media, which is adapted to the electromagnetic properties of commercial lattice array topologies.

[0029] The target reciprocal lattice vector is a selected reference reciprocal lattice vector in the reciprocal lattice space. The target reciprocal lattice vector is used to determine the specific component to be solved in the eigenvalue equation. Each target reciprocal lattice vector corresponds to a set of solutions to the eigenvalue equation. Specifically, the reciprocal lattice basis vectors are calculated based on the positive lattice basis vectors of the commodity lattice array topology. The reciprocal lattice basis vectors are combined in integer multiples to obtain all vectors in the reciprocal lattice space. The vector to be solved is selected from these vectors as the target reciprocal lattice vector.

[0030] The summation reciprocal lattice vector is a set of reciprocal lattice vectors used for traversal summation in the reciprocal lattice space. The summation reciprocal lattice vector covers the key vectors in the reciprocal lattice space, and the superposition effect of the magnetic field can be completely characterized by traversing and summing them. Specifically, with the target reciprocal lattice vector as the center, a finite range of values ​​is set, and all reciprocal lattice vectors within this range are selected to form a set. Each vector in the set is the summation reciprocal lattice vector.

[0031] The vector difference is the vector obtained by subtracting the summed reciprocal lattice vector from the target reciprocal lattice vector. The vector difference is used to match the corresponding Fourier coefficients and establish the relationship between the reciprocal lattice vector and the frequency domain coefficients. Specifically, the vector difference is obtained by subtracting the corresponding components of the summed reciprocal lattice vector from each component of the target reciprocal lattice vector.

[0032] The wave vector is a vector that characterizes the propagation direction and wavelength of an electromagnetic wave. The magnitude of the wave vector is inversely proportional to the wavelength of the electromagnetic wave, and its direction is the propagation direction of the electromagnetic wave. The traversal range of the wave vector is limited to the first Brillouin zone to ensure the integrity and uniqueness of the calculation.

[0033] The vector sum is the vector obtained by adding the wave vector to the summation of the reciprocal lattice point vector. The vector sum is used to calculate the square of the modulus, providing the basic computational quantity for the left-hand side of the eigenvalue equation. Specifically, each component of the wave vector is added to the corresponding component of the summation of the reciprocal lattice point vector, and the resulting vector is the vector sum.

[0034] Modulus squared is the square of the magnitude of the vector sum. Modulus squared is a scalar used to convert vector operations into scalar operations, which facilitates product calculations in eigenvalue equations. Specifically, the square of each component of the vector sum is calculated, and the result of adding the squares of all components is the modulus squared.

[0035] The left-hand side of the equation is the result of the calculation on the left side of the eigenvalue equation. The left-hand side of the equation combines the effects of the Fourier coefficients, the square of the modulus of the sum of the vectors, and the magnetic field expansion coefficient, reflecting the influence of the periodic medium on the magnetic field. Specifically, the product of the Fourier coefficients corresponding to the vector differences, the square of the modulus of the vector sum, and the magnetic field expansion coefficient corresponding to the summed reciprocal lattice vectors is calculated first. Then, the product corresponding to all summed reciprocal lattice vectors is accumulated, and the accumulated result is the left-hand side of the equation.

[0036] Angular frequency is a physical quantity that characterizes the speed of electromagnetic wave oscillation. Angular frequency is directly proportional to the frequency of electromagnetic waves.

[0037] The result of dividing the angular frequency by the speed of light is then squared to construct the right-hand side of the eigenvalue equation, establishing the relationship between the angular frequency and the magnetic field expansion coefficient.

[0038] The right-hand side of the equation is the result of the calculation on the right side of the eigenvalue equation. The right-hand side reflects the effect of angular frequency on the magnetic field expansion coefficient, and together with the left-hand side, they form a complete eigenvalue equation. Specifically, the result of multiplying the square of the ratio with the magnetic field expansion coefficient corresponding to the target reciprocal lattice vector is the right-hand side of the equation.

[0039] The first Brillouin zone is the smallest repeating unit in reciprocal lattice space composed of reciprocal lattice basis vectors. The first Brillouin zone has symmetry and integrity. Traversing wave vectors within the first Brillouin zone can avoid computational redundancy and ensure coverage of all independent wave vector states. The boundary of the first Brillouin zone is formed by the perpendicular bisectors of the reciprocal lattice basis vectors. Specifically, the reciprocal lattice basis vectors are calculated based on the positive lattice basis vectors of the commercial lattice, and the perpendicular bisectors of each reciprocal lattice basis vector are drawn. The smallest closed region enclosed by these planes is the first Brillouin zone.

[0040] The intrinsic frequency set is the set of all angular frequencies obtained by solving the eigenvalue equations for all wave vectors within the first Brillouin zone. The intrinsic frequency set contains all possible frequencies at which electromagnetic waves can propagate in a commercial lattice. Specifically, for each wave vector within the first Brillouin zone, all angular frequency solutions of the eigenvalue equations for the corresponding wave vector are solved, and all solutions are collected and duplicate values ​​are removed. The resulting set is the intrinsic frequency set.

[0041] The electromagnetic bandgap is a frequency range in the intrinsic frequency set where the numerical distribution is discontinuous. Within this frequency range, electromagnetic waves cannot propagate in a commercial crystal lattice. Specifically, all frequencies in the intrinsic frequency set are sorted from smallest to largest, and the interval where the difference between adjacent frequencies exceeds a set threshold is found. This interval is the electromagnetic bandgap.

[0042] In one embodiment of the present invention, the terminal to be controlled is regarded as a dielectric structure defect in a commodity lattice display topology, and the localized defect mode existing in the electromagnetic bandgap frequency range is calculated, including: Based on the physical location and dielectric properties of the terminal to be controlled, a dielectric perturbation matrix is ​​constructed to characterize its perturbation to the periodic lattice. Maxwell's operator matrix is ​​constructed based on the eigenvalue equation operators, and determinant equations are established by combining them with the identity matrix; The process of constructing the determinant equation is as follows: Calculate the sum of the identity matrix and the dielectric perturbation matrix, calculate the square of the ratio of the defect mode frequency to the speed of light, calculate the product of the square of the ratio and the sum, calculate the difference matrix obtained by subtracting the product from the Maxwell operator matrix, and set the determinant of the difference matrix to zero. The numerical solution of the defect mode frequency is obtained by solving the determinant equation, and the solution that satisfies a specific condition is selected as the localized defect mode. The specific condition is that the numerical value of the defect mode frequency is greater than the lower bound frequency of the electromagnetic bandgap and less than the upper bound frequency of the electromagnetic bandgap.

[0043] The physical location of the terminal to be controlled refers to the specific coordinates of the terminal to be controlled in the intelligent display rack coordinate system. The physical location of the terminal to be controlled adopts the same coordinate system as the commodity lattice display topology. The physical location of the terminal to be controlled is used to locate the specific area of ​​the perturbation in the lattice.

[0044] The dielectric properties of the terminal to be controlled refer to the dielectric constant characteristics of the material itself. The dielectric properties of the terminal to be controlled include the average dielectric constant of the terminal as a whole and the dielectric constant distribution of different internal components. The dielectric properties of the terminal to be controlled are used to quantify its disturbance intensity to the lattice dielectric environment. The dielectric properties of the terminal to be controlled are obtained by directly measuring the terminal as a whole and key components through a dielectric constant tester.

[0045] The dielectric perturbation matrix is ​​a matrix that characterizes the interference generated by the terminal to be controlled on the dielectric environment of a perfect commodity lattice. The dimension of the dielectric perturbation matrix is ​​the same as that of the Maxwell operator matrix, and the element values ​​of the dielectric perturbation matrix reflect the dielectric interference intensity of the terminal at the corresponding lattice position. The construction of this matrix is ​​the core of transforming the dielectric characteristics of the terminal into a mathematical model of lattice perturbation. Specifically, based on the dielectric distribution matrix of the perfect commodity lattice, at the matrix element corresponding to the physical position of the terminal to be controlled, the dielectric constant of the terminal to be controlled is subtracted from the lattice dielectric constant at the corresponding position to obtain the perturbation difference. This perturbation difference is filled into the corresponding position of the reference matrix, and the remaining positions are filled with zero. The resulting matrix is ​​the dielectric perturbation matrix.

[0046] Eigenvalue operators are the core operators used in constructing eigenvalue equations. They integrate the operational relationships of parameters such as Fourier coefficients, wave vectors, and magnetic field expansion coefficients, and form the basis for constructing Maxwell's operator matrix.

[0047] Maxwell's operator matrix is ​​a computational tool that transforms Maxwell's equations into matrix form. The dimension of the Maxwell's operator matrix is ​​determined by the number of reciprocal lattice points in the crystal lattice. The Maxwell's operator matrix is ​​used to transform electromagnetic property operations into matrix algebra operations, adapting to the needs of solving determinant equations. Specifically, the left-hand side of the eigenvalue equation is extracted and transformed into matrix form. The rows and columns of the matrix correspond to the target reciprocal lattice point vector and the summation reciprocal lattice point vector, respectively. The matrix elements are the product of Fourier coefficients and the square of the vector sum modulus. The resulting matrix is ​​the Maxwell's operator matrix.

[0048] The identity matrix is ​​a square matrix with 1s on the main diagonal and 0s on the rest. The dimension of the identity matrix is ​​consistent with that of the Maxwell operator matrix and the dielectric perturbation matrix. The identity matrix is ​​used to ensure that the dielectric perturbation matrix and the Maxwell operator matrix can be adapted for operation in determinant equations.

[0049] The determinant equation is the core mathematical equation for solving the defect mode frequency. By integrating parameters such as the Maxwell operator matrix and the dielectric perturbation matrix, the determinant equation transforms the existence condition of defect modes in the electromagnetic bandgap into a matrix determinant problem. The solution of the determinant equation is the possible defect mode frequency.

[0050] The matrix obtained by performing matrix addition on the identity matrix and the dielectric perturbation matrix has the same dimensions as both the identity matrix and the dielectric perturbation matrix. It combines the basic characteristics of the identity matrix with the perturbation characteristics of the dielectric perturbation matrix and is an intermediate matrix constructed from the determinant equation. Specifically, each element of the identity matrix is ​​added to the corresponding element of the dielectric perturbation matrix.

[0051] The defect mode frequency refers to the specific frequency at which electromagnetic waves are allowed to propagate due to disturbances of the terminal to be controlled within the electromagnetic bandgap. The defect mode frequency is the parameter to be solved in the determinant equation. The numerical solution of the defect mode frequency must be filtered through the electromagnetic bandgap before it can be used as an effective localized defect mode.

[0052] The value obtained by dividing the defect mode frequency by the speed of light and then squaring the result is used to quantify the characteristics of the defect mode frequency into a coefficient that can be multiplied by the matrix. It is a key intermediate quantity connecting the frequency parameter and the matrix parameter. Specifically, first calculate the ratio of the defect mode frequency to the speed of light, and then multiply the ratio by itself. The result is the square of the ratio.

[0053] The matrix obtained by performing matrix scalar multiplication on the square of the ratio and the sum has the same dimension as the matrix obtained by performing matrix addition on the identity matrix and the dielectric perturbation matrix. This matrix incorporates the characteristics of the defect mode frequency into the perturbation matrix and is the core intermediate matrix for constructing the difference matrix.

[0054] The difference matrix is ​​the matrix obtained by performing matrix subtraction on the Maxwell operator matrix and the product. The dimension of the difference matrix is ​​the same as that of the Maxwell operator matrix and the product. The difference matrix is ​​the core operation carrier of the determinant equation. The condition for the existence of the defect modulus is that the determinant of the difference matrix is ​​zero. Specifically, the difference matrix is ​​obtained by subtracting the corresponding element of the product from each element of the Maxwell operator matrix.

[0055] The determinant of a difference matrix is ​​a scalar value obtained by performing determinant operations on the difference matrix. The determinant of a difference matrix reflects the singularity of the matrix. Specifically, according to the standard rules of square matrix determinant operations, the elements of the difference matrix are expanded using algebraic cofactors, and the result is the determinant of the difference matrix.

[0056] The numerical solution of the defect mode frequency is all the frequency results obtained after solving the determinant equation. The numerical solution of the defect mode frequency includes all possible frequencies inside and outside the band gap. The numerical solution of the defect mode frequency needs to be screened before it can be used as an effective signal transmission frequency. Specifically, the numerical solution of the defect mode frequency is obtained by solving the equation with the determinant of the difference matrix equal to zero through algebraic solution method.

[0057] Localized defect modes are specific frequencies within the electromagnetic bandgap selected from the numerical solutions of defect mode frequencies. The energy of localized defect modes is concentrated only at the location of the terminal to be controlled. Localized defect modes are the core frequency reference for realizing directional and focused signal transmission.

[0058] The specific conditions are frequency range constraints used to screen effective localized defect modes. The core of the specific conditions is to limit the frequency of the defect mode to be within the electromagnetic bandgap. The specific conditions ensure that the screened frequencies have the characteristic of penetrating the commercial crystal lattice.

[0059] In one embodiment of the present invention, the remote control terminal tunes the carrier center frequency of the wireless transmission signal to the frequency value corresponding to the localized defect mode, including: Calculate the ratio of the defect mode frequency to twice the value of pi, and determine the quotient as the carrier center frequency. Obtain the mode attenuation rate of the localized defect mode, calculate the ratio of the defect mode frequency to the mode attenuation rate, and determine the quotient as the quality factor. Calculate the ratio of the carrier center frequency to the quality factor, and determine the quotient as the transmit bandwidth threshold. Configure the radio frequency transmission parameters of the remote control terminal, set the transmission frequency to the carrier center frequency, and limit the signal bandwidth to the transmission bandwidth threshold value range.

[0060] Twice the value of pi is used to convert the defective mode frequency of the angular frequency property into the carrier center frequency in Hertz units.

[0061] The carrier center frequency is the reference frequency for the wireless transmission signal of the remote control terminal. The unit of the carrier center frequency is Hertz. The carrier center frequency is precisely matched with the localized defect mode to ensure that the signal can excite the defect mode resonance. Specifically, the carrier center frequency is equal to the defect mode frequency divided by twice pi. The calculation is rounded to four decimal places to ensure that the frequency accuracy meets the requirements of radio frequency transmission.

[0062] The mode decay rate of a localized defect mode is a physical quantity characterizing the energy dissipation rate of the defect mode. The unit of the mode decay rate of a localized defect mode is per second. The smaller the value, the stronger the energy storage capacity of the defect mode. The mode decay rate of a localized defect mode is calculated by performing time-domain decay simulation of the defect mode using electromagnetic simulation software, extracting the time required for the energy to decay to a specific proportion of the initial value. Specifically, the energy change curve of the defect mode over time is obtained through electromagnetic simulation software, and the time for the energy to decay from the initial value to the initial value divided by the natural constant is found. The reciprocal of this time is the mode decay rate of the localized defect mode.

[0063] The quality factor is a core parameter for measuring the resonance characteristics of defective modes. The quality factor is a dimensionless quantity. The larger the value, the sharper the resonance peak and the stronger the signal's anti-interference ability. Specifically, the quality factor is equal to the defective mode frequency divided by the mode attenuation rate of the localized defective mode. The calculation result is rounded to two decimal places to meet the accuracy requirements of subsequent bandwidth calculations.

[0064] The transmit bandwidth threshold is the maximum allowable bandwidth of the signal transmitted by the remote control terminal. The unit of the transmit bandwidth threshold is Hertz. The transmit bandwidth threshold is used to constrain the signal bandwidth and avoid resonance excitation failure caused by excessive bandwidth. Specifically, the transmit bandwidth threshold is equal to the carrier center frequency divided by the quality factor. If the calculated result is less than the minimum configurable bandwidth of the RF hardware, then the minimum configurable bandwidth of the hardware is taken as the actual transmit bandwidth threshold.

[0065] The radio frequency (RF) transmission parameters of the remote control terminal are the core configuration items for controlling the operation of the RF module. The RF transmission parameters of the remote control terminal include key sub-parameters such as transmission frequency, signal bandwidth, and transmission power. The RF transmission parameters of the remote control terminal need to be accurately configured according to the calculation results to ensure compatibility with defective models.

[0066] The transmission frequency is the frequency at which the remote control terminal actually transmits signals. The transmission frequency must be completely consistent with the carrier center frequency. The transmission frequency is a core radio frequency parameter that ensures the signal can excite the localized defect mode. The configuration accuracy of the transmission frequency must reach the Hertz level to avoid frequency deviation leading to resonance failure.

[0067] Signal bandwidth is the distribution range of frequency components of the transmitted signal. The signal bandwidth must be strictly controlled within the transmission bandwidth threshold. If the signal bandwidth is too wide, it will cause energy dispersion and fail to effectively excite defect mode resonance. The actual configuration value of the signal bandwidth can be equal to or less than the transmission bandwidth threshold and needs to be adjusted according to the transmission rate requirements of the control command.

[0068] In one embodiment of the present invention, configuring the transmission bandwidth according to the quality factor of the localized defect mode includes: Obtain the preset coupling saturation coefficient; Calculate the ratio of the quality factor to the product of the carrier center frequency and twice pi, and determine the quotient as the resonance time constant. Calculate the product of the coupling saturation coefficient and the resonance time constant, and determine the duration of the command pulse by the product value; Calculate the reciprocal of the command pulse duration and use the resulting value as the configured transmit bandwidth.

[0069] The preset coupling saturation coefficient is a dimensionless constant set to ensure that the control command energy fully fills the local resonant cavity. The preset coupling saturation coefficient ranges from greater than 1 to less than or equal to 5. The value is adjusted according to the density of the product lattice. The denser the product arrangement, the larger the value, which is used to ensure that the duration of the transmitted signal covers the entire resonance establishment process. Specifically, when the horizontal and vertical spacing of the product arrangement is greater than or equal to 10 cm, the preset coupling saturation coefficient is 1.5; when the spacing is between 5 and 10 cm, the preset value is 2.5; and when the spacing is less than 5 cm, the preset value is 4.0.

[0070] The resonance time constant is the time required for the defect mode energy to decay to a specific proportion. The unit of the resonance time constant is seconds. The resonance time constant reflects the time threshold for the defect mode to establish stable resonance and is the basis for determining the duration of the command pulse. Specifically, the resonance time constant is equal to the quality factor divided by (the carrier center frequency multiplied by pi twice). The calculation result is retained to six decimal places to ensure that the time accuracy is adapted to the pulse configuration requirements.

[0071] The command pulse duration is the effective time length of the transmitted signal. The unit of the command pulse duration is seconds. The command pulse duration must be greater than the resonance time constant to ensure that the defect mode resonance can be effectively excited. Specifically, the command pulse duration is equal to the preset coupling saturation coefficient multiplied by the resonance time constant. If the calculation result is less than the minimum pulse duration of the RF module, the minimum pulse duration of the RF module is taken as the actual command pulse duration.

[0072] The configured transmit bandwidth is the signal bandwidth ultimately configured for the transmitter at the remote control end. The unit for configuring the transmit bandwidth is Hertz. The configured transmit bandwidth must be adapted to the narrowband characteristics of the defective mode to avoid energy dispersion caused by excessive bandwidth. Specifically, the configured transmit bandwidth is equal to the value divided by the duration of the command pulse. If the calculation result exceeds the bandwidth configuration range of the RF module, the nearest compatible bandwidth value supported by the module is taken.

[0073] In one embodiment of the present invention, the electromagnetic energy of the control command is focused and coupled to the terminal to be controlled by resonant excitation transmission of the localized defect mode, including: Obtain the electric field distribution function of the defect mode corresponding to the defect mode frequency; The mode volume of the localized defect mode is calculated as follows: the product of the dielectric function and the square of the electric field distribution function of the defect mode is calculated, the total electromagnetic energy is obtained by performing a full-space integration operation on the product, the maximum value of the product in space is obtained to obtain the maximum energy density, and the ratio of the total electromagnetic energy to the maximum energy density is calculated. The resonant energy density at the location of the terminal to be controlled is calculated as follows: obtain the preset coupling efficiency coefficient and the current transmit power, calculate the product of the quality factor and the transmit power, calculate the product of the defective mode frequency and the mode volume, and calculate the ratio of the product of the coupling efficiency coefficient, the product of the quality factor and the transmit power, to the product of the defective mode frequency and the mode volume.

[0074] The defect mode electric field distribution function is a function that describes the distribution of the electric field corresponding to the localized defect mode within the space of the intelligent display rack. The value of the defect mode electric field distribution function reflects the magnitude of the electric field intensity at different locations and is the basis for calculating the mode volume and resonance energy density. This function is obtained by solving the characteristic vector corresponding to the defect mode using electromagnetic simulation software. Specifically, by importing the commodity lattice display topology model and the localized defect mode parameters into three-dimensional electromagnetic simulation software, solving Maxwell's equations, the electric field vector distribution corresponding to the defect mode is obtained, and the distribution law is extracted as the defect mode electric field distribution function.

[0075] The mode volume of a localized defect mode is a key physical quantity that measures the degree to which electromagnetic energy is localized in space. The unit of the mode volume of a localized defect mode is cubic meters. The smaller the value, the better the energy focusing effect, which is an important indicator for judging energy coupling efficiency. Specifically, first calculate the product of the dielectric function and the square of the electric field distribution function of the defect mode. Then, perform an integral operation on this product in the entire space of the intelligent display stand to obtain the total electromagnetic field energy. Next, find the maximum value of this product in the entire space as the maximum energy density. Finally, divide the total electromagnetic field energy by the maximum energy density to obtain the mode volume of the localized defect mode.

[0076] The squared modulus of the defect mode electric field distribution function is a scalar value obtained by squaring the magnitude of the defect mode electric field distribution function. The squared modulus of the defect mode electric field distribution function is used to convert the vector form of the electric field distribution into a scalar operation. Specifically, the vector magnitude of the defect mode electric field distribution function at any position in space is extracted, and the magnitude is multiplied by itself. The result is the squared modulus of the defect mode electric field distribution function.

[0077] The full-space integration operation is a cumulative operation performed on the product of the dielectric function and the square of the modulus of the electric field distribution function of the defect mode within a specified spatial range. The range of the full-space integration operation is limited to the complete physical space where the smart display stand is located, to ensure the integrity of the calculation of the total electromagnetic energy. Specifically, the spatial range of the smart display stand is divided into tiny cubic units, the average value of the product in each unit is calculated and multiplied by the unit volume, and the results of all units are accumulated. The sum is the result of the full-space integration operation.

[0078] The total electromagnetic energy is the total electromagnetic energy stored by the localized defect mode within the entire space of the intelligent display stand.

[0079] The maximum energy density is the peak value of the product of the dielectric function and the square of the defect mode electric field distribution function in the global space.

[0080] Resonant energy density is the actual electromagnetic energy intensity concentrated at the location of the terminal to be controlled. The unit of resonant energy density is joules per cubic meter. The resonant energy density must be greater than the terminal receiving threshold to trigger a control command response. It is the ultimate indicator for judging the energy coupling effect.

[0081] The preset coupling efficiency coefficient is a dimensionless constant characterizing the energy coupling effect between the remote control transmitter and the commercial lattice. The preset coupling efficiency coefficient ranges from 0.6 to 0.95, and is adjusted according to the distance between the transmitter and the display stand. The closer the distance, the larger the value. Specifically, when the distance between the transmitter and the display stand is less than one meter, the preset coupling efficiency coefficient is 0.9; when the distance is between one and two meters, the preset value is 0.75; and when the distance is greater than two meters, the preset value is 0.65.

[0082] The embodiments of this example have been described above. However, this example is not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms based on the guidance of this example, and all of them are within the protection scope of this example.

Claims

1. A remote management and control system for intelligent display racks based on the Internet of Things, characterized in that, include: Based on the physical attributes and arrangement information of the displayed goods on the intelligent display rack, a product lattice display topology representing the periodic distribution of the medium space is constructed. The electromagnetic bandgap is calculated based on the topology of the commodity lattice display, and the terminal to be controlled is regarded as a dielectric structure defect in the topology of the commodity lattice display. The localized defect mode existing in the frequency range of the electromagnetic bandgap is calculated. The remote control terminal tunes the carrier center frequency of the wireless transmission signal to the frequency value corresponding to the localized defect mode, and configures the transmission bandwidth according to the quality factor of the localized defect mode. Through the resonant excitation transmission of the localized defect mode, the electromagnetic energy of the control command is focused and coupled to the terminal to be controlled.

2. The IoT-based intelligent display stand remote management and control system according to claim 1, characterized in that, Based on the physical attributes and arrangement information of the displayed goods on the intelligent display rack, a product lattice display topology representing the periodic distribution of the medium space is constructed, including: Based on the spacing of the product display, determine the grid point position vector of each product unit in the display rack coordinate system; Obtain the background dielectric constant of the air environment and the spatial dielectric distribution function of a single commodity; Calculate the dielectric function at any spatial location vector within the area where the smart display stand is located. The value of the dielectric function is equal to the sum of the background dielectric constant and the dielectric contribution. For each grid point position vector, calculate the difference between the spatial position vector and the grid point position vector. Substitute this difference into the spatial dielectric distribution function of the commodity to obtain the function value. Calculate the difference between the function value and the background dielectric constant as the net dielectric contribution of a single commodity. Perform a summation operation on the net dielectric contributions corresponding to all grid point position vectors to obtain the total dielectric contribution.

3. The IoT-based intelligent display stand remote management and control system according to claim 2, characterized in that, Electromagnetic bandgap calculations based on commodity lattice topology include: The inverse dielectric function is obtained by calculating the reciprocal of the dielectric function, and the Fourier coefficients are obtained by performing a Fourier transform on the inverse dielectric function. The eigenvalue equations for the magnetic field expansion coefficients are constructed as follows: Calculate the vector difference between the target reciprocal lattice vector and the summed reciprocal lattice vector, and obtain the Fourier coefficients corresponding to the vector difference; calculate the vector sum of the wave vector and the summed reciprocal lattice vector, and obtain the squared magnitude of the vector sum; calculate the product of the Fourier coefficients, the squared magnitude, and the magnetic field expansion coefficients corresponding to the summed reciprocal lattice vectors; perform a summation operation on the products corresponding to all summed reciprocal lattice vectors to obtain the left-hand side of the equation; calculate the ratio of the angular frequency to the speed of light, and obtain the square of the ratio; calculate the product of the square and the magnetic field expansion coefficients corresponding to the target reciprocal lattice vector to obtain the right-hand side of the equation; Let the left-hand term of the equation equal the right-hand term of the equation; By traversing the wave vectors and solving the eigenvalue equations within the first Brillouin zone, the set of eigenfrequency is obtained. The frequency range with discontinuous numerical distributions in the intrinsic frequency set is selected and defined as the electromagnetic bandgap.

4. The IoT-based intelligent display stand remote management and control system according to claim 3, characterized in that, Treating the terminal to be controlled as a dielectric structure defect in a commodity lattice display topology, the localized defect modes existing within the electromagnetic bandgap frequency range are calculated, including: Based on the physical location and dielectric properties of the terminal to be controlled, a dielectric perturbation matrix is ​​constructed to characterize its perturbation to the periodic lattice. Maxwell's operator matrix is ​​constructed based on the eigenvalue equation operators, and determinant equations are established by combining them with the identity matrix; The process of constructing the determinant equation is as follows: Calculate the sum of the identity matrix and the dielectric perturbation matrix, calculate the square of the ratio of the defect mode frequency to the speed of light, calculate the product of the square of the ratio and the sum, calculate the difference matrix obtained by subtracting the product from the Maxwell operator matrix, and set the determinant of the difference matrix to zero. The numerical solution of the defect mode frequency is obtained by solving the determinant equation, and the solution that satisfies a specific condition is selected as the localized defect mode. The specific condition is that the numerical value of the defect mode frequency is greater than the lower bound frequency of the electromagnetic bandgap and less than the upper bound frequency of the electromagnetic bandgap.

5. The IoT-based intelligent display stand remote management and control system according to claim 4, characterized in that, The remote control unit tunes the carrier center frequency of the wireless transmission signal to the frequency value corresponding to the localized defect mode, including: Calculate the ratio of the defect mode frequency to twice the value of pi, and determine the quotient as the carrier center frequency. Obtain the mode attenuation rate of the localized defect mode, calculate the ratio of the defect mode frequency to the mode attenuation rate, and determine the quotient as the quality factor. Calculate the ratio of the carrier center frequency to the quality factor, and determine the quotient as the transmit bandwidth threshold. Configure the radio frequency transmission parameters of the remote control terminal, set the transmission frequency to the carrier center frequency, and limit the signal bandwidth to the transmission bandwidth threshold value range.

6. The IoT-based intelligent display stand remote management and control system according to claim 5, characterized in that, Configure the transmission bandwidth based on the quality factor of the localized defect mode, including: Obtain the preset coupling saturation coefficient; Calculate the ratio of the quality factor to the product of the carrier center frequency and twice pi, and determine the quotient as the resonance time constant. Calculate the product of the coupling saturation coefficient and the resonance time constant, and determine the duration of the command pulse by the product value; Calculate the reciprocal of the command pulse duration and use the resulting value as the configured transmit bandwidth.

7. The IoT-based intelligent display stand remote management and control system according to claim 6, characterized in that, By resonantly exciting and transmitting localized defect modes, the electromagnetic energy of the control command is focused and coupled to the terminal to be controlled, including: Obtain the electric field distribution function of the defect mode corresponding to the defect mode frequency; The mode volume of the localized defect mode is calculated as follows: the product of the dielectric function and the square of the electric field distribution function of the defect mode is calculated, the total electromagnetic energy is obtained by performing a full-space integration operation on the product, the maximum value of the product in space is obtained to obtain the maximum energy density, and the ratio of the total electromagnetic energy to the maximum energy density is calculated. The resonant energy density at the location of the terminal to be controlled is calculated as follows: obtain the preset coupling efficiency coefficient and the current transmit power, calculate the product of the quality factor and the transmit power, calculate the product of the defective mode frequency and the mode volume, and calculate the ratio of the product of the coupling efficiency coefficient, the product of the quality factor and the transmit power, to the product of the defective mode frequency and the mode volume.

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