Function Of Angle Research Articles

Dynamical Investigation of a Modified Cubic Map with a Discrete Memristor Using Microcontrollers

This study presents a novel approach by implementing an active memristor in a hyperchaotic discrete system, based on a cubic map, which is implemented by using two different microcontrollers. The key contributions of this work are threefold. The use of two microcontrollers with improved characteristics, such as speed and memory, for faster and more accurate computations significantly improves upon previous systems. Also, for the first time, an active memristor is used in a discrete-time system, which is implemented by using a microcontroller. Furthermore, the system is compared with two different types of microcontrollers regarding the execution time and the quality of the produced bifurcation diagrams. The proposed memristive cubic map uses computationally efficient polynomial functions, which are well suited to microcontroller-based systems, in contrast to more resource-intensive trigonometric and exponential functions. Bifurcation diagrams and a Lyapunov exponent analysis from simulating the system in Mathematica revealed hyperchaotic behavior, along with other significant dynamical phenomena, such as regular orbits, chaotic trajectories, and transitions to chaos through mechanisms like period doubling and crisis phenomena. Experimental verification confirmed the consistency of the results across microcontroller platforms, underscoring the practicality and potential applications of active memristor-based chaotic systems.

Model-Free Speed Control for Pumping Kite Generator Systems Based on Nonlinear Hyperbolic Tangent Tracking Differentiator

This paper investigates the emerging field of grid-connected wind-powered pumping kite generator system (PKGS), focusing on the challenges associated with the generator/motor speed control. Conventional use of proportional–integral (PI) controllers faces difficulties in meeting requirements for dynamic response, tracking performance, stability, and disturbance rejection encountered in this technology, notably the periodical variation in the rotational speed reference in maximum power point tracking in generation phases and the dynamic response for the step reference in transient ones. To overcome these limitations, a model-free controller (MFC) approach is introduced, also known as intelligent PID controllers. Unlike traditional methods, MFC does not rely on a control model of the system and adapts to uncertainties and disturbances through online estimation based on the system’s input–output behavior. To further improve the control performances, a tracking differentiator based on a nonlinear hyperbolic tangent function is integrated in the MFC. The effectiveness of the proposed strategy is proved through simulations in MATLAB/Simulink. The results highlight the superior performances of the proposed MFC approach in terms of speed control accuracy, response time, and robustness.

Impact and analysis of corrosion on elastic stress in a composite disk under parabolic temperature distribution using the Rayleigh-Ritz method with trigonometric Ritz functions

This study conducts an in-depth impact and analysis of corrosion on the elastic stresses within a composite disk exposed to a parabolic temperature distribution. The disk, reinforced with steel fibers, is modeled as a thermo-elastic composite material to evaluate its performance under thermal and corrosive conditions. The Rayleigh-Ritz method, a widely recognized numerical approach for solving boundary value problems, is utilized to derive analytical solutions for both radial and tangential stresses. This method applies the principle of minimum potential energy to approximate displacement fields through Trigonometric Ritz Functions, which are subsequently employed to calculate stress components. The parabolic temperature distribution imposes a non-uniform thermal load across the disk, significantly altering the stress distribution. The study explores how the inherent thermal properties of the composite material interact with temperature variations, resulting in intricate stress patterns. By systematically varying temperature parameters, the analysis uncovers the sensitivity of stress components to thermal gradients. Comparative evaluations are performed for different temperature profiles, identifying critical regions of stress concentration. The findings offer essential insights into the behavior of thermo-elastic composites under non-uniform thermal and corrosive conditions, establishing a robust analytical framework for future research and practical engineering applications. This research emphasizes the necessity of integrating both thermal effects and Trigonometric Ritz Functions in the design and analysis of composite structures exposed to varying temperature loads and corrosion.

Analysis of elastic stresses and thermal creep effect for a composite disk under the parabolic distribution of temperature using the Rayleigh-Ritz method with trigonometric Ritz functions

This research provides a detailed examination of the thermal creep effect on elastic stresses in a composite disk exposed to a parabolic temperature distribution. The disk, reinforced with steel fibers, is treated as a thermo-elastic composite material. The Rayleigh-Ritz method, a widely recognized numerical approach for solving boundary value problems, is utilized to derive analytical solutions for the radial and tangential stresses. This method employs the principle of minimum potential energy to approximate displacement fields using Trigonometric Ritz Functions, which are subsequently applied to calculate the stress components. The parabolic temperature distribution imparts a non-uniform thermal load across the disk, significantly affecting the stress distribution. The study explores how the thermal creep effect, intrinsic to the composite material, interacts with thermal variations, resulting in intricate stress patterns. By adjusting temperature parameters, the analysis demonstrates the sensitivity of stress components to thermal gradients. Comparative assessments are performed for various temperature profiles, identifying critical areas of stress concentration. The findings offer significant insights into the behavior of thermo-elastic composites under non-uniform thermal conditions, providing a robust analytical foundation for future research and engineering applications. This research emphasizes the necessity of considering both thermal creep effects and Trigonometric Ritz Functions in the design and analysis of composite structures subjected to varying temperature loads.

Prescribed Performance Control for High-Order Odd-Rational-Power Nonlinear Systems with Actuator Faults and Unknown Powers

A global prescribed performance control method is proposed for a class of uncertain high-order odd-rational-power nonlinear systems (a chain of integrators whose power is the ratio of odd integers) with actuator faults, where the high-order odd-rational powers and the parameters of actuator faults are unknown. A new coordinate transformation on the state and tracking errors is introduced based on the tangent function and its inverse function, resulting in a global low-complexity prescribed performance controller. The proposed controller does not require any knowledge of system nonlinearities or powers, and it also does not require the time derivatives of virtual control signals without using any filters, which implies the controller is of low complexity. Finally, two simulation examples, including a practical high-maneuver flight control example, are given to demonstrate the effectiveness of our method.

Application of Video Game Algorithm Based on Deep Q-Network Learning in Music Rhythm Teaching

The difficulty of music rhythm teaching makes its teaching effect limited. Some game algorithms show problems of stuttery and unclear picture when they are introduced into teaching, which greatly restricts the development of teaching content. Therefore, it is proposed to activate the deep Q network and improve the filter to improve the processing performance of game image data and the integrity of information retention. The model fuses the extracted features and processes them through the neural network. According to the performance characteristics and forms of music rhythm, constant Q transformation, dynamic programming algorithm and hidden Markov model are proposed to analyze and design music signal, beat point analysis and signal traveling speed, so as to realize the identification and matching of music rhythm. The performance test and application analysis of the proposed fusion improvement algorithm are carried out: the video game algorithm can effectively extract data feature information, and its accuracy rate is basically 90% or above. The improved Deep Q-network (DQN) and Artificial Fish Swarms Algorithm (AFSA) algorithms can maintain an accuracy of over 75%, followed by the ABC algorithm, which maintains an accuracy of over 70%, but exhibits significant fluctuations in the curve changes and nodes. The recognition accuracy of music signal feature extraction is over 70%, and it is less affected by signal-to-noise ratio. The improved activation function showed that the highest game score exceeded 10 points, while the scores of Rectified Linear Unit (ReLU) function and Hyperbolic tangent function (Tanh) function were basically hovering below 5 points, and the overall score curve fluctuated significantly. The recognition accuracy of music signal features extraction is above 70% and is less affected by Signal to Noise Ratio. The algorithm has a good effect of music rhythm teaching, the students' interest in classroom learning is more than 45%, and the learning weakness is less. The average score of students in music style judgment, rhythm division and index is 85 points and 90 points respectively, which is much higher than the 40 points and 63 points of traditional teaching. The proposed algorithm can better combine video games with music teaching and help students improve their learning effect under the gamification teaching method, and has good application value

Novel insights into high-order dispersion and soliton dynamics in optical fibers via the perturbed Schrödinger–Hirota equation

This study offers a comprehensive analysis of the Perturbed Schrödinger -Hirota Equation (PSHE), crucial for understanding soliton dynamics in modern optical communication systems. We extended the traditional Nonlinear Schrödinger Equation (NLSE) to include higher-order nonlinearities and spatiotemporal dispersion, capturing the complexities of light pulse propagation. Employing the modified auxiliary equation method and Adomian Decomposition Method (ADM), we derived a spectrum of exact traveling wave solutions, encompassing exponential, rational, trigonometric, and hyperbolic functions. These solutions provide insights into soliton behaviors across diverse parameters, essential for optimizing fiber optic systems. The precision of our analytical solutions was validated through numerical solutions, and we explored modulation instability, revealing conditions for soliton formation and evolution. The findings have significant implications for the design and optimization of next-generation optical communication technologies.

An Analytical Solution for the Steady Seepage of Localized Line Leakage in Tunnels

This paper proposes an analytical solution for the seepage field when a localized line leakage occurs in a tunnel by accurately considering the boundary conditions at the leakage site, which overcomes the problem of current methods, such as the equivalent method or methods improving on the existing analytical solution for fully drained tunnels, being unable to give an accurate analytical solution. First, the semi-infinite seepage region is converted into a rectangular seepage region using two conformal transformations. Subsequently, in order to accurately consider the boundary conditions at the leakage site, the rectangular seepage region with a discontinuous boundary is divided into three subregions with continuous boundaries, and the water head solution for each subregion is given by using the separated variable method. Finally, the principle of orthogonality of trigonometric functions is specially adopted to construct a non-homogeneous system of equations to solve the unknowns in the analytical solution, and through the inverse transformation of the conformal transformation, an analytical solution for the steady-state seepage field when localized line leakage occurs in a tunnel is obtained. The solution proposed is verified by its satisfactory agreement with the numerical simulation results and existing experimental results, and is much more accurate than the existing analytical solution. In addition, the proposed analytical solution is much less computationally demanding compared to numerical simulations. Finally, the capability of the proposed analytical solution is demonstrated by a parametric analysis of the tunnel burial depth, leakage location, and leakage width, and some meaningful conclusions are drawn.

Neural network model for autonomous navigation of a water drone

Water drones have significant potential for use in environmental monitoring, search and rescue operations, and marine infrastructure inspection, but the specific conditions of the water environment make it difficult to implement stable autonomous navigation. The object of research presented in this paper is the machine learning process for autonomous navigation of a water drone model in a simulated water environment. The purpose of the study is to implement a neural network model for autonomous navigation of a water drone using a reinforcement learning method that provides improved obstacle avoidance and adaptation to water currents. To achieve this purpose, a new neural network model for autonomous drone navigation in the water environment based on the reinforcement learning method is proposed, which differs from the existing ones in that it uses an improved drone control algorithm that takes into account the speed and direction of the water current, which makes it possible to stabilize the process of generating neural network coefficients. To ensure an effective learning process and optimization of the model, a simulation training environment was developed using the USVSim simulator, which contains various factors that interfere with the drone's movement, such as water current and the presence of other objects. The water drone, acting as an agent, gradually learns to choose the most effective actions to maximize positive rewards through trial and error, interacting with the environment and adapting to changing conditions. This process takes place through the use of a Deep Q-Network: the drone provides the value of its current state to a deep neural network; the neural network processes the data, predicts the value of the most effective action, and gives it to the agent. The current state of the drone is information in the form of a set of sensor readings measuring the distance to the nearest obstacles, drone’s heading and current distance to goal. The value of the effective action received from the neural network is converted into a command for the rudder that the drone can understand. The value of the drone's thruster power is calculated by separate formulas using trigonometric functions. The results of the study showed that the use of the proposed model allows the drone to make decisions in a dynamic water environment when rapid adaptation to changes is required. The model successfully adapted its strategy based on feedback from the environment, so it can be concluded that the implemented model shows significant potential for further research and applications in the field of autonomous water drones, especially in changing and unpredictable environments.

Off-equatorial deflections and gravitational lensing. I. In Kerr spacetime and effect of spin

Abstract This paper investigates off-equatorial plane deflections and gravitational lensing of both null and timelike signals in Kerr spacetime in the weak deflection limit, with the finite distance effect of the source and detector taken into account. This is the effect caused by the fact that both the source and detector are located at finite distances from the lens, while many researchers often use the deflection angle for infinite distances from sources and detectors. The deflection in both the $\phi$ and $\theta$ directions is computed as power series of $M/r_0$ and $r_0/r_{\mathrm{s,d}}$, where $M,\,r_{\mathrm{s,d}}$ are the spacetime mass and source and detector radii respectively, and $r_0$ is the minimal radial coordinate of the trajectory. The coefficients of these series are simple trigonometric functions of $\theta_\te$, the extreme value of the $\theta$ coordinate of the trajectory. A set of exact gravitational lensing equations is used to solve for $r_0$ and $\theta_\te$ for given deviation angles $\delta\theta$ and $\delta\phi$ of the source, and two lensed images are always obtained. The apparent angles and their magnifications of these images, and the time delays between them are solved and their dependence on various parameters, especially spacetime spin $\hat{a}$ are analyzed in great detail. It is found that there generally exist two critical spacetime spin values that separate the case of signals reaching the detector from different sides of the $z$ axis from the cases in which the images appear from the same side in the celestial plane. Three potential applications of these results are discussed.

Dynamical insights into bifurcation, chaos and solitons in the space-time fractional symmetric regularized long wave equation

Abstract The nonlinear conformable time-fractional Symmetric Regularized Long Wave (SRLW) equation is a significant model in physics, particularly for describing ion acoustic and space charge waves with weak nonlinearity. In this study, we apply the modified Sardar sub equation method and the modified extended auxiliary equation method to solve the SRLW equation. We effectively manage the fractional derivatives in the equation by employing Jumarie’s modified Riemann-Liouville derivative. Various types of soliton solutions, including kink, periodic, dark, bright, and singular solitary waves, are obtained in forms such as rational, hyperbolic, trigonometric, and exponential functions. A comparative analysis of the methods and the results is conducted, along with an exploration of fractional derivative effects by varying their values. The study also includes 2D and 3D plots that show how the solutions behave over time. It demonstrates that the methods used can be applied to other nonlinear models in mathematical physics. The research looks closely at the model’s behavior, including bifurcation, chaos, and stability. Phase portrait analysis at key points shows changes in the system’s behavior, and adding an external periodic force leads to chaotic patterns. The stability analysis proves that these methods
are reliable for studying phase portraits and soliton solutions in different nonlinear systems.

Addressing Students’ Challenges in Acquiring Trigonometric Function Concepts: A Didactic Approach to Education for Sustainable Development

The concepts of trigonometric functions constitute one of the main challenges that students face when studying mathematics in secondary and higher education. This paper addresses these challenges through a sustainable educational approach aligned with the principles of Education for Sustainable Development (ESD). The study identifies the main difficulties, such as graphical representation, real-life application of trigonometric functions and the conceptual understanding of angles and ratios. Through the methodology of observing students during lessons, weak points in the understanding of concepts such as the graphical representation of trigonometric functions, the use of trigonometric equations in real situations, and the difficulties arising from the lack of a clear connection between angles and ratios have been trigonometric identified. Based on these observations, didactic strategies have been proposed that include more interactive methods and the use of technology to improve student’s skills. The results of this study suggest that a new didactic approach, based on concrete examples and practical experience, helps to create a more stable and in-depth understanding of trigonometric functions. The findings of this study contribute to the development of educational practices focused on ESD, supporting students’ capacity to adapt, innovate, and engage in complex problem solving within mathematics education. Through a didactic approach that focuses on advanced teaching methods and the use of educational technology, this paper offers recommendations for improving teaching practices to facilitate the acquisition of complex mathematical concepts.

The propagation of hyper-geometric optical soliton waves in plasma dynamics for the integrable Zhanbota-IIA equation

This research utilizes the new auxiliary equation method to investigate solitary wave patterns in the integrable Zhanbota-IIA equation, a model relevant to phenomena like tidal waves and tsunamis. This method simplifies complex nonlinear-coupled partial differential equations into ordinary differential equation through a traveling wave transformation. Previous studies have not achieved such solutions. The main aim is to enhance comprehension of the integrable Zhanbota-IIA equation behavior under various conditions. Prior to this study, there does not exist any study in which such kinds of solutions are discussed by using the new auxiliary equation method. The new auxiliary equation method is utilized to derive analytical solutions for the underlying model equation. These solutions are expressed in the form of hyperbolic, trigonometric, exponential, and rational functions such as dark, bright, periodic, dark–bright, smooth topological with high peaks, dark-singular, bright singular and periodic singular. The key advantage of this method compared to others lies in its capacity to yield more comprehensive solutions with certain flexible parameters. To illustrate the dynamic structures of these solutions, 3D and 2D graphs are employed with suitable parameter values. This study explores soliton behavior and its telecommunication applications, integrating mathematics, computer science, and physics for technological advancements.

An Improved SOGI-Higher-Order Sliding Mode Observer-Based Induction Motor Speed Estimation

Abstract This article presents a novel adaptive gain tuning second-order generalised integrator (SOGI)-higher-order sliding mode (HOSM) observer for robust speed estimation for an induction motor’s entire speed range. This article introduces a hyperbolic tangent function and a varying gain exponent that ensures accurate speed estimation under noisy conditions and significantly reduces chattering observed in conventional sliding mode observers (SMOs). The robustness of the proposed speed estimation method is verified through simulations conducted on MATLAB/Simulink R2024a developed by MathWorks, demonstrating its capability to effectively track the motor’s actual speed even under varying load torque conditions, parameter variations and additional sensor noise. The proposed approach’s superiority and robustness were compared with the conventional SOGI-frequency locked loop (FLL) and super twisting algorithm (STA) SMO.

Theoretical Aspects of Soil Layer Turnover Within the Boundaries of Its Own Furrow

The paper highlights that soil layer turnover remains the most widely used method of primary tillage. Among the existing techniques, smooth plowing without producing back ridges or furrows, which is achieved using reversible plows, best meets the high standards of modern agricultural practices. (Research purpose) The study aims to substantiate the kinematics of soil layer turnover within the boundaries of its own furrow without lateral displacement. (Materials and methods) In analyzing the kinematics, the soil layer is assumed to behave as a cohesive elastic substance undergoing deformation during turnover within its own furrow, without disintegration. This assumption is quite reasonable, as it is well-established that a sodded and moist layer can be extracted as a continuous, intact strip that retains its geometric dimensions when turned 180°. The trajectory of the layer is derived using classical methods of theoretical mechanics. (Results and discussions) The equations governing the motion of the soil layer points during turnover within its own furrow are analyzed. During this process, all points in the cross-section of the layer undergo spatial displacement. Changes in displacement, velocity, and acceleration of the i-th point of the hypothetical layer exhibit smooth dependencies described by trigonometric functions. However, at a rotation angle of ωt = π/2, an abrupt change occurs in the trajectories of displacement, velocity and acceleration graphs, indicating sharply variable loads acting on the soil layer at this point. The abrupt change is attributed to a shift in the support rib which serves as the axis for the rotation of the soil layer's crosssection. The center of gravity of the cross-section moves with variable velocity and acceleration, which indicates the presence of inertial forces. Overcoming these forces requires a certain amount of energy. (Conclusions) The energy required largely depends on the geometric parameters of the layer a, b and its rotation modes (ω). When the layer cross-section rotates by an angle When the layer cross-section rotates by an angle ωt = π/2 – γ, the vertical acceleration of the central point (О) reaches its maximum value. Under certain conditions, the soil layer may detach from the furrow bottom in this position. The kinematics analysis of a soil layer turnover within the boundaries of its own furrow reveals new phenomena occurring during its motion to identifies the patterns of influence that the soil layer's geometric parameters exert on its dynamic characteristics.

A Novel Megastable Chaotic System with Hidden Attractors and Its Parameter Estimation Using the Sparrow Search Algorithm

This work proposes a new two-dimensional dynamical system with complete nonlinearity. This system inherits its nonlinearity from trigonometric and hyperbolic functions like sine, cosine, and hyperbolic sine functions. This system gives birth to infinite but countable coexisting attractors before and after being forced. These two megastable systems differ in the coexisting attractors’ type. Only limit cycles are possible in the autonomous version, but torus and chaotic attractors can emerge after transforming to the nonautonomous version. Because of the position of equilibrium points in different attractors’ attraction basins, this system can simultaneously exhibit self-excited and hidden coexisting attractors. This system’s dynamic behaviors are studied using state space, bifurcation diagram, Lyapunov exponents (LEs) spectrum, and attraction basins. Finally, the forcing term’s amplitude and frequency are unknown parameters that need to be found. The sparrow search algorithm (SSA) is used to estimate these parameters, and the cost function is designed based on the proposed system’s return map. The simulation results show this algorithm’s effectiveness in identifying and estimating parameters of the novel megastable chaotic system.

A Mixture Transition Distribution Modeling for Higher‐Order Circular Markov Processes

ABSTRACTThis study considers the stationary higher‐order Markov process for circular data by employing the mixture transition distribution modeling. The underlying circular transition distribution is based on Wehrly and Johnson's bivariate joint circular models. The structures of the circular autocorrelation function, together with the circular partial autocorrelation function, are investigated. They are found to be similar to those of the autocorrelation and partial autocorrelation functions of the real‐valued autoregressive process when the underlying binding density has zero sine moments. The validity of the model is assessed by applying it to some Monte Carlo simulations and real directional data.

Random Traveling Wave Equations for the Heisenberg Ferromagnetic Spin Chain Model and Their Optical Stochastic Solutions in a Ferromagnetic Materials

In this paper, we investigate the stochastic Heisenberg ferromagnetic equation (SHFE) derived by a multiplicative Wiener process. We use a suitable transformation to change the SHF equation into another Heisenberg ferromagnetic equation with random variable coefficients (HFE-RVCs). We employ the mapping approach to obtain novel rational, trigonometric, elliptic and hyperbolic function solutions for HFE-RVCs. Following that, we can attain the solutions of the SHFE. For the first time in the Heisenberg ferromagnetic equation, we postulate that the solution to the wave equation is stochastic, whereas all previous investigations supposed that it was deterministic. Moreover, we give various visual representations to demonstrate the impact of the multiplicative Wiener process on the exact solutions to the stochastic Heisenberg ferromagnetic equation.

Development of a Local Instruction Theory for Trigonometric Ratios

Some students find trigonometric ratios challenging. Research on the application of Local Instruction Theory (LIT) in trigonometry is limited, particularly in secondary school understanding of trigonometric ratios. This study aims to develop an LIT for trigonometric ratios using Realistic Mathematics Education (RME). The researcher designed a learning pathway to help students grasp the fundamental concepts of trigonometric ratios. The study employs a research design methodology, developing a Hypothetical Learning Trajectory (HLT) to improve students' understanding. The development of LIT for Trigonometric Ratios follows three stages: initial design, teaching experiments, and retrospective analysis. Students demonstrated the ability to understand trigonometric ratios through the learning process. The findings suggest that the use of LIT-based instructional materials, incorporating RME principles, significantly enhances students' conceptual understanding of trigonometric ratios in high school. Beberapa siswa menganggap materi perbandingan trigonometri cukup sulit. Penelitian tentang penerapan Local Instruction Theory (LIT) dalam pembelajaran trigonometri masih sangat terbatas, khususnya terkait dengan pemahaman rasio trigonometri di sekolah menengah. Penelitian ini bertujuan untuk mengembangkan Local Instruction Theory (LIT) perbandingan trigonometri dengan menggunakan Realistic Mathematic Education (RME). Dalam upaya membantu siswa membangun konsep dasar pada materi perbandingan trigonometri, peneliti mengembangkan alur LIT dengan menemukan jalur pembelajaran yang efektif. Pencapaian tujuan penelitian menggunakan desain penelitian. Serangkaian kegiatan mengembangkan Hypothetical Learning Trajectory (HLT) sehingga siswa sekolah menengah atas (SMA) memiliki pemahaman yang lebih baik tentang perbandingan trigonometri. Pengembangan Local Instruction Theory untuk Perbandingan Trigonometri meliputi tiga tahap yaitu mengembangkan desain awal, melakukan percobaan pengajaran, dan melaksanakan analisis retrospektif. Siswa mampu membangun pemahaman tentang perbandingan trigonometri selama proses pembelajaran berlangsung. Berdasarkan analisis kualitatif eksperimen pengajaran, penelitian ini berimplikasi pada penguatan Local Instruction Theory (LIT) perbandingan trigonometri dan pengembangan bahan ajar berbasis RME.

Broadband tunable multi-functional polarization converter based on a graphene metasurface

In this paper, a tunable multi-functional polarization converter based on a graphene metasurface has been designed. For the chemical potential of 1 eV, the structure has a polarization conversion ratio higher than 0.9 in the frequency range of 8.08 to 8.29 THz and also in the wide frequency range of 10.28 to 12.56 THz. Therefore, broadband linear to linear polarization conversion has been obtained. Also, in four frequency ranges, linear to circular polarization conversion has been realized. In addition to linear to linear and linear to circular functions, the structure also has circular to linear and circular to circular polarization conversion capabilities. The effects of chemical potential, geometrical parameters, and incident and polarization angles on the polarization conversion performance have been investigated. By changing the chemical potential, the reflected wave switches between different polarizations. Moreover, the results show that polarization conversion is insensitive to the incident angle up to 40°. The physical mechanism and analytical methods of multiple interference theory and equivalent circuit model for the suggested polarization converter have been presented. The presented structure with appropriate features such as different polarization conversions, adjustability, switching capability between different polarizations, broad bandwidth, good incident angle stability, and simple construction has many applications in communication, biological detection, imaging, and sensing.