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hyperbolic function Based DOA Estimator in the Presence of Impulsive Noise

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2025年第3期74卷 5276-5280页

作者： Zhang, Jiacheng Wang, Mengjia Luan, Shengyang Liu, Tao Nanjing Univ Informat Sci & Technol Sch Artificial Intelligence Nanjing 210044 Peoples R China Chengdu Univ Inst Higher Educ Sichuan Prov Key Lab Pattern Recognit & Intelligent Informat Pr Chengdu 610106 Peoples R China Nanjing Univ Informat Sci & Technol Sch Elect & Informat Engn Nanjing 210044 Peoples R China Jiangsu Normal Univ Sch Elect Engn & Automat Xuzhou 221008 Peoples R China

In this paper, a novel method is proposed for direction of arrival (DOA) estimation in the presence of impulsive noise. By introducing the hyperbolic secant function into the framework, a novel DOA estimator is designed. Based on the proposed estimator and low-rank decomposition, a robust subspace is obtained through alternative optimization. DOA estimation is achieved by applying the multiple signal classification (MUSIC) algorithm to the derived subspace. A detailed optimization procedure is outlined, and the convergence of the proposed estimator is proven. Comprehensive simulation results demonstrate that the proposed method could achieve superior performance in impulsive noise environments, especially under strongly impulsive conditions.

关键词： Noise Direction-of-arrival estimation Estimation Sensors Optimization Vectors Matrix decomposition Simulation Sensor arrays Pattern classification DOA estimation impulsive noise hyperbolic function

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Nonlinear PI speed controller based on hyperbolic function and its application in the vector control of an induction motor

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Diangong Jishu Xuebao/Transactions of China Electrotechnical Society 2004年第6期19卷 85-89页

作者： Jiang, Xianglong Zhao, Jin Wan, Shuyun Huazhong Univ. of Sci. and Technol. Wuhan 430074 China

The indirect field-oriented control system of an induction motor is still coupling and nonlinear. It is not satisfied to control the speed of the induction motor based on field-oriented control using conventional PI control. In order to improve the dynamic characteristics of above motor drive, a nonlinear PI type speed controller based on hyperbolic tangent function was presented, and applied in the indirect vector control of an induction motor. According to modal equivalence principle, it is proved that the controller is equivalent to a robust fuzzy logic controller. However, comparing with fuzzy logic control (FLC), the nonlinear controller has some advantages such as simple implementation, no high-frequency quiver. Simulations and experiments results demonstrate good dynamic performance can be achieved based on this nonlinear PI speed controller in the vector control of induction motor.

关键词： FLC hyperbolic function Induction motor Modal equivalence principle

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Approximations for certain hyperbolic functions by partial sums of their Taylor series and completely monotonic functions related to gamma function

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2016年第2期441卷 549-564页

作者： Yang, Zhen-Hang ZPEPC Elect Power Res Inst Power Supply Serv Ctr Hangzhou 310009 Zhejiang Peoples R China

In this paper, we establish some lower and upper bounds for certain hyperbolic functions in terms of partial sums of their Taylor series. These allow us to present two completely monotonic functions involving gamma function. As consequences, sharp Burnside type approximations for gamma function, sharp Detemple-Wang type approximations for psi function, and sharp bounds for polygamma functions are deduced, which generalize and improve some known results. (c) 2016 Elsevier Inc. All rights reserved.

关键词： hyperbolic function Bernoulli number Gamma function Psi function Complete monotonicity

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Asymptotic expansions for the gamma function in terms of hyperbolic functions

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2019年第1期478卷 133-155页

作者： Yang, Zhenhang Tian, Jing-Feng North China Elect Power Univ Coll Sci & Technol Baoding 071051 Hebei Peoples R China

The Smith's approximation formula for the gamma function is given by Gamma(x+1/2)=root 2 pi(x/e)(x) (2xtanh 1/2x)(x/2) (1 +O (1/x(5))), as x -> infinity. In this paper, by means of a little known power series, we develop this formula to an asymptotic expansions: Gamma(x+1/2)/root 2 pi(x/e)(x) similar to(2x tanh1/2x)(x/2) exp (Sigma(n=3) [(2n)!-(2n-1)2(2n-1)](1-2(1-2n))/2n(2n-1)(2n)!) B-2n/x(2n-1));as x -> infinity, and give an estimate of remainder in the above asymptotic series, where B2, is the Bernoulli number. Moreover, as relevant results, *** type asymptotic expansions for the gamma function F (x 1/2) are obtained;an asymptotic expansion for Wallis ratio and an estimate of the remainder are established. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Gamma function hyperbolic function Asymptotic expansion Inequalities

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Robust Position Control of VTOL UAVs Using a Linear Quadratic Rate-Varying Integral Tracker: Design and Validation

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DRONES 2025年第1期9卷 73-73页

作者： Saleem, Omer Kazim, Muhammad Iqbal, Jamshed Natl Univ Comp & Emerging Sci Dept Elect Engn Lahore 54770 Pakistan Khalifa Univ Ctr Robot & Autonomous Syst Abu Dhabi 127788 U Arab Emirates Univ Hull Fac Sci & Engn Sch Comp Sci Kingston Upon Hull HU6 7RX England

This article presents an optimal tracking controller retrofitted with a nonlinear adaptive integral compensator, specifically designed to ensure robust and accurate positioning of Vertical Take-Off and Landing (VTOL) Unmanned Aerial Vehicles (UAVs) that utilize contra-rotating motorized propellers for differential thrust generation. The baseline position controller is synthesized by employing a fixed-gain Linear Quadratic Integral (LQI) tracking controller that stabilizes position by tracking both state variations and pitch-axis tracking error integral, which adjusts the voltage to control each coaxial propeller's speed accurately. Additionally, the baseline tracking control law is supplemented with a rate-varying integral compensator. It operates as a nonlinear scaling function of the tracking-error velocity and the braking acceleration to enhance the accuracy of reference tracking without sacrificing its robustness against exogenous disruptions. The controller's performance is analyzed by performing experiments on a tailored hardware-in-the-loop aero-pendulum testbed, which is representative of VTOL UAV dynamics. Experimental results demonstrate significant improvements over the nominal LQI tracking controller, achieving 17.9%, 61.6%, 83.4%, 43.7%, 35.8%, and 6.8% enhancement in root mean squared error, settling time, overshoot during start-up, overshoot under impulsive disturbance, disturbance recovery time, and control energy expenditure, respectively, underscoring the controller's effectiveness for potential UAV and drone applications under exogenous disturbances.

关键词： VTOL UAVs position tracking linear quadratic integral control rate-varying integral compensator hyperbolic function hardware-in-the-loop validation

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Design of a Global Sliding Mode Controller Using hyperbolic functions for Nonlinear Systems and Application in Chaotic Systems 27

Design of a Global Sliding Mode Controller Using Hyperbolic ...

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27th Iranian Conference on Electrical Engineering (ICEE)

作者： Barhaghtalab, Mojtaba Hadi Mobayen, Saleh Merrikh-Bayat, Farshad Univ Zanjan Fac Engn Dept Elect Engn Zanjan Iran

ISBN: (纸本)9781728115085

In this research, an LMI-based global sliding mode controller law with a novel switching function for the sliding surface using hyperbolic functions is presented and is used for stabilization and robustness of three-dimensional nonlinear systems with uncertainty. The asymptotic stability of the system's state variables is guaranteed by Linear Matrix Inequality (LMI) and furthermore, considering the uncertainty and nonlinear terms, the reaching phase of the sliding surface is deleted. Finally, the proposed control technique is implemented on Genesio-Tesi chaotic system and the results of the simulation are analyzed.

关键词： Global sliding mode non-linear system chaotic system hyperbolic function linear matrix inequality

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Lazarević and Cusa type inequalities for hyperbolic functions with two parameters and their applications

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Journal of Inequalities and Applications 2015年第1期2015卷 1-19页

作者： Yang, Zhen-Hang Chu, Yu-Ming School of Mathematics and Computation Sciences Hunan City University Yiyang 413000 China Department of Mathematics Huzhou University Huzhou 313000 China

In the article, we establish several Lazarević and Cusa type inequalities involving the hyperbolic sine and cosine functions with two parameters. As applications, we find some new bounds for certain bivariate means. &... 详细信息

关键词： Cusa type inequality hyperbolic function Lazarević inequality Schwab-Borchardt mean

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Circuit Model Analysis of General Charge-controlled MemristorBased on hyperbolic functions br

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JOURNAL OF ELECTRONICS & INFORMATION TECHNOLOGY 2023年第2期45卷 725-733页

作者： Sun, Junwei Yang, Jianlin Liu, Peng Wang, Yanfeng Zhengzhou Univ Light Ind Inst Elect & Informat Engn Zhengzhou 450000 Peoples R China

At present, most of the researches on the memristor simulators are flux-controlled, there are fewresearches on the charge-controlled memristor simulator, and the hyperbolic function simulator is seldommentioned. Therefore, a general-purpose simulator of charge-controlled memristor based on hyperbolic functionis proposed. The simulator realizes the conversion between voltage and current signals in the circuit throughthe voltage-current mutual conversion circuit, and calculates the generated signals through the correspondingmodule in the circuit, and finally obtains the universal hyperbolic charge-controlled memristor model. Thesimulator can realize the charge-controlled memristor corresponding to hyperbolic sine, hyperbolic cosine andhyperbolic tangent function. The equivalent circuit of the general-purpose hyperbolic function charge-controlledmemristor simulator is mainly composed of operational amplifier, resistor, capacitor, triode and other basiccomponents. By analyzing the volt-ampere characteristic curves of the simulator at different amplitudes anddifferent frequencies, it is concluded that the simulator conforms to the basic characteristics of memory *** model of hyperbolic charge-controlled memristor presented in this paper has a certain reference significancefor the development of memristor model.

关键词： Charge-controlled memristor Circuit model hyperbolic function Volt-ampere characteristic curve

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Some Evaluation of Infinite Series Involving Trigonometric and hyperbolic functions

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RESULTS IN MATHEMATICS 2018年第4期73卷 128-128页

作者： Xu, Ce Xiamen Univ Sch Math Sci Xiamen 361005 Peoples R China

In this paper, by using the residue theorem and asymptotic formulas of trigonometric and hyperbolic functions at the poles, we establish many relations involving two or more infinite series of trigonometric and hyperbolic functions. In particular, we evaluate in closed form certain classes of infinite series containing hyperbolic functions, which are related to Gamma functions and power of pi. Moreover, some interesting new consequences and illustrative examples are considered.

关键词： Infinite series hyperbolic function trigonometric function Riemann zeta function Gamma function residue theorem

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Establishment, maintenance, and re-establishment of the safe and efficient steady-following state

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Chinese Physics B 2015年第8期24卷 651-657页

作者：潘登郑应平 School of Electronic and Information Engineering Tongji University

We present an integrated mathematical model of vehicle-following control for the establishment, maintenance, and re-establishment of the previous or new safe and efficient steady-following state. The hyperbolic functions are introduced to establish the corresponding mathematical models, which can describe the behavioral adjustment of the following vehicle steered by a well-experienced driver under complex vehicle following situations. According to the proposed mathematical models, the control laws of the following vehicle adjusting its own behavior can be calculated for its moving in safety,efficiency, and smoothness(comfort). Simulation results show that the safe and efficient steady-following state can be well established, maintained, and re-established by its own smooth(comfortable) behavioral adjustment with the synchronous control of the following vehicle’s velocity, acceleration, and the actual following distance.

关键词： vehicle following system safe following distance hyperbolic function vehicle following control steady-following state

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