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Design and Implementation of Digital Fractional Order PID Controller Using Optimal Pole-Zero Approximation Method for Magnetic Levitation System 认领 引用 被引量：6
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作者 Amit S.Chopade Swapnil W.Khubalkar +2 位作者 A.S.Junghare M.V.Aware Shantanu Das 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2018年第5期977-989,共13页
The aim of this paper is to employ fractional order proportional integral derivative(FO-PID)controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system(M... The aim of this paper is to employ fractional order proportional integral derivative(FO-PID)controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system(MLS),which is inherently nonlinear and unstable system.The proposal is to deploy discrete optimal pole-zero approximation method for realization of digital fractional order controller.An approach of phase shaping by slope cancellation of asymptotic phase plots for zeros and poles within given bandwidth is explored.The controller parameters are tuned using dynamic particle swarm optimization(d PSO)technique.Effectiveness of the proposed control scheme is verified by simulation and experimental results.The performance of realized digital FO-PID controller has been compared with that of the integer order PID controllers.It is observed that effort required in fractional order control is smaller as compared with its integer counterpart for obtaining the same system performance. 展开更多
关键词 Approximation methods digital control dis-cretization fractional calculus fractional order PID controller(FO-PID) magnetic levitation particle swarm optimization(PSO) position control.
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A generalized Padé approximation method of solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators 认领 引用 被引量：1
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作者 李震波 唐驾时 蔡萍 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第12期78-84,共7页
An intrinsic extension of Pad′e approximation method, called the generalized Pad′e approximation method, is proposed based on the classic Pad′e approximation theorem. According to the proposed method, the numerator... An intrinsic extension of Pad′e approximation method, called the generalized Pad′e approximation method, is proposed based on the classic Pad′e approximation theorem. According to the proposed method, the numerator and denominator of Pad′e approximant are extended from polynomial functions to a series composed of any kind of function, which means that the generalized Pad′e approximant is not limited to some forms, but can be constructed in different forms in solving different problems. Thus, many existing modifications of Pad′e approximation method can be considered to be the special cases of the proposed method. For solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators, two novel kinds of generalized Pad′e approximants are constructed. Then, some examples are given to show the validity of the present method. To show the accuracy of the method, all solutions obtained in this paper are compared with those of the Runge–Kutta method. 展开更多
关键词 generalized Pad′e approximation method homoclinic and heteroclinic orbits strongly nonlinear oscillators
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Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings 认领 引用 被引量：2
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作者 WANG Ya-qin 《Journal of Zhejiang University-SCIENCE A》 SCIE EI CAS 2007年第10期1691-1694,共4页
Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K ... Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K be the unique fixed point of the weak contraction x1→tf（x）＋（1-t）Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^＊, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in （Xu, 2004）. 展开更多
关键词 Viscosity approximation methods Weakly contractive mapping Fixed point Weakly sequentially continuous duality mapping
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Range of applicability of real mode superposition approximation method for seismic response calculation of non-classically damped industrial buildings 认领 引用
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作者 Li Xiaodong Sun Hongyang +2 位作者 Ji Xiaodong Sanjukta Chakraborty Wang Lijun 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2022年第2期475-488,共14页
An industrial building is a non-classically damped system due to the different damping properties of the primary structure and equipment.The objective of this paper is to quantify the range of applicability of the rea... An industrial building is a non-classically damped system due to the different damping properties of the primary structure and equipment.The objective of this paper is to quantify the range of applicability of the real model superposition approximation method to the seismic response calculation of industrial buildings.The analysis using lumped mass-and-shear spring models indicates that for the equipment-to-structure frequency ratiosγf>1.1 orγf0.07.Furthermore,extensive parametric analyses are conducted,where both steel structures and reinforced concrete structures with equipment with various damping ratios are considered.Finally,the finite element analysis of a five-story industrial building is adopted to validate the proposed range of applicability. 展开更多
关键词 non-classical damping structure-equipment interaction real mode superposition approximation method complex mode superposition method seismic response calculation
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AN APPLICABLE APPROXIMATION METHOD AND ITS APPLICATION 认领 引用
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作者 曹怀信 陈峥立 +1 位作者 李莉 余保民 《Acta Mathematica Scientia》 SCIE CSCD 2015年第5期1189-1202,共14页
In this work, by choosing an orthonormal basis for the Hilbert space L^2[0, 1], an approximation method for finding approximate solutions of the equation （I ＋ K）x = y is proposed, called Haar wavelet approximation ... In this work, by choosing an orthonormal basis for the Hilbert space L^2[0, 1], an approximation method for finding approximate solutions of the equation （I ＋ K）x = y is proposed, called Haar wavelet approximation method （HWAM）. To prove the applicabifity of the HWAM, a more general applicability theorem on an approximation method （AM） for an operator equation Ax = y is proved first. As an application, applicability of the HWAM is obtained. Fhrthermore, four steps to use the HWAM are listed and three numerical examples are given in order to illustrate the effectiveness of the method. 展开更多
关键词 Hilbert space applicability Haar wavelet approximation method operatorequation
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Investigation of multiple metal nanoparticles near-field coupling on the surface by discrete dipole approximation method 认领 引用 被引量：1
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作者 Yin Ping Lin Qiang +1 位作者 Ruan Yi Chen Jing-jing 《Optoelectronics Letters》 EI 2021年第5期257-261,共5页
We use the method of discrete dipole approximation with surface interaction to construct a model in which a plurality of nanoparticles is arranged on the surface of BK7 glass. Nanoparticles are in air medium illuminat... We use the method of discrete dipole approximation with surface interaction to construct a model in which a plurality of nanoparticles is arranged on the surface of BK7 glass. Nanoparticles are in air medium illuminated by evanescent wave generated from total internal reflection. The effects of the wavelength, the polarization of the incident wave, the number of nanoparticles and the spacing of multiple nanoparticles on the field enhancement and extinction efficiency are calculated by our model. Our work could pave the way to improve the field enhancement of multiple nanoparticles systems. 展开更多
关键词 Investigation of multiple metal nanoparticles near-field coupling on the surface by discrete dipole approximation method
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AN APPROXIMATION METHOD TO ESTIMATE THE HAUSDORFF MEASURE OF THE SIERPINSKI GASKET 认领 引用 被引量：1
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作者 RuanHuojun SuWeiyi 《Analysis in Theory and Applications》 2004年第2期158-166,共9页
In this paper, we firstly define a decreasing sequence {Pn(S)} by the generation of the Sierpinski gasket where each Pn(S) can be obtained in finite steps. Then we prove that the Hausdorff measure Hs(S) of the Sierpin... In this paper, we firstly define a decreasing sequence {Pn(S)} by the generation of the Sierpinski gasket where each Pn(S) can be obtained in finite steps. Then we prove that the Hausdorff measure Hs(S) of the Sierpinski gasket S can be approximated by {Pn(S)} with Pn(S)/(l + l/2n-3)s≤Hs(S)≤ Pn(S). An algorithm is presented to get Pn(S) for n ≤5. As an application, we obtain the best lower bound of Hs(S) till now: Hs(S)≥0.5631. 展开更多
关键词 Hausdorff measure sierpinski gasket approximation method
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LOCAL SALINE APPROXIMATION METHODS FOR SINGULAR PRODUCT INTEGRATION 认领 引用 被引量：1
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作者 C. Dagnino V. Demichelis E. Santi 《Analysis in Theory and Applications》 1996年第3期37-51,共15页
The purpose of this paper is to propose and study local spline approximation methods for singular product integration,for which;i)the precision degree is the highest possible using splint approximation; ii) the nodes ... The purpose of this paper is to propose and study local spline approximation methods for singular product integration,for which;i)the precision degree is the highest possible using splint approximation; ii) the nodes fan be assumed equal to arbitrary points,where the integrand function f is known; iii) the number of the requested evaluations of f at the nodes is low,iv) a satisfactory convergence theory can be proved. 展开更多
关键词 LOCAL SALINE APPROXIMATION METHODS FOR SINGULAR PRODUCT INTEGRATION
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The New Viscosity Approximation Methods for Nonexpansive Nonself-Mappings 认领 引用
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作者 Chao Liu Meimei Song 《International Journal of Modern Nonlinear Theory and Application》 2016年第2期104-113,共10页
In this paper, to find the fixed points of the nonexpansive nonself-mappings, we introduced two new viscosity approximation methods, and then we prove the iterative sequences defined by above viscosity approximation m... In this paper, to find the fixed points of the nonexpansive nonself-mappings, we introduced two new viscosity approximation methods, and then we prove the iterative sequences defined by above viscosity approximation methods which converge strongly to the fixed points of nonexpansive nonself-mappings. The results presented in this paper extend and improve the results of Song-Chen [1] and Song-Li [2]. 展开更多
关键词 Fixed Points Nonexpansive Nonself-Mappings Viscosity Approximation Methods Real Banach Space
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SAMPLE AVERAGE APPROXIMATION METHOD FOR A CLASS OF STOCHASTIC VARIATIONAL INEQUALITY PROBLEMS 认领 引用 被引量：8
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作者 Mingzheng WANG Guihua LIN +1 位作者 Yuli GAO M.Montaz ALI 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2011年第6期1143-1153,共11页
This paper considers a class of stochastic variational inequality problems.As proposed by Jiang and Xu(2008),by using the so-called regularized gap function,the authors formulate the problems as constrained optimizati... This paper considers a class of stochastic variational inequality problems.As proposed by Jiang and Xu(2008),by using the so-called regularized gap function,the authors formulate the problems as constrained optimization problems and then propose a sample average approximation method for solving the problems.Under some moderate conditions,the authors investigate the limiting behavior of the optimal values and the optimal solutions of the approximation problems.Finally,some numerical results are reported to show efficiency of the proposed method. 展开更多
关键词 Convergence gap function sample average approximation method stochastic variational inequality.
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Algebraic Independence by Approximation Method(Ⅱ) 认领 引用 被引量：1
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作者 Yaochen Zhu Institute of Applied Mathematics,Academy of Mathematics and Systems Sciences,Academia Sinica,Beijing 100080,P.R.China Fax:010-62541689 《Acta Mathematica Sinica,English Series》 SCIE 2000年第3期395-398,共4页
Let f（x）be a continued fraction with elements anx,where coefficients an are positive alge- braic numbers.Using the criterion of[1]for any nonzero real algebraic numbers α1,...,αs with distinct absolute values the ... Let f（x）be a continued fraction with elements anx,where coefficients an are positive alge- braic numbers.Using the criterion of[1]for any nonzero real algebraic numbers α1,...,αs with distinct absolute values the algebraic independence of the values f（α1）,...,f（αs）is proved under certain as- sumption concerning only with an.For some transcendental numbers ζ the algebraic independence of values f（ζj）（j∈Z）is also established. 展开更多
关键词 Algebraic independence Continued fraction Approximation method
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High-precision shape approximation low-thrust trajectory optimization method satisfying bi-objective index 认领 引用 被引量：2
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作者 Ruiye JIANG Ming YANG +2 位作者 Songyan WANG Tao CHAO Rajan SHANKARAN 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2022年第1期436-457,共22页
The shape approximation method has been proven to be rapid and practicable in resolving low-thrust trajectory;however,it still faces the challenges of large deviation from the optimal solution and inability to satisfy... The shape approximation method has been proven to be rapid and practicable in resolving low-thrust trajectory;however,it still faces the challenges of large deviation from the optimal solution and inability to satisfy the specific flight time and fuel mass constraints.In this paper,a modified shape approximation low-thrust model is presented,and a novel constrained optimization algorithm is developed to solve this problem.The proposed method aims at settling the bi-objective optimization orbit involving the twin objectives of minimum flight time and low fuel consumption and enhancing the accuracy of optimized orbit.In particular,a transformed high-order polynomial model based on finite Fourier series is proposed,which can be characterized as a multi-constraint optimization problem.Then,a novel optimization algorithm is specifically developed to optimize the large-scale multi-constraint dynamical equations of shape trajectory.The key performance indicators of the index include minimum flight time,low fuel consumption and bi-objective optimization of the two.Simulation results prove that this approach possesses both the high precision achievable by numerical methods and low computational complexity offered by shape approximation techniques.Besides,the Pareto front of the fuel-time bi-objective optimization orbit is firstly introduced to analyze an intact optimal solution set.Furthermore,we have demonstrated that our proposed approach is appropriate to generate the preliminary orbit for pseudo-spectral method. 展开更多
关键词 Constrained optimization Intelligent optimization Low-thrust trajectory Multi-objective optimization Shape approximation method
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A comparison between filtering approach and spline approximation method in smoothing flight data 认领 引用
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作者 O.N.Korsun Sekou Goro M.H.Om 《Aerospace Systems》 2023年第3期473-480,共8页
Onboard measurement system,the function of which is to collect,record and process measurement information,performs these tasks by obtaining information from the sensors.However,the sensors are noisy,so it is necessary... Onboard measurement system,the function of which is to collect,record and process measurement information,performs these tasks by obtaining information from the sensors.However,the sensors are noisy,so it is necessary to combine multiple pieces of information to give a good accuracy to the signals provided by the onboard measurement system.The extended Kalman filter,which is one of the most widely used data fusion methods,is also one of the derivatives of the standard Kalman filter used for non-linear problems.On the other hand,the spline approximation,especially the cubic and Hermitian splines provide a very good and smooth estimate.It is known that the implementation of spline method is simpler than Kalman filtering.This paper describes an empirical comparative analysis of the extended Kalman filter and spline method.The impressive result is that a simple spline approximation in many cases performs better than a sophisticated Kalman filter. 展开更多
关键词 Kalman filter Extended Kalman filter Spline approximation method Flight data Smoothing of signals Nonlinear filtering
Algebraic Independence by Approximation Method 认领 引用 被引量：4
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作者 Zhu Yaochen Institute of Applied Mathematics, Academia Sinica, Beijing 100080, China 《Acta Mathematica Sinica,English Series》 SCIE 1998年第3期295-302,共8页
By the use of approximation method a general criterion of algebraic independence of complex numbers is established. As its application the algebraic independence of values of certain gap series at algebraic and transc... By the use of approximation method a general criterion of algebraic independence of complex numbers is established. As its application the algebraic independence of values of certain gap series at algebraic and transcendental points is given. 展开更多
关键词 Algebraic independence Approximation method Gap series
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Viscosity Approximation Methods for Equilibrium Problems in Hilbert Spaces Involving the New Iterative Process with Error 认领 引用 被引量：4
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作者 RAO Ruo Feng ZHANG Shi Sheng 《Journal of Mathematical Research and Exposition》 2009年第3期535-543,共9页
In this paper, we introduce an iterative scheme with error by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpan... In this paper, we introduce an iterative scheme with error by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. A strong convergence theorem is given, which generalizes all the results obtained by S.Takahashi and W.Takahashi in 2007. In addition, some of the methods applied in this paper improve those of S.Takahashi and W.Takahashi. 展开更多
关键词 viscosity approximation method equilibrium problem nonexpansive mapping
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Strong Approximation Method and the(Functional)Law of Iterated Logarithm for GI/G/1 Queue 认领 引用 被引量：2
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作者 GUO Yongjiang HOU Xiyang 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2017年第5期1097-1106,共10页
In this paper, a unified method based on the strong approximation(SA) of renewal process(RP) is developed for the law of the iterated logarithm(LIL) and the functional LIL(FLIL), which quantify the magnitude of the as... In this paper, a unified method based on the strong approximation(SA) of renewal process(RP) is developed for the law of the iterated logarithm(LIL) and the functional LIL(FLIL), which quantify the magnitude of the asymptotic rate of the increasing variability around the mean value of the RP in numerical and functional forms respectively. For the GI/G/1 queue, the method provides a complete analysis for both the LIL and the FLIL limits for four performance functions: The queue length, workload, busy time and idle time processes, covering three regimes divided by the traffic intensity. 展开更多
关键词 GI/G/1 queue renewal process （RP） strong approximation （SA） method the functional LIL （FLIL） the law of the iterated logarithm （LIL）
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PROJECTION METHODS AND APPROXIMATIONS FOR ORDINARY DIFFERENTIAL EQUATIONS 认领 引用 被引量：1
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作者 A. Bensebah F. Dubeau J. Gelinas 《Analysis in Theory and Applications》 1997年第3期78-90,共13页
A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in th... A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in the L2 norm and nodal supercnnvergence. These results generalize those obtained earlier by Hulme for continuous piecevjise polynomials and by Delfour-Dubeau for discontinuous pieceuiise polynomials. A duality relationship for the two types of approximations is also given. 展开更多
关键词 PROJECTION METHODS AND APPROXIMATIONS FOR ORDINARY DIFFERENTIAL EQUATIONS ODE
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A NEW ITERATIVE METHOD FOR FINDING COMMON SOLUTIONS OF GENERALIZED EQUILIBRIUM PROBLEM,FIXED POINT PROBLEM OF INFINITE k-STRICT PSEUDO-CONTRACTIVE MAPPINGS,AND QUASI-VARIATIONAL INCLUSION PROBLEM 认领 引用 被引量：5
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作者 刘敏 张石生 《Acta Mathematica Scientia》 SCIE CSCD 2012年第2期499-519,共21页
In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseu... In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12]. 展开更多
关键词 k-strict pseudo-contractive mappings generalized equilibrium problem vis-cosity approximation method variational inclusion problem multi-valuedmaximal monotone mappings s-inverse-strongly monotone mapping
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THE CONVERGENCE OF APPROACH PENALTY FUNCTION METHOD FOR APPROXIMATE BILEVEL PROGRAMMING PROBLEM 认领 引用 被引量：2
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作者 万仲平 周树民 《Acta Mathematica Scientia》 SCIE 2001年第1期69-76,共8页
In this paper, a new algorithm-approximate penalty function method is designed, which can be used to solve a bilevel optimization problem with linear constrained function. In this kind of bilevel optimization problem.... In this paper, a new algorithm-approximate penalty function method is designed, which can be used to solve a bilevel optimization problem with linear constrained function. In this kind of bilevel optimization problem. the evaluation of the objective function is very difficult, so that only their approximate values can be obtained. This algorithm is obtained by combining penalty function method and approximation in bilevel programming. The presented algorithm is completely different from existing methods. That convergence for this algorithm is proved. 展开更多
关键词 bilevel programming approximation method penalty function method convergence
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Improved response surface method based on sample point selection strategies 认领 引用
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作者 李炜 康海贵 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2010年第6期756-760,共5页
In the reliability analysis of complex structures,response surface method(RSM)has been suggested as an efficient technique to estimate the actual but implicit limit state function.A set of sample points are needed to ... In the reliability analysis of complex structures,response surface method(RSM)has been suggested as an efficient technique to estimate the actual but implicit limit state function.A set of sample points are needed to fit to the implicit function.It has been noted that the accuracy of RSM depends highly on the so-called sample points.However,the technique for point selection has had little attention.In the present study,an improved response surface method(IRSM)based on two sample point selection techniques,named the direction cosines projected strategy(DCS)and the limit step length iteration strategy(LSS),is investigated.Since it uses the sampling points selected to be located in the region close to the original failure surface,and since it needs only one response surface,the IRSM should be accurate and simple in practical structural problems.Applications to several typical examples have helped to elucidate the successful working of the IRSM. 展开更多
关键词 sample points linear approximation method RSM reliability
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