在永磁直线同步电机(permanent-magnet linear synchr-onous motor,PMLSM)伺服系统中,模型的阶次高,且速度和电流等变量间存在的耦合严重影响速度跟踪的快速性和精度。采用基于奇异摄动理论的对角化方法将永磁直线同步电机伺服系统分解...在永磁直线同步电机(permanent-magnet linear synchr-onous motor,PMLSM)伺服系统中,模型的阶次高,且速度和电流等变量间存在的耦合严重影响速度跟踪的快速性和精度。采用基于奇异摄动理论的对角化方法将永磁直线同步电机伺服系统分解成慢变和快变子系统。为了保证系统的鲁棒性,利用2阶滑模控制的次优算法分别独立设计慢变和快变子系统的控制律,再将2个控制律合成得到永磁直线同步电机的复合控制律。仿真结果表明,所提出的策略具有良好的速度跟踪性能,同时对负载扰动和参数变化具有很强的鲁棒性。展开更多
The singularly perturbed boundary value problem of scalar integro-differential equations has been studied extensively by the differential inequality method . However, it does not seem possible to carry this method ove...The singularly perturbed boundary value problem of scalar integro-differential equations has been studied extensively by the differential inequality method . However, it does not seem possible to carry this method over to a corresponding nonlinear vector integro-differential equation. Therefore , for n-dimensional vector integro-differential equations the problem has not been solved fully. Here, we study this nonlinear vector problem and obtain some results. The approach in this paper is to transform the appropriate integro-differential equations into a canonical or diagonalized system of two first-order equations.展开更多
An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byu...An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byusing SU(2), SU(1,1) Lie algebraic method, respectively. Meanwhile, the eigenstates of the above two models are revealedto be SU(2), SU(1,1) coherent states, respectively. The relation between the usual Bogoliubov Valatin transformationand the algebraic method in a special case is also discussed.展开更多
We present the existence of solution for a coupled system of fractional integro-differential equations. The differential operator is taken in the Caputo fractional sense. We combine the diagonalization method with Arz...We present the existence of solution for a coupled system of fractional integro-differential equations. The differential operator is taken in the Caputo fractional sense. We combine the diagonalization method with Arzela-Ascoli theorem to show a fixed point theorem of Schauder.展开更多
In order to deal with unmodeled dynamics in large vehicle systems, which have an ill condition of the state matrix, the use of model order reduction methods is a good approach. This article presents a new construction...In order to deal with unmodeled dynamics in large vehicle systems, which have an ill condition of the state matrix, the use of model order reduction methods is a good approach. This article presents a new construction of the sliding mode controller for singularly perturbed systems. The controller design is based on a linear diagonal transformation of the singularly perturbed model. Furthermore, the use of a single sliding mode controller designed for the slow component of the diagonalized system is investigated. Simulation results indicate the performance improvement of the proposed controllers.展开更多
The finite temperature Lanczos method(FTLM),which is an exact diagonalization method intensively used in quantum many-body calculations,is formulated in the framework of orthogonal polynomials and Gauss quadrature.The...The finite temperature Lanczos method(FTLM),which is an exact diagonalization method intensively used in quantum many-body calculations,is formulated in the framework of orthogonal polynomials and Gauss quadrature.The main idea is to reduce finite temperature static and dynamic quantities into weighted summations related to one-and twodimensional Gauss quadratures.Then lower order Gauss quadrature,which is generated from Lanczos iteration,can be applied to approximate the initial weighted summation.This framework fills the conceptual gap between FTLM and kernel polynomial method,and makes it easy to apply orthogonal polynomial techniques in the FTLM calculation.展开更多
In this paper the method and technique of the diagonalization are employed to transform a vector second-order nonlinear system into two first-order approximate diagonalized systems. The existence and the asymptotic be...In this paper the method and technique of the diagonalization are employed to transform a vector second-order nonlinear system into two first-order approximate diagonalized systems. The existence and the asymptotic behavior of the solutions are obtained for a vector second-order nonlinear Robin problem of singular perturbation type.展开更多
文摘在永磁直线同步电机(permanent-magnet linear synchr-onous motor,PMLSM)伺服系统中,模型的阶次高,且速度和电流等变量间存在的耦合严重影响速度跟踪的快速性和精度。采用基于奇异摄动理论的对角化方法将永磁直线同步电机伺服系统分解成慢变和快变子系统。为了保证系统的鲁棒性,利用2阶滑模控制的次优算法分别独立设计慢变和快变子系统的控制律,再将2个控制律合成得到永磁直线同步电机的复合控制律。仿真结果表明,所提出的策略具有良好的速度跟踪性能,同时对负载扰动和参数变化具有很强的鲁棒性。
文摘The singularly perturbed boundary value problem of scalar integro-differential equations has been studied extensively by the differential inequality method . However, it does not seem possible to carry this method over to a corresponding nonlinear vector integro-differential equation. Therefore , for n-dimensional vector integro-differential equations the problem has not been solved fully. Here, we study this nonlinear vector problem and obtain some results. The approach in this paper is to transform the appropriate integro-differential equations into a canonical or diagonalized system of two first-order equations.
文摘An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byusing SU(2), SU(1,1) Lie algebraic method, respectively. Meanwhile, the eigenstates of the above two models are revealedto be SU(2), SU(1,1) coherent states, respectively. The relation between the usual Bogoliubov Valatin transformationand the algebraic method in a special case is also discussed.
文摘We present the existence of solution for a coupled system of fractional integro-differential equations. The differential operator is taken in the Caputo fractional sense. We combine the diagonalization method with Arzela-Ascoli theorem to show a fixed point theorem of Schauder.
文摘In order to deal with unmodeled dynamics in large vehicle systems, which have an ill condition of the state matrix, the use of model order reduction methods is a good approach. This article presents a new construction of the sliding mode controller for singularly perturbed systems. The controller design is based on a linear diagonal transformation of the singularly perturbed model. Furthermore, the use of a single sliding mode controller designed for the slow component of the diagonalized system is investigated. Simulation results indicate the performance improvement of the proposed controllers.
基金supported by the National Natural Science Foundation of China(Grant Nos.11734002 and U1930402)。
文摘The finite temperature Lanczos method(FTLM),which is an exact diagonalization method intensively used in quantum many-body calculations,is formulated in the framework of orthogonal polynomials and Gauss quadrature.The main idea is to reduce finite temperature static and dynamic quantities into weighted summations related to one-and twodimensional Gauss quadratures.Then lower order Gauss quadrature,which is generated from Lanczos iteration,can be applied to approximate the initial weighted summation.This framework fills the conceptual gap between FTLM and kernel polynomial method,and makes it easy to apply orthogonal polynomial techniques in the FTLM calculation.
基金Supported by the Natural Science Foundation of China ( The Youth Foundation)(10901068)CCNU Project (CCNU09A01004)the Hubei Key Laboratory of Mathematical Physics
文摘In this paper the method and technique of the diagonalization are employed to transform a vector second-order nonlinear system into two first-order approximate diagonalized systems. The existence and the asymptotic behavior of the solutions are obtained for a vector second-order nonlinear Robin problem of singular perturbation type.
