Orbital angular momentum(OAM),emerging as an inherently high-dimensional property of photons,has boosted information capacity in optical communications.However,the potential of OAM in optical computing remains almost ...Orbital angular momentum(OAM),emerging as an inherently high-dimensional property of photons,has boosted information capacity in optical communications.However,the potential of OAM in optical computing remains almost unexplored.Here,we present a highly efficient optical computing protocol for complex vector convolution with the superposition of high-dimensional OAM eigenmodes.We used two cascaded spatial light modulators to prepare suitable OAM superpositions to encode two complex vectors.Then,a deep-learning strategy is devised to decode the complex OAM spectrum,thus accomplishing the optical convolution task.In our experiment,we succeed in demonstrating 7-,9-,and 11-dimensional complex vector convolutions,in which an average proximity better than 95%and a mean relative error<6%are achieved.Our present scheme can be extended to incorporate other degrees of freedom for a more versatile optical computing in the high-dimensional Hilbert space.展开更多
In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder...In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder inequality,and the Minkowski inequality in the setting of dual complex numbers.Second,we define the p-norm of a dual complex vector,which is a nonnegative dual number,and show some related properties.Third,we study the properties of eigenvalues of unitary matrices and unitary triangulation of arbitrary dual complex matrices.In particular,we introduce the operator norm of dual complex matrices induced by the p-norm of dual complex vectors,and give expressions of three important operator norms of dual complex matrices.展开更多
New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations a...New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations and provide all Jordan basesby which the Jordan canonical form is constructed. Accordingly, they can result in thecelebrated Jordan theorem and the third decomposition theorem of space directly. and,moreover, they can give a new deep insight into the exquisite and subtle structure ofthe Jordan form. The latter indicates that the Jordan canonical form of a complexlinear transformation is an invariant structure associated with double arbitrary. choices.展开更多
Properties of the current controller are essential for permanent magnet synchronous machine(PMSM)drives,but the conventional continuous-time current controller cannot fully decouple the cross-coupling terms when appli...Properties of the current controller are essential for permanent magnet synchronous machine(PMSM)drives,but the conventional continuous-time current controller cannot fully decouple the cross-coupling terms when applied in the digital processor.Its performance is related closely to the rotational speed.To improve the performance of the current loop,the direct design method in the discrete-time domain is adopted using the accurate discrete-time complex vector model.An integrated accurate hold-equivalent discrete model for PMSM is derived considering the difference between the output of the voltage source inverter and the back electro-motive force.Then an accurate two-degree-of-freedom(2DOF)current controller with a third-order closed-loop transfer function is designed.The 2DOF controller has more freedom in pole placement,and two schemes with a different cancelled pole-zero pair are investigated.Analysis is conducted by the robust root locus method via the complex vector root locus and sensitivity functions,showing properties in disturbance rejection and sensitivity to parameter variation of two schemes.Both schemes have their own advantages.Finally,the dynamic performance and flexibility of the proposed current controller is verified on a 2.5-kW PMSM test bench.展开更多
By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at t...By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at the eigenfrequencies of the corresponding interior problems is proposed. By adding appropriate damp to the virtual source system of the wave superposition method, the unique solutions for all wave numbers can be ensured. Based on this thought, a novel method-wave superposition method with complex radius vector is constructed. Not only is the computational time of this method approximately equal to that of the standard wave superposition method, but also the accuracy is much higher compared with other correlative methods. Finally, by taking the pulsating sphere and oscillating sphere as examples, the results of calculation show that the present method can effectively overcome the non-uniqueness problem.展开更多
The mobility of the vectored thruster AUV in different environment is the important premise of control system design. The new type of autonomous underwater vehicle (AUV) equipped with rudders and vectored thrusters wh...The mobility of the vectored thruster AUV in different environment is the important premise of control system design. The new type of autonomous underwater vehicle (AUV) equipped with rudders and vectored thrusters which are combined to control the course is studied. Firstly, Euler angles representation and quaternion method are applied to establish six-DOF kinematic model respectively, then Newton second law and Lagrangian approach are used to deduce the vectored thruster AUV’s nonlinear dynamic equations with six degrees of freedom (DOF) respectively in complex sea conditions based on the random wave theory according to the structural and kinetic characteristics of the vectored thruster AUV in this paper. The kinematic models and dynamic models based on different theories have the same expression and conclusion, which shows that the kinematic models and dynamic models of the vectored thruster AUV are accurate. The Runge-Kutta arithmetic is used to solve the dynamic equations, which not only can simulate the motions such as cruise and hover but also can describe the vehicle’s low-frequency and high-frequency motion. The results of computation show that the mobility of the vectored thruster AUV in interference-free environment and the integrated signals including low-frequency motion signal and high-frequency motion signal in environmental disturbance accord with practical situation, which not only solve the problem of especial singularities when the pitch angle θ = ±90° but also clears up the difficulties of computation and display of the coupled nonlinear motion equations in complex sea conditions. Moreover, the high maneuverability of the vectored thruster AUV equipped with rudders and vectored thrusters is validated, which lays a foundation for the control system design.展开更多
This paper provides derivation of some basic identities for complex four-component vectors defined in a complex four-dimensional spacetime frame specified by an imaginary temporal axis. The resulting four-vector ident...This paper provides derivation of some basic identities for complex four-component vectors defined in a complex four-dimensional spacetime frame specified by an imaginary temporal axis. The resulting four-vector identities take exactly the same forms of the standard vector identities established in the familiar three-dimensional space, thereby confirming the consistency of the definition of the complex four-vectors and their mathematical operations in the general complex spacetime frame. Contravariant and covariant forms have been defined, providing appropriate definitions of complex tensors, which point to the possibility of reformulating differential geometry within a spacetime frame.展开更多
The electromagnetic scattering computation has developed rapidly for many years; some computing problems for complex and coated targets cannot be solved by using the existing theory and computing models. A computing m...The electromagnetic scattering computation has developed rapidly for many years; some computing problems for complex and coated targets cannot be solved by using the existing theory and computing models. A computing model based on data is established for making up the insufficiency of theoretic models. Based on the ＂support vector regression method＂, which is formulated on the principle of minimizing a structural risk, a data model to predicate the unknown radar cross section of some appointed targets is given. Comparison between the actual data and the results of this predicting model based on support vector regression method proved that the support vector regression method is workable and with a comparative precision.展开更多
The dual three-phase PMSM(DTP-PMSM)drives have received wide attention at high-power high-efficiency applications due to their merits of high output current ability and copper-loss-free field excitation.Meanwhile,the ...The dual three-phase PMSM(DTP-PMSM)drives have received wide attention at high-power high-efficiency applications due to their merits of high output current ability and copper-loss-free field excitation.Meanwhile,the DTPPMSM drive provides higher fault-tolerant capability for highreliability applications,e.g.,pumps and actuators in aircraft.For high-power drives with limited switching frequencies and highspeed drives with large fundamental frequencies,the ratio of switching frequency to fundamental frequency,i.e.,the carrier ratio,is usually below 15,which would significantly degrade the control performance.The purpose of this paper is to review the recent work on the modulation and control schemes for improving the operation performance of DTP-PMSM drives with low carrier ratios.Specifically,three categories of methods,i.e.,the space vector modulation based control,the model predictive control(MPC),and the optimized pulse pattern(OPP)based control are reviewed with principles and performance.In addition,brief discussions regarding the comparison and future trends are presented for low-carrier-ratio(LCR)modulation and control schemes of DTP-PMSM drives.展开更多
Nowadays, power quality issues are becoming a significant research topic because of the increasing inclusion of very sensitive devices and considerable renewable energy sources. In general, most of the previous power ...Nowadays, power quality issues are becoming a significant research topic because of the increasing inclusion of very sensitive devices and considerable renewable energy sources. In general, most of the previous power quality classification techniques focused on single power quality events and did not include an optimal feature selection process. This paper presents a classification system that employs Wavelet Transform and the RMS profile to extract the main features of the measured waveforms containing either single or complex disturbances. A data mining process is designed to select the optimal set of features that better describes each disturbance present in the waveform. Support Vector Machine binary classifiers organized in a “One Vs Rest” architecture are individually optimized to classify single and complex disturbances. The parameters that rule the performance of each binary classifier are also individually adjusted using a grid search algorithm that helps them achieve optimal performance. This specialized process significantly improves the total classification accuracy. Several single and complex disturbances were simulated in order to train and test the algorithm. The results show that the classifier is capable of identifying >99% of single disturbances and >97% of complex disturbances.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12034016,61975169,and 11904303)the Youth Innovation Fund of Xiamen(Grant No.3502Z20206045)+2 种基金the Fundamental Research Funds for the Central Universities at Xiamen University(Grant Nos.20720200074 and 20720220030)the Natural Science Foundation of Fujian Province of China(Grant No.2021J02002)and for Distinguished Young Scientists(Grant No.2015J06002)the Program for New Century Excellent Talents in University of China(Grant No.NCET-13-0495).
文摘Orbital angular momentum(OAM),emerging as an inherently high-dimensional property of photons,has boosted information capacity in optical communications.However,the potential of OAM in optical computing remains almost unexplored.Here,we present a highly efficient optical computing protocol for complex vector convolution with the superposition of high-dimensional OAM eigenmodes.We used two cascaded spatial light modulators to prepare suitable OAM superpositions to encode two complex vectors.Then,a deep-learning strategy is devised to decode the complex OAM spectrum,thus accomplishing the optical convolution task.In our experiment,we succeed in demonstrating 7-,9-,and 11-dimensional complex vector convolutions,in which an average proximity better than 95%and a mean relative error<6%are achieved.Our present scheme can be extended to incorporate other degrees of freedom for a more versatile optical computing in the high-dimensional Hilbert space.
基金the National Natural Science Foundation of China(Grant No.11871051).
文摘In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder inequality,and the Minkowski inequality in the setting of dual complex numbers.Second,we define the p-norm of a dual complex vector,which is a nonnegative dual number,and show some related properties.Third,we study the properties of eigenvalues of unitary matrices and unitary triangulation of arbitrary dual complex matrices.In particular,we introduce the operator norm of dual complex matrices induced by the p-norm of dual complex vectors,and give expressions of three important operator norms of dual complex matrices.
文摘New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations and provide all Jordan basesby which the Jordan canonical form is constructed. Accordingly, they can result in thecelebrated Jordan theorem and the third decomposition theorem of space directly. and,moreover, they can give a new deep insight into the exquisite and subtle structure ofthe Jordan form. The latter indicates that the Jordan canonical form of a complexlinear transformation is an invariant structure associated with double arbitrary. choices.
基金Project supported by the National Natural Science Foundation of China(No.51777191)the Natural Science Foundation of Zhejiang Province,China(No.LZ13E070001)the Collaborative Innovation Center for Advanced Aero-engine,China
文摘Properties of the current controller are essential for permanent magnet synchronous machine(PMSM)drives,but the conventional continuous-time current controller cannot fully decouple the cross-coupling terms when applied in the digital processor.Its performance is related closely to the rotational speed.To improve the performance of the current loop,the direct design method in the discrete-time domain is adopted using the accurate discrete-time complex vector model.An integrated accurate hold-equivalent discrete model for PMSM is derived considering the difference between the output of the voltage source inverter and the back electro-motive force.Then an accurate two-degree-of-freedom(2DOF)current controller with a third-order closed-loop transfer function is designed.The 2DOF controller has more freedom in pole placement,and two schemes with a different cancelled pole-zero pair are investigated.Analysis is conducted by the robust root locus method via the complex vector root locus and sensitivity functions,showing properties in disturbance rejection and sensitivity to parameter variation of two schemes.Both schemes have their own advantages.Finally,the dynamic performance and flexibility of the proposed current controller is verified on a 2.5-kW PMSM test bench.
基金Project supported by the National Natural Science Foundation of China (No. 10172038).
文摘By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at the eigenfrequencies of the corresponding interior problems is proposed. By adding appropriate damp to the virtual source system of the wave superposition method, the unique solutions for all wave numbers can be ensured. Based on this thought, a novel method-wave superposition method with complex radius vector is constructed. Not only is the computational time of this method approximately equal to that of the standard wave superposition method, but also the accuracy is much higher compared with other correlative methods. Finally, by taking the pulsating sphere and oscillating sphere as examples, the results of calculation show that the present method can effectively overcome the non-uniqueness problem.
基金supported by National Hi-tech Research and Development Program of China(863 Program, Grant No. 2006AA09Z235)Hunan Provincial Innovation Foundation For Postgraduate of China(Grant No. CX2009B003)
文摘The mobility of the vectored thruster AUV in different environment is the important premise of control system design. The new type of autonomous underwater vehicle (AUV) equipped with rudders and vectored thrusters which are combined to control the course is studied. Firstly, Euler angles representation and quaternion method are applied to establish six-DOF kinematic model respectively, then Newton second law and Lagrangian approach are used to deduce the vectored thruster AUV’s nonlinear dynamic equations with six degrees of freedom (DOF) respectively in complex sea conditions based on the random wave theory according to the structural and kinetic characteristics of the vectored thruster AUV in this paper. The kinematic models and dynamic models based on different theories have the same expression and conclusion, which shows that the kinematic models and dynamic models of the vectored thruster AUV are accurate. The Runge-Kutta arithmetic is used to solve the dynamic equations, which not only can simulate the motions such as cruise and hover but also can describe the vehicle’s low-frequency and high-frequency motion. The results of computation show that the mobility of the vectored thruster AUV in interference-free environment and the integrated signals including low-frequency motion signal and high-frequency motion signal in environmental disturbance accord with practical situation, which not only solve the problem of especial singularities when the pitch angle θ = ±90° but also clears up the difficulties of computation and display of the coupled nonlinear motion equations in complex sea conditions. Moreover, the high maneuverability of the vectored thruster AUV equipped with rudders and vectored thrusters is validated, which lays a foundation for the control system design.
文摘This paper provides derivation of some basic identities for complex four-component vectors defined in a complex four-dimensional spacetime frame specified by an imaginary temporal axis. The resulting four-vector identities take exactly the same forms of the standard vector identities established in the familiar three-dimensional space, thereby confirming the consistency of the definition of the complex four-vectors and their mathematical operations in the general complex spacetime frame. Contravariant and covariant forms have been defined, providing appropriate definitions of complex tensors, which point to the possibility of reformulating differential geometry within a spacetime frame.
文摘The electromagnetic scattering computation has developed rapidly for many years; some computing problems for complex and coated targets cannot be solved by using the existing theory and computing models. A computing model based on data is established for making up the insufficiency of theoretic models. Based on the ＂support vector regression method＂, which is formulated on the principle of minimizing a structural risk, a data model to predicate the unknown radar cross section of some appointed targets is given. Comparison between the actual data and the results of this predicting model based on support vector regression method proved that the support vector regression method is workable and with a comparative precision.
基金supported by the National Key Research and Development Program of China under the grant of 2022YFB3403100。
文摘The dual three-phase PMSM(DTP-PMSM)drives have received wide attention at high-power high-efficiency applications due to their merits of high output current ability and copper-loss-free field excitation.Meanwhile,the DTPPMSM drive provides higher fault-tolerant capability for highreliability applications,e.g.,pumps and actuators in aircraft.For high-power drives with limited switching frequencies and highspeed drives with large fundamental frequencies,the ratio of switching frequency to fundamental frequency,i.e.,the carrier ratio,is usually below 15,which would significantly degrade the control performance.The purpose of this paper is to review the recent work on the modulation and control schemes for improving the operation performance of DTP-PMSM drives with low carrier ratios.Specifically,three categories of methods,i.e.,the space vector modulation based control,the model predictive control(MPC),and the optimized pulse pattern(OPP)based control are reviewed with principles and performance.In addition,brief discussions regarding the comparison and future trends are presented for low-carrier-ratio(LCR)modulation and control schemes of DTP-PMSM drives.
文摘Nowadays, power quality issues are becoming a significant research topic because of the increasing inclusion of very sensitive devices and considerable renewable energy sources. In general, most of the previous power quality classification techniques focused on single power quality events and did not include an optimal feature selection process. This paper presents a classification system that employs Wavelet Transform and the RMS profile to extract the main features of the measured waveforms containing either single or complex disturbances. A data mining process is designed to select the optimal set of features that better describes each disturbance present in the waveform. Support Vector Machine binary classifiers organized in a “One Vs Rest” architecture are individually optimized to classify single and complex disturbances. The parameters that rule the performance of each binary classifier are also individually adjusted using a grid search algorithm that helps them achieve optimal performance. This specialized process significantly improves the total classification accuracy. Several single and complex disturbances were simulated in order to train and test the algorithm. The results show that the classifier is capable of identifying >99% of single disturbances and >97% of complex disturbances.
