The exact solutions of the generalized (2+1)-dimensional nonlinear Zakharov-Kuznetsov (Z-K) equationare explored by the method of the improved generalized auxiliary differential equation.Many explicit analytic solutio...The exact solutions of the generalized (2+1)-dimensional nonlinear Zakharov-Kuznetsov (Z-K) equationare explored by the method of the improved generalized auxiliary differential equation.Many explicit analytic solutionsof the Z-K equation are obtained.The methods used to solve the Z-K equation can be employed in further work toestablish new solutions for other nonlinear partial differential equations.展开更多
To reduce typhoon-caused damages, numerical and empirical methods are often used to forecast typhoon storm surge. However, typhoon surge is a complex nonlinear process that is difficult to forecast accurately. We appl...To reduce typhoon-caused damages, numerical and empirical methods are often used to forecast typhoon storm surge. However, typhoon surge is a complex nonlinear process that is difficult to forecast accurately. We applied a principal component back-propagation neural network (PCBPNN) to predict the deviation in typhoon storm surge, in which data of the typhoon, upstream flood, and historical case studies were involved. With principal component analysis, 15 input factors were reduced to five principal components, and the application of the model was improved. Observation data from Huangpu Park in Shanghai, China were used to test the feasibility of the model. The results indicate that the model is capable of predicting a 12-hour warning before a typhoon surge.展开更多
The semi-round rigid feet would cause position-posture deviation problem because the actual foothold position is hardly known due to the rolling effect of the semi-round rigid feet during the robot walking. The positi...The semi-round rigid feet would cause position-posture deviation problem because the actual foothold position is hardly known due to the rolling effect of the semi-round rigid feet during the robot walking. The position-posture deviation problem may harm to the stability and the harmony of the robot, or even makes the robot tip over and fail to walk forward. Focused on the position-posture deviation problem of multi-legged walking robots with semi-round rigid feet, a new method of position-posture closed-loop control is proposed to solve the position-posture deviation problem caused by semi-round rigid feet, based on the inverse velocity kinematics of the multi-legged walking robots. The position-posture closed-loop control is divided into two parts: the position closed-loop control and the posture closed-loop control. Thus, the position-posture control for the robot which is a tight coupling and nonlinear system is decoupled. Co-simulations of position-posture open-loop control and position-posture closed-loop control by MATLAB and ADAMS are implemented, respectively. The co-simulation results verify that the position-posture closed-loop control performs well in solving the position-posture deviation problem caused by semi-round rigid feet.展开更多
This paper presents a simple solution of the dynamic buckling of stiffened plates under in-plane impact loading. Based on large deflection theory, a discretely stiffened plate model has been used. The tangential stres...This paper presents a simple solution of the dynamic buckling of stiffened plates under in-plane impact loading. Based on large deflection theory, a discretely stiffened plate model has been used. The tangential stresses of stiffeners and in-plane displacement are neglected. Appling the Hamilton's principle, the motion equations of stiffened plates are obtained. The deflection of the plate is taken as Fourier series, and using Galerkin method the discrete equations can be deduced, which can be solved easily by Runge-Kutta method. The dynamic buckling loads of the stiffened plates are obtained form Budiansky-Roth criterion.展开更多
In this paper,a two-layer hierarchical structure of optimization and control for polypropylene grade transition was raised to overcome process uncertain disturbances that led to the large deviation between the open-lo...In this paper,a two-layer hierarchical structure of optimization and control for polypropylene grade transition was raised to overcome process uncertain disturbances that led to the large deviation between the open-loop reference trajectory and the actual process.In the upper layer,the variant time scale based control vector parametric methods(VTS-CVP) was used for dynamic optimization of transition reference trajectory,while nonlinear model predictive controller(NMPC) based on closed-loop subspace and piece-wise linear(SSARX-PWL) model in the lower layer was tracking to the reference trajectory from the upper layer for overcoming high-frequency disturbances.Besides,mechanism about trajectory deviation detection and optimal trajectory updating online were introduced to ensure a smooth transition for the entire process.The proposed method was validated with the real data from an industrial double-loop propylene polymerization reaction process with developed dynamic mechanism mathematical model.展开更多
This paper presented a novel wide-area nonlinear excitation control strategy for multi-machine power systems. A simple and effective model transformation method was proposed for the system's mathematical model in ...This paper presented a novel wide-area nonlinear excitation control strategy for multi-machine power systems. A simple and effective model transformation method was proposed for the system's mathematical model in the COI (center of inertia) coordinate system. The system was transformed to an uncertain linear one where deviation of generator terminal voltage became one of the new state variables. Then a wide-area nonlinear robust voltage controller was designed utilizing a LMI (linear matrix inequality) based robust control theory. The proposed controller does not rely on any preselected system operating point, adapts to variations of network parameters and system operation conditions, and assures regulation accuracy of generator terminal voltages. Neither rotor angle nor any variable's differentiation needs to be measured for the proposed controller, and only terminal voltages, rotor speeds, active and reactive power outputs of generators are required. In addition, the proposed controller not only takes into account time delays of remote signals, but also eliminates the effect of wide-area information's incompleteness when not all generators are equipped with PMU (phase measurement unit). Detailed tests were conducted by PSCAD/EMTDC for a three-machine and four-machine power systems respectively, and simulation results illustrate high performance of the proposed controller.展开更多
Due to the difficulty in obtaining the a priori estimate,it is very hard to establish the optimal point-wise error bound of a finite difference scheme for solving a nonlinear partial differential equation in high dime...Due to the difficulty in obtaining the a priori estimate,it is very hard to establish the optimal point-wise error bound of a finite difference scheme for solving a nonlinear partial differential equation in high dimensions(2D or 3D).We here propose and analyze finite difference methods for solving the coupled GrossPitaevskii equations in two dimensions,which models the two-component Bose-Einstein condensates with an internal atomic Josephson junction.The methods which we considered include two conservative type schemes and two non-conservative type schemes.Discrete conservation laws and solvability of the schemes are analyzed.For the four proposed finite difference methods,we establish the optimal convergence rates for the error at the order of O(h^2+τ~2)in the l~∞-norm(i.e.,the point-wise error estimates)with the time stepτand the mesh size h.Besides the standard techniques of the energy method,the key techniques in the analysis is to use the cut-off function technique,transformation between the time and space direction and the method of order reduction.All the methods and results here are also valid and can be easily extended to the three-dimensional case.Finally,numerical results are reported to confirm our theoretical error estimates for the numerical methods.展开更多
The particular challenges of modeling control systems for the middle route of the south-to-north water transfer project are illustrated.Open channel dynamics are approximated by well-known Saint-Venant nonlinear parti...The particular challenges of modeling control systems for the middle route of the south-to-north water transfer project are illustrated.Open channel dynamics are approximated by well-known Saint-Venant nonlinear partial differential equations.For better control purpose,the finite difference method is used to discretize the Saint-Venant equations to form the state space model of channel system.To avoid calculation divergence and improve control stability,balanced model reduction together with poles placement procedure is proposed to develop the control scheme.The entire process to obtain this scheme is described in this paper,important application issue is considered as well.Experimental results show the adopted techniques are properly used in the control scheme design,and the system is able to drive the discharge to the demanded set point or maintain it around a reasonable range even if comes across big withdrawals.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.10974160
文摘The exact solutions of the generalized (2+1)-dimensional nonlinear Zakharov-Kuznetsov (Z-K) equationare explored by the method of the improved generalized auxiliary differential equation.Many explicit analytic solutionsof the Z-K equation are obtained.The methods used to solve the Z-K equation can be employed in further work toestablish new solutions for other nonlinear partial differential equations.
基金Supported by National Marine Public Scientific Research Fund of China(No. 200905010)the Talent Training Fund Project for Basic Sciences of the National Natural Science Foundation of China (No. J0730534)+2 种基金the Fundamental Research Funds for the Central Universitiesthe Open Research Funding Program of KLGIS (No. KLGIS2011A12)the Open Fund from Key Laboratory of Marine Management Technique of State Oceanic Administration (No. 201112)
文摘To reduce typhoon-caused damages, numerical and empirical methods are often used to forecast typhoon storm surge. However, typhoon surge is a complex nonlinear process that is difficult to forecast accurately. We applied a principal component back-propagation neural network (PCBPNN) to predict the deviation in typhoon storm surge, in which data of the typhoon, upstream flood, and historical case studies were involved. With principal component analysis, 15 input factors were reduced to five principal components, and the application of the model was improved. Observation data from Huangpu Park in Shanghai, China were used to test the feasibility of the model. The results indicate that the model is capable of predicting a 12-hour warning before a typhoon surge.
基金Project(51221004)supported by the Science Fund for Creative Research Groups of National Natural Science Foundation of ChinaProject supported by the Program for Zhejiang Leading Team of S&T Innovation,China
文摘The semi-round rigid feet would cause position-posture deviation problem because the actual foothold position is hardly known due to the rolling effect of the semi-round rigid feet during the robot walking. The position-posture deviation problem may harm to the stability and the harmony of the robot, or even makes the robot tip over and fail to walk forward. Focused on the position-posture deviation problem of multi-legged walking robots with semi-round rigid feet, a new method of position-posture closed-loop control is proposed to solve the position-posture deviation problem caused by semi-round rigid feet, based on the inverse velocity kinematics of the multi-legged walking robots. The position-posture closed-loop control is divided into two parts: the position closed-loop control and the posture closed-loop control. Thus, the position-posture control for the robot which is a tight coupling and nonlinear system is decoupled. Co-simulations of position-posture open-loop control and position-posture closed-loop control by MATLAB and ADAMS are implemented, respectively. The co-simulation results verify that the position-posture closed-loop control performs well in solving the position-posture deviation problem caused by semi-round rigid feet.
文摘This paper presents a simple solution of the dynamic buckling of stiffened plates under in-plane impact loading. Based on large deflection theory, a discretely stiffened plate model has been used. The tangential stresses of stiffeners and in-plane displacement are neglected. Appling the Hamilton's principle, the motion equations of stiffened plates are obtained. The deflection of the plate is taken as Fourier series, and using Galerkin method the discrete equations can be deduced, which can be solved easily by Runge-Kutta method. The dynamic buckling loads of the stiffened plates are obtained form Budiansky-Roth criterion.
基金Supported by the Electronic Information Industry Development Foundation of China(20140806)the National Natural Science Foundation of China(61374121,61134007)
文摘In this paper,a two-layer hierarchical structure of optimization and control for polypropylene grade transition was raised to overcome process uncertain disturbances that led to the large deviation between the open-loop reference trajectory and the actual process.In the upper layer,the variant time scale based control vector parametric methods(VTS-CVP) was used for dynamic optimization of transition reference trajectory,while nonlinear model predictive controller(NMPC) based on closed-loop subspace and piece-wise linear(SSARX-PWL) model in the lower layer was tracking to the reference trajectory from the upper layer for overcoming high-frequency disturbances.Besides,mechanism about trajectory deviation detection and optimal trajectory updating online were introduced to ensure a smooth transition for the entire process.The proposed method was validated with the real data from an industrial double-loop propylene polymerization reaction process with developed dynamic mechanism mathematical model.
文摘This paper presented a novel wide-area nonlinear excitation control strategy for multi-machine power systems. A simple and effective model transformation method was proposed for the system's mathematical model in the COI (center of inertia) coordinate system. The system was transformed to an uncertain linear one where deviation of generator terminal voltage became one of the new state variables. Then a wide-area nonlinear robust voltage controller was designed utilizing a LMI (linear matrix inequality) based robust control theory. The proposed controller does not rely on any preselected system operating point, adapts to variations of network parameters and system operation conditions, and assures regulation accuracy of generator terminal voltages. Neither rotor angle nor any variable's differentiation needs to be measured for the proposed controller, and only terminal voltages, rotor speeds, active and reactive power outputs of generators are required. In addition, the proposed controller not only takes into account time delays of remote signals, but also eliminates the effect of wide-area information's incompleteness when not all generators are equipped with PMU (phase measurement unit). Detailed tests were conducted by PSCAD/EMTDC for a three-machine and four-machine power systems respectively, and simulation results illustrate high performance of the proposed controller.
基金supported by National Natural Science Foundation of China(Grant No.11201239)the Singapore A*STAR SERC PSF(Grant No.1321202067)
文摘Due to the difficulty in obtaining the a priori estimate,it is very hard to establish the optimal point-wise error bound of a finite difference scheme for solving a nonlinear partial differential equation in high dimensions(2D or 3D).We here propose and analyze finite difference methods for solving the coupled GrossPitaevskii equations in two dimensions,which models the two-component Bose-Einstein condensates with an internal atomic Josephson junction.The methods which we considered include two conservative type schemes and two non-conservative type schemes.Discrete conservation laws and solvability of the schemes are analyzed.For the four proposed finite difference methods,we establish the optimal convergence rates for the error at the order of O(h^2+τ~2)in the l~∞-norm(i.e.,the point-wise error estimates)with the time stepτand the mesh size h.Besides the standard techniques of the energy method,the key techniques in the analysis is to use the cut-off function technique,transformation between the time and space direction and the method of order reduction.All the methods and results here are also valid and can be easily extended to the three-dimensional case.Finally,numerical results are reported to confirm our theoretical error estimates for the numerical methods.
基金supported by the National Key Basic Research Program of China ("973" Progject) (Grant No. 2007CB714100)
文摘The particular challenges of modeling control systems for the middle route of the south-to-north water transfer project are illustrated.Open channel dynamics are approximated by well-known Saint-Venant nonlinear partial differential equations.For better control purpose,the finite difference method is used to discretize the Saint-Venant equations to form the state space model of channel system.To avoid calculation divergence and improve control stability,balanced model reduction together with poles placement procedure is proposed to develop the control scheme.The entire process to obtain this scheme is described in this paper,important application issue is considered as well.Experimental results show the adopted techniques are properly used in the control scheme design,and the system is able to drive the discharge to the demanded set point or maintain it around a reasonable range even if comes across big withdrawals.
