To enhance the stability of helicopter maneuvers during task execution,a composite trajectory tracking controller design based on the implicit model(IM)and linear active disturbance rejection control(LADRC)is proposed...To enhance the stability of helicopter maneuvers during task execution,a composite trajectory tracking controller design based on the implicit model(IM)and linear active disturbance rejection control(LADRC)is proposed.Initially,aerodynamic models of the main and tail rotor are created using the blade element theory and the uniform inflow assumption.Subsequently,a comprehensive flight dynamic model of the helicopter is established through fitting aerodynamic force fitting.Subsequently,for precise helicopter maneuvering,including the spiral,spiral up,and Ranversman maneuver,a regular trim is undertaken,followed by minor perturbation linearization at the trim point.Utilizing the linearized model,controllers are created for the IM attitude inner loop and LADRC position outer loop of the helicopter.Ultimately,a comparison is made between the maneuver trajectory tracking results of the IM‑LADRC and the conventional proportional-integral-derivative(PID)control method is performed.Experimental results demonstrate that utilizing the post-trim minor perturbation linearized model in combination with the IM‑LADRC method can achieve higher precision in tracking results,thus enhancing the accuracy of helicopter maneuver execution.展开更多
In this paper, we extend the mapping deformation method proposed by Lou. It is used to find new exacttravelling wave solutions of nonlinear partial differential equation or coupled nonlinear partial differential equat...In this paper, we extend the mapping deformation method proposed by Lou. It is used to find new exacttravelling wave solutions of nonlinear partial differential equation or coupled nonlinear partial differential equations(PDEs). Based on the idea of the homogeneous balance method, we construct the general mapping relation betweenthe solutions of the PDEs and those of the cubic nonlinear Klein-Gordon (NKG) equation. By using this relation andthe abundant solutions of the cubic NKG equation, many explicit and exact travelling wave solutions of three systemsof coupled PDEs, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic functionsolutions, and rational solutions, are obtained.展开更多
A modified Lindstedt-Poincaré (LP) method for obtaining the resonance periodic solutions of nonlinear non-autonomous vibration systems is proposed in this paper. In the modified method, nonlinear non-autonomou...A modified Lindstedt-Poincaré (LP) method for obtaining the resonance periodic solutions of nonlinear non-autonomous vibration systems is proposed in this paper. In the modified method, nonlinear non-autonomous equa-tions are converted into a group of linear ordinary differential equations by introducing a set of simple transformations. An approximate resonance solution for the original equation can then be obtained. The periodic solutions of primary, super-harmonic, sub-harmonic, zero-frequency and combination resonances can be solved effectively using the modi-fied method. Some examples, such as damped cubic nonlinear systems under single and double frequency excitation, and damped quadratic nonlinear systems under double frequency excitation, are given to illustrate its convenience and effectiveness. Using the modified LP method, the first-order approximate solutions for each equation are obtained. By comparison, the modified method proposed in this paper produces the same results as the method of multiple scales.展开更多
By using the general solutions of a new coupled Riccati equations, a direct algebraic method is described to construct doubly periodic solutions (Jacobi elliptic function solution) for the coupled nonlinear Klein-Gord...By using the general solutions of a new coupled Riccati equations, a direct algebraic method is described to construct doubly periodic solutions (Jacobi elliptic function solution) for the coupled nonlinear Klein-Gordon equations.It is shown that more doubly periodic solutions and the corresponding solitary wave solutions and trigonometric function solutions can be obtained in a unified way by this method.展开更多
A numerical model of a coupled bubble jet and wall was built on the assumption of potential flow and calculated by the boundary integral method. A three-dimensional computing program was then developed. Starting with ...A numerical model of a coupled bubble jet and wall was built on the assumption of potential flow and calculated by the boundary integral method. A three-dimensional computing program was then developed. Starting with the basic phenomenon of the interaction between a bubble and a wall, the dynamics of bubbles near rigid walls were studied systematically with the program. Calculated results agreed well with experimental results. The relationship between the Bjerknes effect of a wall and characteristic parameters was then studied and the calculated results of various cases were compared and discussed with the Blake criterion based on the Kelvin-impulse theory. Our analyses show that the angle of the jet’s direction and the pressure on the rigid wall have a close relationship with collapse force and the bubble’s characteristic parameters. From this, the application range of Blake criterion can be determined. This paper aims to provide a basis for future research on the dynamics of bubbles near a wall.展开更多
With the deployment of small cells and device to device communications in future heterogeneous networks,in many situations we would encounter mobile radio channels with partly blocked line of sight component,which are...With the deployment of small cells and device to device communications in future heterogeneous networks,in many situations we would encounter mobile radio channels with partly blocked line of sight component,which are well modeled by the Rician shadowed(RS) fading channel.In this paper,by the usage of Kummer transformation,a simplified representation of the RS fading channel with integral fading parameter is given.It is a finite series representation involving only exponential function and low order polynomials.This allows engineers not only the closed-form expressions for exact performance analysis over RS fading channel,but also the insights on the system design tactics.展开更多
This paper proposes a two-piece update of projected reduced Hessian algorithmwith nonmonotonic trust region strategy for solving nonlinear equality constrained optimizationproblems. In order to deal with large problem...This paper proposes a two-piece update of projected reduced Hessian algorithmwith nonmonotonic trust region strategy for solving nonlinear equality constrained optimizationproblems. In order to deal with large problems, a two-piece update of two-side projected reducedHessian is used to replace full Hessian matrix. By adopting the Fletcher's penalty function as themerit function, a nonmonotonic trust region strategy is suggested which does not require the meritfunction to reduce its value in every iteration. The two-piece update of projected reduced Hessianalgorithm which switches to nonmonotonic trust region technique possesses global convergence whilemaintaining a two-step Q-superlinear local convergence rate under some reasonable conditions.Furthermore, one step Q-superlinear local convergence rate can be obtained if at least one of theupdate formulas is updated at each iteration by an alternative update rule. The numerical experimentresults are reported to show the effectiveness of the proposed algorithm.展开更多
The author studies the h-transforms of symmetric Markov processes and corresponding Dirichlet spaces, and also discusses the drift transformation of Fukushima and Takeda’s type[2] and improves their result by a diffe...The author studies the h-transforms of symmetric Markov processes and corresponding Dirichlet spaces, and also discusses the drift transformation of Fukushima and Takeda’s type[2] and improves their result by a different approach.展开更多
By introducing the block estimate technique and directly using the Newton iteration method, the author constructs Cantor families of time periodic solutions to a class of nonlinear wave equations with periodic boundar...By introducing the block estimate technique and directly using the Newton iteration method, the author constructs Cantor families of time periodic solutions to a class of nonlinear wave equations with periodic boundary conditions. The Lyapunov-Schmidt decomposition used by J. Bourgain, W. Craig and C. E. Wayne is avoided. Thus this work simplifies their framework for KAM theory for PDEs.展开更多
基金supported in part by the National Natural Science Foundation of China(No.12032012)the Key Discipline Construction Project of Colleges and Universities in Jiangsu Province.
文摘To enhance the stability of helicopter maneuvers during task execution,a composite trajectory tracking controller design based on the implicit model(IM)and linear active disturbance rejection control(LADRC)is proposed.Initially,aerodynamic models of the main and tail rotor are created using the blade element theory and the uniform inflow assumption.Subsequently,a comprehensive flight dynamic model of the helicopter is established through fitting aerodynamic force fitting.Subsequently,for precise helicopter maneuvering,including the spiral,spiral up,and Ranversman maneuver,a regular trim is undertaken,followed by minor perturbation linearization at the trim point.Utilizing the linearized model,controllers are created for the IM attitude inner loop and LADRC position outer loop of the helicopter.Ultimately,a comparison is made between the maneuver trajectory tracking results of the IM‑LADRC and the conventional proportional-integral-derivative(PID)control method is performed.Experimental results demonstrate that utilizing the post-trim minor perturbation linearized model in combination with the IM‑LADRC method can achieve higher precision in tracking results,thus enhancing the accuracy of helicopter maneuver execution.
文摘In this paper, we extend the mapping deformation method proposed by Lou. It is used to find new exacttravelling wave solutions of nonlinear partial differential equation or coupled nonlinear partial differential equations(PDEs). Based on the idea of the homogeneous balance method, we construct the general mapping relation betweenthe solutions of the PDEs and those of the cubic nonlinear Klein-Gordon (NKG) equation. By using this relation andthe abundant solutions of the cubic NKG equation, many explicit and exact travelling wave solutions of three systemsof coupled PDEs, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic functionsolutions, and rational solutions, are obtained.
基金Supported by the National Natural Science Foundation of China(No.11172199)the Key Project of Tianjin Municipal Natural Science Foundation(No.11JCZDJC25400)
文摘A modified Lindstedt-Poincaré (LP) method for obtaining the resonance periodic solutions of nonlinear non-autonomous vibration systems is proposed in this paper. In the modified method, nonlinear non-autonomous equa-tions are converted into a group of linear ordinary differential equations by introducing a set of simple transformations. An approximate resonance solution for the original equation can then be obtained. The periodic solutions of primary, super-harmonic, sub-harmonic, zero-frequency and combination resonances can be solved effectively using the modi-fied method. Some examples, such as damped cubic nonlinear systems under single and double frequency excitation, and damped quadratic nonlinear systems under double frequency excitation, are given to illustrate its convenience and effectiveness. Using the modified LP method, the first-order approximate solutions for each equation are obtained. By comparison, the modified method proposed in this paper produces the same results as the method of multiple scales.
文摘By using the general solutions of a new coupled Riccati equations, a direct algebraic method is described to construct doubly periodic solutions (Jacobi elliptic function solution) for the coupled nonlinear Klein-Gordon equations.It is shown that more doubly periodic solutions and the corresponding solitary wave solutions and trigonometric function solutions can be obtained in a unified way by this method.
基金the National Natural Science Foundation of China under Grant No. 50779007the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20070217074)+1 种基金the Defence Advance Research Program of Science and Technology of Ship Industry under Grant No. 07J1.1.6Harbin Engineering University Foundation under Grant No. HEUFT07069
文摘A numerical model of a coupled bubble jet and wall was built on the assumption of potential flow and calculated by the boundary integral method. A three-dimensional computing program was then developed. Starting with the basic phenomenon of the interaction between a bubble and a wall, the dynamics of bubbles near rigid walls were studied systematically with the program. Calculated results agreed well with experimental results. The relationship between the Bjerknes effect of a wall and characteristic parameters was then studied and the calculated results of various cases were compared and discussed with the Blake criterion based on the Kelvin-impulse theory. Our analyses show that the angle of the jet’s direction and the pressure on the rigid wall have a close relationship with collapse force and the bubble’s characteristic parameters. From this, the application range of Blake criterion can be determined. This paper aims to provide a basis for future research on the dynamics of bubbles near a wall.
基金sponsored by the National Natural Science Foundation of China under grant No.61171089the Training Program of the Major Research Plan of the National Natural Science Foundation of China under grant No.91438104
文摘With the deployment of small cells and device to device communications in future heterogeneous networks,in many situations we would encounter mobile radio channels with partly blocked line of sight component,which are well modeled by the Rician shadowed(RS) fading channel.In this paper,by the usage of Kummer transformation,a simplified representation of the RS fading channel with integral fading parameter is given.It is a finite series representation involving only exponential function and low order polynomials.This allows engineers not only the closed-form expressions for exact performance analysis over RS fading channel,but also the insights on the system design tactics.
基金The author gratefully acknowledges the partial supports of the National Science Foundation of China Grant (10071050)Science Foundation of Shanghai Technical Sciences Committee Grant (02ZA14070) Science Foundation of Shanghai Education Committee Grant
文摘This paper proposes a two-piece update of projected reduced Hessian algorithmwith nonmonotonic trust region strategy for solving nonlinear equality constrained optimizationproblems. In order to deal with large problems, a two-piece update of two-side projected reducedHessian is used to replace full Hessian matrix. By adopting the Fletcher's penalty function as themerit function, a nonmonotonic trust region strategy is suggested which does not require the meritfunction to reduce its value in every iteration. The two-piece update of projected reduced Hessianalgorithm which switches to nonmonotonic trust region technique possesses global convergence whilemaintaining a two-step Q-superlinear local convergence rate under some reasonable conditions.Furthermore, one step Q-superlinear local convergence rate can be obtained if at least one of theupdate formulas is updated at each iteration by an alternative update rule. The numerical experimentresults are reported to show the effectiveness of the proposed algorithm.
文摘The author studies the h-transforms of symmetric Markov processes and corresponding Dirichlet spaces, and also discusses the drift transformation of Fukushima and Takeda’s type[2] and improves their result by a different approach.
基金the Special Funds for Major State Basic Research Projects of China theLaboratory of Mathematics for Nonlinear Sciences, Fuda
文摘By introducing the block estimate technique and directly using the Newton iteration method, the author constructs Cantor families of time periodic solutions to a class of nonlinear wave equations with periodic boundary conditions. The Lyapunov-Schmidt decomposition used by J. Bourgain, W. Craig and C. E. Wayne is avoided. Thus this work simplifies their framework for KAM theory for PDEs.