This paper presents an efficient numerical scheme for calculating the periodic motion of a harmonically forced piecewise linear oscillator very accurately. The scheme is based on the shooting technique with the tradi...This paper presents an efficient numerical scheme for calculating the periodic motion of a harmonically forced piecewise linear oscillator very accurately. The scheme is based on the shooting technique with the traditional numerical Poincare mapping and its Jacobian replaced by the piecewise analytic ones. Thus, the scheme gets rid of the requirement of the current schemes for an assumed order of the oscillator trajectory passing through different linear regions. The numerical examples in the paper demonstrate that the new scheme, compared with the current schemes, enables one to cope with more complicated dynamics of harmonically forced piecewise linear oscillators.展开更多
Periodic motion planning for an under-actuated system is rather difficult due to differential dynamic constraints imposed by passive dynamics, and it becomes more difficult for a system with higher underactuation degr...Periodic motion planning for an under-actuated system is rather difficult due to differential dynamic constraints imposed by passive dynamics, and it becomes more difficult for a system with higher underactuation degree, that is with a higher difference between the number of degrees of freedom and the number of independent control inputs. However, from another point of view, these constraints also mean some relation between state variables and could be used in the motion planning.We consider a double rotary pendulum, which has an underactuation degree 2. A novel periodic motion planning is presented based on an optimization search. A necessary condition for existence of the whole periodic trajectory is given because of the higher underactuation degree of the system. Moreover this condition is given to make virtual holonomic constraint(VHC) based control design feasible. Therefore, an initial guess for the optimization of planning a feasible periodic motion is based on this necessary condition. Then, VHCs are used for the system transformation and transverse linearization is used to design a static state feedback controller with periodic matrix function gain. The controller gain is found through another optimization procedure. The effectiveness of initial guess and performance of the closed-loop system are illustrated through numerical simulations.展开更多
The periodic motion and stability for a class of two-degree-of-freedom nonlinear oscillating systems are studied by using the method of Liapunov function. The sufficient conditions which guarantee the existence, uniqu...The periodic motion and stability for a class of two-degree-of-freedom nonlinear oscillating systems are studied by using the method of Liapunov function. The sufficient conditions which guarantee the existence, uniqueness and asymptotic stability of the periodic solutions are obtained.展开更多
The motion of a magnetized axisymmetric spacecraft about its center of mass in a circular orbit is considered, taking the gravitational and magnetic effects of the central body into account. Equations of motion of the...The motion of a magnetized axisymmetric spacecraft about its center of mass in a circular orbit is considered, taking the gravitational and magnetic effects of the central body into account. Equations of motion of the reduced system are transformed to equations of plane motion of a charged particle under the action of electric and magnetic fields. Stationary motions of the system are determined and periodic motions near to them are constructed using the Lyapounoff theorem of the holomorphic integral.展开更多
Rotor systems supported by angular contact ball bearings are complicated due to nonlinear Hertzian contact force. In this paper, nonlinear bearing forces of ball bearing under five-dimensional loads are given, and 5-D...Rotor systems supported by angular contact ball bearings are complicated due to nonlinear Hertzian contact force. In this paper, nonlinear bearing forces of ball bearing under five-dimensional loads are given, and 5-DOF dynamic equations of a rigid rotor ball bearing system are established. Continuation-shooting algorithm for periodic solutions of the nonlinear non-autonomous dynamic system and Floquet multipliers of the system are used. Furthermore, the bifurcation and stability of the periodic motion of the system in different parametric domains are also studied. Results show that the bifurcation and stability of period-1 motion vary with structural parameters and operating parameters of the rigid rotor ball bearing system. Avoidance of unbalanced force and bending moment, appropriate initial contact angle, axial load and damping factor help enhance the unstable rotating speed of period-1 motion.展开更多
In order to realize high accuracy control for periodic motion,a hybrid controller with grey prediction was presented in this paper.Incorporating the grey prediction,repetitive control,and the traditional Proportional-...In order to realize high accuracy control for periodic motion,a hybrid controller with grey prediction was presented in this paper.Incorporating the grey prediction,repetitive control,and the traditional Proportional-Integral-Differential(PID)control,a design method of the grey prediction repetitive PID(GRPID)control algorithm was investigated,according to the characteristics of the periodic motion control.The hybrid control algorithm can estimate unsure parameters and disturbance of system using grey prediction,and compensate control in terms of the prediction results,and this may improve control quality and robustness of repetitive control for controlling periodic motion.An example was carried out to verify the feasibility of the controller.The simulation results show that this algorithm has better performances than that of the conventional repetitive control system.It indicates the presented control method is more suitable for control system of periodic motion.展开更多
This paper investigates long-period ground motion characteristic of the 1999 Jiji （Chi-Chi）, Taiwan, mainshock and aftershocks on the basis of lots of high quality digital strong motion records. The study attaches t...This paper investigates long-period ground motion characteristic of the 1999 Jiji （Chi-Chi）, Taiwan, mainshock and aftershocks on the basis of lots of high quality digital strong motion records. The study attaches the importance to the variation of strength of the long-period ground motion with the magnitude, distance, and site condition. In the meantime, the near-fault long-period ground motion characteristic is analyzed. The result shows that the shape of the long-period response spectrum is mainly controlled by site condition and magnitude （the spectrum of class D＋E is wider than that of class B＋C, and the spectrum of larger magnitude is wider than that of smaller magni- tude）, and the effect of fault distance on the shape is not evident. And near-fault long-period ground motion characteristic depends on fault activity apparently, that is to say, the long-term ground motion in the hanger is stronger than that in the footwall, and the long-term ground motion in the north is stronger than that in the south.展开更多
文摘This paper presents an efficient numerical scheme for calculating the periodic motion of a harmonically forced piecewise linear oscillator very accurately. The scheme is based on the shooting technique with the traditional numerical Poincare mapping and its Jacobian replaced by the piecewise analytic ones. Thus, the scheme gets rid of the requirement of the current schemes for an assumed order of the oscillator trajectory passing through different linear regions. The numerical examples in the paper demonstrate that the new scheme, compared with the current schemes, enables one to cope with more complicated dynamics of harmonically forced piecewise linear oscillators.
基金supported by China Scholarship Council (201504980073) for Zeguo Wang to visit Umea University
文摘Periodic motion planning for an under-actuated system is rather difficult due to differential dynamic constraints imposed by passive dynamics, and it becomes more difficult for a system with higher underactuation degree, that is with a higher difference between the number of degrees of freedom and the number of independent control inputs. However, from another point of view, these constraints also mean some relation between state variables and could be used in the motion planning.We consider a double rotary pendulum, which has an underactuation degree 2. A novel periodic motion planning is presented based on an optimization search. A necessary condition for existence of the whole periodic trajectory is given because of the higher underactuation degree of the system. Moreover this condition is given to make virtual holonomic constraint(VHC) based control design feasible. Therefore, an initial guess for the optimization of planning a feasible periodic motion is based on this necessary condition. Then, VHCs are used for the system transformation and transverse linearization is used to design a static state feedback controller with periodic matrix function gain. The controller gain is found through another optimization procedure. The effectiveness of initial guess and performance of the closed-loop system are illustrated through numerical simulations.
文摘The periodic motion and stability for a class of two-degree-of-freedom nonlinear oscillating systems are studied by using the method of Liapunov function. The sufficient conditions which guarantee the existence, uniqueness and asymptotic stability of the periodic solutions are obtained.
文摘The motion of a magnetized axisymmetric spacecraft about its center of mass in a circular orbit is considered, taking the gravitational and magnetic effects of the central body into account. Equations of motion of the reduced system are transformed to equations of plane motion of a charged particle under the action of electric and magnetic fields. Stationary motions of the system are determined and periodic motions near to them are constructed using the Lyapounoff theorem of the holomorphic integral.
基金Supported by National Natural Science Foundation of China (No.50905061)the Fundamental Research Funds for Central Universities
文摘Rotor systems supported by angular contact ball bearings are complicated due to nonlinear Hertzian contact force. In this paper, nonlinear bearing forces of ball bearing under five-dimensional loads are given, and 5-DOF dynamic equations of a rigid rotor ball bearing system are established. Continuation-shooting algorithm for periodic solutions of the nonlinear non-autonomous dynamic system and Floquet multipliers of the system are used. Furthermore, the bifurcation and stability of the periodic motion of the system in different parametric domains are also studied. Results show that the bifurcation and stability of period-1 motion vary with structural parameters and operating parameters of the rigid rotor ball bearing system. Avoidance of unbalanced force and bending moment, appropriate initial contact angle, axial load and damping factor help enhance the unstable rotating speed of period-1 motion.
基金Science Fund of Shanghai Institute of Technology,China(No.YJ200609)
文摘In order to realize high accuracy control for periodic motion,a hybrid controller with grey prediction was presented in this paper.Incorporating the grey prediction,repetitive control,and the traditional Proportional-Integral-Differential(PID)control,a design method of the grey prediction repetitive PID(GRPID)control algorithm was investigated,according to the characteristics of the periodic motion control.The hybrid control algorithm can estimate unsure parameters and disturbance of system using grey prediction,and compensate control in terms of the prediction results,and this may improve control quality and robustness of repetitive control for controlling periodic motion.An example was carried out to verify the feasibility of the controller.The simulation results show that this algorithm has better performances than that of the conventional repetitive control system.It indicates the presented control method is more suitable for control system of periodic motion.
基金National Natural Science Foundation of China (50278090).
文摘This paper investigates long-period ground motion characteristic of the 1999 Jiji （Chi-Chi）, Taiwan, mainshock and aftershocks on the basis of lots of high quality digital strong motion records. The study attaches the importance to the variation of strength of the long-period ground motion with the magnitude, distance, and site condition. In the meantime, the near-fault long-period ground motion characteristic is analyzed. The result shows that the shape of the long-period response spectrum is mainly controlled by site condition and magnitude （the spectrum of class D＋E is wider than that of class B＋C, and the spectrum of larger magnitude is wider than that of smaller magni- tude）, and the effect of fault distance on the shape is not evident. And near-fault long-period ground motion characteristic depends on fault activity apparently, that is to say, the long-term ground motion in the hanger is stronger than that in the footwall, and the long-term ground motion in the north is stronger than that in the south.
