The open-plus-closed loop （OPCL） method for chaotic systems with multiple strange attractors

Based on the open-plus-closed-loop （OPCL） control method a systematic and comprehensive controller is presented in this paper for a chaotic system, that is, the Newton-Leipnik equation with two strange attractors： the upper attractor （UA） and the lower attractor （LA）. Results show that the final structure of the suggested controller for stabilization has a simple linear feedback form. To keep the integrity of the suggested approach, the globality proof of the basins of entrainment is also provided. In virtue of the OPCL technique, three different kinds of chaotic controls of the system are investigated, separately： the original control forcing the chaotic motion to settle down to the origin from an arbitrary position of the phase space; the chaotic intra-attractor control for stabilizing the equilibrium points only belonging to the upper chaotic attractor or the lower chaotic one; and the inter-attractor control for compelling the chaotic oscillation from one basin to another one. Both theoretical analysis and simulation results verify the validity of the proposed means.

An open-plus-closed-loop control for chaotic Mathieu-Duffing oscillator

By using the idea of open-plus-closed-loop（OPCL） control, a controller composed of an external excitation and a linear feedback is designed to entrain chaotic trajectories of Mathieu-Duffing oscillator to its periodic and higher periodic orbits. The global basin of entrainment of this open-plus-closed-loop control is proved by combining the Lyapunov stability theory with a comparative theorem of initial value problems for second-order ordinary differential equations. Numerical simulations are performed to verify the theoretical results.

利用改进的OPCL控制实现二连杆机构的同步运动

研究了一种改进的开闭环控制(OPC控制)方法,将这种方法应用于二连杆机构的同步运动控制,实现了二连杆机构的小幅摆和大回环两种同步运动形式.通过仿真,对比了二连杆机构的同步的不同运动特征,并对不同控制参数对同步过程的影响进行了研究.

Open-plus-closed-loop control for chaotic motion of 3D rigid pendulum

An open-plus-closed-loop （OPCL） control problem for the chaotic motion of a 3D rigid pendulum subjected to a constant gravitationM force is studied. The 3D rigid pendulum is assumed to be consist of a rigid body supported by a fixed and frictionless pivot with three rotational degrees. In order to avoid the singular phenomenon of Euler＇s angular velocity equation, the quaternion kinematic equation is used to describe the motion of the 3D rigid pendulum. An OPCL controller for chaotic motion of a 3D rigid pendulum at equilibrium position is designed. This OPCL controller contains two parts： the open-loop part to construct an ideal trajectory and the closed-loop part to stabilize the 3D rigid pendulum. Simulation results show that the controller is effective and efficient.

Synchronization motions of a two-link mechanism with an improved OPCL method

An improved OPCL method is developed and applied to both small swing and giant rotation synchronization of a two-link mechanism. Transition processes of the two kinds of synchronization are discussed. Comparisons of different motion characteristics of the two-link synchronization and the effects of different control parameters on synchronous processes are investigated with numerical simulations.

混沌Mathieu-Duffing振子的开闭环控制

基于开闭环控制的思想,设计了一类由外激力与线性误差反馈组成的开闭环控制器,研究了Mathieu-Duffing振子混沌轨道至任意目标周期轨道的控制问题;同时,利用Liapunov稳定性理论与二阶常微分方程初值问题的一个比较定理,证明了上述开闭环控制夹带盆(basin of entrainment)的全局性.最后,利用数值模拟,验证了理论结果的正确性.

基于ADAMS的非线性隔振系统吸引子迁移仿真研究

针对非线性隔振系统多值性导致系统存在多个不同拓扑特性的吸引子,通过ADAMS软件对非线性隔振系统吸引子迁移控制进行了仿真。首先,分别推导单自由度和两自由度非线性隔振系统的吸引子迁移控制规律;其次,以准零刚度隔振系统为对象,分析其静力学特性并确定系统参数;最后,分别建立刚性基础和柔性基础准零刚度隔振系统的ADAMS模型,基于开环加线性闭环算法进行吸引子迁移控制仿真。仿真结果证明了吸引子共存现象是真实存在的,并可通过开环加线性闭环算法使非线性隔振系统由大振幅吸引子迁移至小振幅吸引子,从而实现减振降噪。