基于最优参数控制方法的齿轮系统混沌控制

Chaos Control for Nonlinear Gear System Based on Method of Optimal Parameter

基于最优参数控制方法,实现了齿轮传动系统中的混沌控制.以经典的间隙单齿轮副非线性动力学模型为研究对象,以啮合静载荷为控制参数,通过混沌吸引子中轨线的观测近似得到目标周期不动点、系统在目标不动点处的雅克比矩阵以及在控制原始参量处的梯度矩阵.最后运用最优参数控制策略计算得到啮合静载荷的小扰动量,实现了把齿轮系统的混沌运动镇定周期一轨道上的目的.研究结果表明,基于最优参数控制方法的控制过程,只是在控制的前几个周期内需要控制参数产生相对较大的扰动量,随着控制的继续进行,扰动量几乎稳定到了某一固定值,不再需要较大的变动.而且控制参数计算所需要的中间参量可以直接由混沌吸引子中轨线的观测近似得到,因而控制容易实现.

Control method of optimal parameter was used to stabilize the unstable periodic orbits which embedded in the chaotic attractor of chaos in nonlinear gear system. Taking the classical nonlinear gear system with clearance as dynamic model, the chaos control was realized by disturbing control parameter that is considered as meshing static load. The control process includes searching target period orbit, calculating Jacobi matrix in target period orbit and gradient matrix in original control parameter and utilizing formula about control method of optimal parameter. The numerical simulation shows that, a relatively large disturbance of control parameters is needed on the initial control periods of the control process, and the disturbance quantity changes into a stable value when the control reach a steady state. These conclusions offers reference for gear system＇s chaos control.