与输出变量相关的非线性三阶系统运动行为

对三通阀控制液压缸的研究,主要采用传递函数来建立其数学模型。这种方法将稳定性局限于工作点附近,且不适合用于讨论全工作范围内的系统稳定性,以及系统结构参数变化对系统带来的影响。为了突出液压缸容腔中油液体积变化对系统非线性的影响,这里采用将阀口流量方程表达成增量形式,利用流量连续性方程和液压缸负载动力学方程,建立了适合于全工作范围的阀控缸系统数学模型;并以此建立了与输出变量相关的三阶非线性微分方程。借助状态空间表达式的方法,对方程进行研究,讨论了方程的李亚谱若夫意义稳定性;并侧重讨论了系统输出量运动行为中的极限环和初值敏感行为。结果表明:液压缸容积随位移这一输出量变化是导致阀控缸系统非线性重要因素;并在各阶微分系数中均有体现;在平衡点附近,微小的初始值变动会使系统运动行为产生较大变化;方程系数取值在某些特定的范围时,系统运动行为呈现出极限环;最后,确定出方程稳定的系数取值区域。

Movement behavior of three order nonlinear system correlation with output variables

For the three-ways valve controlled hydraulic cylinder the transfer function is usually used to establish the mathematic model. In this method, stability will be limited near the working point, and it is not suitable for the discussion of the system stability within the scope of the whole work and the effects of structural parameters on the system. In order to highlight the effect of the oil volume change in the hydraulic cylinder chamber on the nonlinear of the system, the valve port flow equation expressed by the incremental form, the flow continuity equation and dynamics equation of hydraulic cylinder load were used here, the valve-controlled cylinder system mathematical model which is suitable for the whole working range was established, and thus, established the third order nonlinear differential equation related to the output variables. The equation was studied with the aid of state space expression method, the Lyapunov significance stability of the equation was discussed, and the limit cycle and initial value sensitivity behavior of the system output movement behavior was focused on in the discussion. The result shows, the hydraulic cylinder volume change with the displacement output is an important factor lead to valve control cylinder system is nonlinear which reflects in each order differential coefficient. Small changes of the initial value will make the system motion behavior a great change near the equilibrium point. When equation coefficient value was chosen in certain scope, the system movement behavior presented a limit cycle. Finally, the stable coefficient value area of the equation was determined.