基于δ法高阶非线性系统相平面实现

Realization of Phase Plane for Higher Order Nonlinear System Based onδ Method

基于二阶线性系统δ法绘制相平面原理,提出一种新而简单计算圆弧圆心和半径的方法实现高阶非线性控制系统相轨迹的作图算法,从而得到高阶非线性控制系统相平面。数值仿真结果表明,该算法与龙格-库塔法等解析法相比具有良好的动静态性能,高的控制精度和较强的鲁棒性。数值结果说明了方法的有效性,算法具有计算简单,易于实现的特点。

A new simple algorithm to calculate the center and radius of an arc in order to realize the phase locus of higher order nonlinear control system based on the principle of plotting the phase plane of second-order linear system usingδmethod is proposed, and thus, the phase plane of the high-order nonlinear system has been obtained. The numerical simulation results show that the algorithm have the superior static and dynamic performance, higher control accuracy and better robustness compared with Runge-Kutta methods. The numerical result has shown the feasibility and efficiency of the method, and additionally, the algorithm is very easy to be implemented with low computational complexity.