高阶非线性控制系统相平面的图解实现

Graphic Realization of Phase Plane for Higher Order Nonlinear Control Systems

非线性控制系统在实际中的存在非常普遍,分析方法有多种。而非线性系统的相平面法既能提供稳态性能信息,又能提供时间响应信息,因而被广泛使用,但相平面法只限于一阶、二阶线性系统的分析。为得到高阶非线性系统的相平面,借助状态空间法,提出一种利用图解方法实现高阶非线性系统相轨迹的作图方法。数值仿真结果表明该算法与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适应性,同时结果说明了该方法的有效性,算法具有计算简单、易于实现的特点。

Nonlinear control systems exist everywhere in the real word and they have many analysis methods. Phase plane analysis method is widely used in the nonlinear control systems because it can provide information of steady-state performance and time response, however, this method is restricted our attentions only to the first- and second-order linear systems. In order to obtain the phase plane of higher order nonlinear control system, a new graphic method of phase locus of phase plane for higher order nonlinear control systems in terms of state space method was proposed. The numerical simulation results show that the algorithm has superior static and dynamic performance, higher control accuracy and better robustness compared with analytical method. The numerical result shows the feasibility and efficiency of the method, and additionally, the algorithm is very easy to be implemented with low computational complexity.