非线性系统的线性等价及应用

采用对系统的基底坐标变换后,可以使一个非线性系统在输入输出特性上与线性系统等价。文中给出了这种等价变换的条件、计算方法和步骤。等价的线性系统采用可控标准型,并引入可任意配置的系数。这样,就可以利用线性系统的理论对系统进行极点配置得到所期望的特性,为非线性控制系统的设计提供了一种新的方法。作者最后对某种非线性控制系统,用上述方法进行设计,并用仿真结果验证了这种方法的可行性。

Linear Equiva lence of Non-linear System and Its Application

This paper by using differential geometry to study the linear equivalencea large category of multivariable nonlinear systems,presents a kind oftransformation of base coordinates,so that a linear system can be achievedwhich is equivalentto a given nonlinear system in input-output charictevistics.Thesufficient and necessary conditions and algorithm of the equivalent.Transformationare also studied and described in detail.The equivalent linear system assumesa controllable canonical form in which the elements can be set arbitrarily.As aresult of that,we can use the linear control theories such as pole placement andoptimal control to achieve the desired charicteristics of a given nonlinear system,which provides a useful method for the design of a nonlinear control systm.Finally,an example of the application of this method is given.By simulatingthe exampleon a computer,the feasibility of the method is verified withsatisfactory results.