两输入非线性前馈系统的镇定方法

Approach to the stabilization for two-input nonlinear feedforward systems

为了便于构造两输入非线性前馈系统的镇定控制器,通过变换构造出与原系统等价的复数域低维单输入非线性前馈系统,再利用已有的单输入系统的控制方法对该等价系统设计一个复数域镇定控制器,采用逆变换得到原系统的两个镇定控制器,提出了将原系统转化为等价系统后再进行设计的镇定方法。用Lyapunov稳定性定理证明了闭环控制系统状态的渐进稳定性。结果表明:等价系统比原系统具有更少的输入和更低的维数,基于等价系统的设计方法降低了系统的分析难度,简化了控制器的设计步骤。

Stabilizing controllers for a class of two-input feedforward systems were designed based on a class of equivalent single-input systems. The stabilizing controller for the equivalent systems in the complex plane was constructed using the design method for single-input feedforward systems in the real plane, with the two stabilizing controllers for the original systems obtained from the real and imaginary parts of the controller in the complex plane. The global asymptotical stability of the closed-loop systems using these stabilizing controllers was proven using Lyapunov＇s stability theorem. The controller design method based on the equivalent systems significantly reduces the difficulties in analysis of the systems and simplifies the design process, because the equivalent systems have fewer inputs and lower dimension than the original systems.