带非线性项的积分器链嵌套饱和时滞控制

Nested Saturation Delay Control of Integrator Chains with Nonlinear Terms

针对带有高阶非线性项的四阶积分器链,在输入包含时滞的情形下,提出了一种嵌套饱和控制器,实现系统的全局渐进稳定。稳定分析分为饱和退化分析和退饱和系统的渐进稳定分析两个阶段。该控制器利用平面转换构造标准型,进行自然对消,完成饱和退化分析;然后,利用一个重要矩阵不等式和李雅普诺夫定理,完成渐进稳定分析;最后,通过一个惯性摆系统的仿真实验,验证了控制器的有效性。

In view of a fourth-order integrator chain with higher-order nonlinear terms,a nested saturation controller is proposed for a realization of the global asymptotic stability of the system with an input time delay.The stability analysis can be divided into two stages:saturation degradation analysis and asymptotic stability analysis of desaturated systems.The controller uses planar transformation to construct a standard type,followed by a natural cancellation,thus completing the saturation degradation analysis.Then,an important matrix inequality and Lyapunov theorem are used to complete the asymptotic stability analysis.Finally,the effectiveness of the controller is verified by a simulation experiment of an inertial pendulum system.