河海大学学报（自然科学版）
河海大學學報（自然科學版）
하해대학학보（자연과학판）
JOURNAL OF HOHAI UNIVERSITY (NATURAL SCIENCES)
2014年
2期
183-188
,共6页
非线性控制器%非最小相位%零动态%微分几何%精确反馈线性化
非線性控製器%非最小相位%零動態%微分幾何%精確反饋線性化
비선성공제기%비최소상위%령동태%미분궤하%정학반궤선성화
nonlinear controller%non-minimum phase%zero dynamics%differential geometry%exact feedback linearization
为解决非线性系统状态反馈线性化过程中出现的非最小相位问题，设计了一种非线性控制器实现对非最小相位环节的有效控制；通过微分同胚映射将原非线性系统变换为线性化标准型形式，此标准型由线性子系统描述的外部动态和由非线性子系统描述的内部动态(即零动态)构成；基于极点配置和李雅普诺夫稳定性理论，给出了一种零动态不稳定系统(即非最小相位系统)非线性控制器设计方法。数值算例仿真结果表明，该方法所设计的控制器既能确保外部动态满足性能要求同时也能保证零动态稳定。
為解決非線性繫統狀態反饋線性化過程中齣現的非最小相位問題，設計瞭一種非線性控製器實現對非最小相位環節的有效控製；通過微分同胚映射將原非線性繫統變換為線性化標準型形式，此標準型由線性子繫統描述的外部動態和由非線性子繫統描述的內部動態(即零動態)構成；基于極點配置和李雅普諾伕穩定性理論，給齣瞭一種零動態不穩定繫統(即非最小相位繫統)非線性控製器設計方法。數值算例倣真結果錶明，該方法所設計的控製器既能確保外部動態滿足性能要求同時也能保證零動態穩定。
위해결비선성계통상태반궤선성화과정중출현적비최소상위문제，설계료일충비선성공제기실현대비최소상위배절적유효공제；통과미분동배영사장원비선성계통변환위선성화표준형형식，차표준형유선성자계통묘술적외부동태화유비선성자계통묘술적내부동태(즉령동태)구성；기우겁점배치화리아보낙부은정성이론，급출료일충령동태불은정계통(즉비최소상위계통)비선성공제기설계방법。수치산례방진결과표명，해방법소설계적공제기기능학보외부동태만족성능요구동시야능보증령동태은정。
In order to solve the non-minimum phase problem that arises from the nonlinear control method of state-feedback linearization, a nonlinear controller was designed to control the non-minimum phase effectively. First, through a differential homeomorphism transformation, the original nonlinear systems were transformed into a linearization canonical form, which was composed of the external dynamics described by a linear sub-system and the internal dynamics ( namely zero dynamics ) described by a nonlinear sub-system. Then, a nonlinear controller design method was developed for the non-minimum phase system, in which zero dynamics were unstable, based on pole assignment and Lyapunov stability theory. Numerical simulations show that, not only can the controller designed by the developed method meet the performance requirements of external dynamics, it can also guarantee the stability of zero dynamics.
