A New Procedure for Linearizing Dynamic Error and Establishing Absolute Robustness to Lipschitz Nonlinearity

Journal of control, automation and electrical systems

article

Mobki, Hamed¹  Sadeghi, Morteza H.²  Eskandari, Mir Mohammad³ 

[1] Department of Engineering, German University of Technology;Department of Mechanical Engineering, University of Tabriz;Department of Mechanical Engineering, University of Tehran

关键词: Dynamic error linearization;    Lipschitz nonlinearity;    State estimation;    Uncertainty;   

DOI  :  10.1007/s40313-020-00578-9

学科分类：自动化工程

来源: Springer

【 摘 要 】

A new procedure for linearizing dynamic error, without using state transformation, and linearizing nonlinear terms has been presented. The nonlinear term in the error differential equation has been analyzed in terms of the dynamic error and then has been replaced in the matrix of error factors. With stabilizing this matrix, the differential equation can be linearized and the gains of the observer have been obtained in nonlinear terms of the estimated state and the actual output. In other words, utilizing nonlinear gain factors, the nonlinearity in the final form of differential equation can be removed, and thus, differential equation of dynamic error can be linearized. The required conditions for observer construction and the procedure for linearizing of dynamic error have thoroughly been presented in detail. The robustness of designed observer to Lipschitz constant has been studied, and the absolute robustness of observer has been proved. Additionally, robustness to uncertainty has been investigated, and finally, the results for a sample nonlinear Lipschitz system, in the absence and the presence of uncertainty, are elicited and presented. The extracted results have shown good ability of observer in state estimation of studied system in the presence and absence of uncertainty. Furthermore, the presented results proved absolute robustness of designed observer to Lipschitz nonlinearity.

【 授权许可】

CC BY