ANALYSIS AND DESIGN OF THE FWL DIGITAL OBSERVER/CONTROLLER IMPLEMENTATIONS: EIGENVALUE SENSITIVITY APPROACH

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題名:	ANALYSIS AND DESIGN OF THE FWL DIGITAL OBSERVER/CONTROLLER IMPLEMENTATIONS: EIGENVALUE SENSITIVITY APPROACH
作者:	游文雄;Yu, Wen-Shyong;柯賢儒;Ko, Hsien-Ju;李正吉;Lee, Cheng-Chi
貢獻者:	光電與通訊學系
關鍵詞:	Finite word length, Floating point, Roundoﬀ error, Computational error, Pole sensitivity, Phase sensitivity, Small gain theorem
日期:	2010-09
上傳時間:	2012-11-26 02:22:23 (UTC+0)
摘要:	In this paper, a methodology using small-gain theorem and eigenvalue sensitivity for analyzing the stability of the closed-loop digital control system subject to ﬁnite word length ﬂoating point (FWLFP) operations is proposed. The roundoﬀ and computational errors of the observer/controller parameters caused by FWLFP operations are expressed in function of mantissa bit number. First, a suﬃcient stability criterion in terms of the mantissa bit number for the closed-loop system is derived based on small gain theorem. Then, the magnitude and supplemental angle measures are derived from the sensitivities of the closed-loop system eigenvalues with respect to observer/controller parameters, respectively, in the sense of mixed matrix-2/Frobenius norms. Therefore, an optimal similarity transformation can be obtained from Hermitian solution by considering both the magnitude and supplemental angle measures simultaneously. Based upon the optimal similarity transformation as well as the stability criterion, a minimum mantissa bit number for implementing observers/controllers in FWLFP digital computers can be obtained. The advantages of the proposed methodology are that it can handle the closedloop systems with complex eigenvalues and give an implementable real-valued optimal similarity transformation by easily algebraic operations. Finally, detailed numerical design processes and simulation results are performed to illustrate the eﬀectiveness of the proposed scheme.
關聯:	International Journal of Innovative Computing Information and Control
顯示於類別:	[光電與通訊學系] 期刊論文

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