Set-Point Regulation of LTI Nonminimum Phase Systems with a Single Positive Zero Using Two Sliding Lines

Hajoon LEE  Cheol Hoon PARK  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E92-A    No.3    pp.862-870
Publication Date: 2009/03/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E92.A.862
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Systems and Control
nonminimum phase systems,  sliding mode control,  undershoot,  

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We deal with LTI nonminimum phase (NMP) systems which are difficult to control with conventional methods because of their inherent characteristics of undershoot. In such systems, reducing the undesirable undershoot phenomenon makes the response time of the systems much longer. Moreover, it is impossible to control the magnitude of undershoot in a direct way and to predict the response time. In this paper, we propose a novel two sliding mode control scheme which is capable of stably determining the magnitude of undershoot and thus the response time of NMP systems a priori. To do this, we introduce two sliding lines which are in charge of control in turn. One is used to stabilize the system and achieve asymptotic regulation eventually like the conventional sliding mode methods and the other to stably control the magnitude of undershoot from the beginning of control until the state meets the first sliding line. This control scheme will be proved to have an asymptotic regulation property. The computer simulation shows that the proposed control scheme is very effective and suitable for controlling the NMP systems compared with the conventional ones.