Design of parameter-scheduled state-feedback controllers using shifting specifications. Issue 1 (January 2015)

• Record Type: Journal Article
• Authors: Rotondo, Damiano; Nejjari, Fatiha; Puig, Vicenç
• Is Part Of: Journal of the Franklin Institute. Volume 352:Issue 1(2015:Jan.)
• Page Start: 93
• Page End: 116
• Publication Date: 2015-01
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2014.10.015
• Languages: English
• ISSNs: 0016-0032

Abstract

<abstract abstract-type="author" id="ab0005"> <title id="sect0005">Abstract</title> <sec> <p id="sp0065">In this paper, the problem of designing a parameter-scheduled state-feedback controller is investigated. The paper presents an extension of the classical regional pole placement, <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh30vh7z51" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="si0029.gif" overflow="scroll" id="d13e968" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></alternatives></inline-formula> control and <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh30vgzw5p" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="si0030.gif" overflow="scroll" id="d13e977" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mrow><mml:mo>∞</mml:mo></mml:mrow></mml:msub></mml:math></alternatives></inline-formula> control problems, so as to satisfy new specifications, that will be referred to as <italic>shifting pole placement control</italic>, <italic>shifting</italic><inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh30vh0fgv" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="si0031.gif" overflow="scroll" id="d13e992" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></alternatives></inline-formula><italic>control</italic> and <italic>shifting</italic><inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh30vh4bmf" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="si0032.gif" overflow="scroll" id="d13e1008" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mrow><mml:mo>∞</mml:mo></mml:mrow></mml:msub></mml:math></alternatives></inline-formula><italic>control</italic>, respectively. By introducing some parameters, or using the existing ones, the controller can be designed in such a way that different values of these parameters imply different regions where the closed-loop poles are situated, or different performances in the <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh30vgzkbs" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="si0033.gif" overflow="scroll" id="d13e1020" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></alternatives></inline-formula> or <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh30vgmnmd" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="si0034.gif" overflow="scroll" id="d13e1029" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mrow><mml:mo>∞</mml:mo></mml:mrow></mml:msub></mml:math></alternatives></inline-formula> sense. The proposed approach is derived within the so-called Lyapunov Shaping Paradigm, where a single quadratic Lyapunov function is used for ensuring stability and desired performances in spite of arbitrary parameter time variation. The problem is analyzed in the continuous-time LPV case, even though the developed theory could be applied to LTI systems in cases when it is desired to vary the control system performances online. Results obtained in simulation demonstrate the effectiveness and the relevant features of the proposed approach.</p> </sec> </abstract>