Study On Some Problems In Analysis And Control Of Fractionalorder Systems  Posted on:20100717  Degree:Master  Type:Thesis  Country:China  Candidate:J Xu  Full Text:PDF  GTID:2178360278463086  Subject:Control theory and control engineering  Abstract/Summary:  PDF Full Text Request  Fractional calculus as an extension of ordinary calculus has a history ofmore than 300 years. Fractionalorder systems are represented by di?erential equations with noninteger order. It has been found that the behaviorof many physical systems can be more properly described by fractionalorder systems than those of integerorder models. At present, the studyof fractionalorder systems is still at its beginning stage. As for a generalfractionalorder system, e?cient stability analysis and controller designmethods are still absent. This paper considers two classes of system inthe fractionalorder system theory, i.e. the fractional generalized systemand the fractional delayed system. To the best knowledge of the author,it is the first time that the fractional generalized system is studied in ourcountry. For the fractional linear timeinvariant generalized system, wediscuss its stability problem using linear matrix inequalities(LMI) method,and then address the robust stability of the fractional generalized systemwith parametric uncertainties and its robust controller design. For thefractionalorder system with constant delays, we analyze the relation be tween its characteristic roots and its stability, and investigate its frequencydomain analysis via complex Lyapunov function and matrix measure theory. The main contributions and achievements of this paper are detailedbelow:1. The regularity and the impulsiveness of fractional generalized systems are investigated. On the basis of the presented statespace descriptionof the fractional generalized system, its state response is obtained by usingLaplace transform. The problem of the existence and the uniqueness ofthe fractional generalized system solution, as well as that of its impulsiveness is discussed, some conclusions on regularity and nonimpulsiveness areproposed for the fractional generalized system.2. Studies are made on the stability and the admissibility of the fractional generalized system. Through the analysis of the pole distribution ofthe fractional generalized system in the complex plane, a stability criterionis obtained in the form of argument. Then a new su?cient and necessary LMI conditions are proposed for generalized systems, from which twoforms of su?cient and necessary condition are derived to determine theadmissibility of the fractional generalized system, i.e. strict LMI conditionand nonstrict LMI one with equality constraint.3. With the help of LMI method, the problem of robust admissibilitycontrol for the fractional generalized system with parametric uncertainties is addressed. For two types of uncertainty, i.e. the normbounded uncertainty and the polytopic uncertainty, a few su?cient conditions areprovided to guarantee the robust admissibility of uncertain fractional generalized system. From these conditions and with the use of variable substitution, the LMIbased state feedback controller and dynamic outputfeedback controller design methods are developed. Finally the simulationresults of several examples demonstrate the validity and the feasibility ofour methods.4. The stability of the fractionalorder system with constant delayis dealt with. The definition of the stability, as well as independentofdelay stability of fractional delayed systems is first given. By adoptingcomplex Lyapunov matrix function and matrix measure methods, somedelayindependent criteria are advanced, and then delaydependent criteriaare also presented by taking into account of the size of timedelay.  Keywords/Search Tags:  Fractionalorder systems, generalized systems, time delay, robust stability, normbound uncertainty, polytopic uncertainty, linear matrix matrix (LMI), state feedback, dynamic output feedback  PDF Full Text Request  Related items 
 
