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Research On Fault Diagnosis And Fault Tolerant Control For Fractional Order Systems

Posted on:2020-03-28Degree:DoctorType:Dissertation
Country:ChinaCandidate:H LiFull Text:PDF
GTID:1488306353463264Subject:Control theory and control engineering
Abstract/Summary:PDF Full Text Request
With the deepening of the research on fractional calculus theory and the rapid development of computer technology,it has been found that fractional calculus can better describe the physical process with memory and history.So far,researchers have begun to use fractional mode in control engineering,rheology,soft matter and other fields.The model has been established and some meaningful results have been achieved,which greatly stimulates people’s enthusiasm for the research of fractional order theory and application.For a practical system,there will be various unpredictable faults,such as actuator and sensor interruption,system parameter jump,and so on.The same is true for fractionalorder systems.In order to improve the security and reliability of fractional order systems,the research on fault diagnosis and fault tolerant control is of theoretical and practical significance.On the basis of previous work,some new fault diagnosis and fault-tolerant control methods are proposed for fractional-order systems.Based on fractional order theory and combining linear matrix inequality(LMI)and adaptive technology,the design conditions of fault diagnosis filter and controller for fractional order systems are obtained.The main results are proved theoretically,and the effectiveness of the proposed theoretical method is verified by simulation examples.The main contents are outlined as follows:Chapters 1-2 systematically analyze and summarize the background and development of the fractional-order control systems.Preliminaries about the considered problem are also given.Chapter 3 considers the fault detection problem for fractional-order linear systems with disturbances.The and performance indices of fractional-order systems in finite frequency domains are applied to measure the fault sensitivity and the disturbance robustness.A fractional-order fault detection observer is designed to satisfy the two finite frequency performance indices simultaneously.Based on the Generalized KalmanYakubovich-Popov lemma and the Projection Lemma,the design conditions are obtained in terms of linear matrix inequalities.Compared with the existing full frequency approaches,the proposed finite frequency one can get better results when the frequency ranges of faults and disturbances are known.The effectiveness of the proposed method is validated by numerical examples.Chapter 4 investigates the problem of simultaneous fault detection and control for fractional-order linear systems.A fractional order dynamic observer is designed as a detector and a controller is designed based on the observer.Based on the new bounded real lemma corresponding to H-norm of fractional-order systems and the generalized Kalman-Yakubovich-Popov Lemma,the designed conditions for the detector/controller to achieve H-disturbance attenuation performance and H∞ fault sensitivity performance in finite-frequency domain are derived.In particular,a linearising change-of-variables and a tangent hyperplane technique are introduced to convert the design conditions into a set of linear matrix inequalities.Finally,simulation examples are given to illustrate the effectiveness of the proposed design method.Chapter 5 focus on the problem of fault estimation for fractional-order systems with poly topic uncertainties.The faults and disturbances are considered to belong to finite frequency domains,and a fractional-order robust fault estimation filter is proposed for fault estimation with the known frequency ranges.As applications of the generalized KalmanYakubovich-Popov lemma,the fault estimation filter design problem is transformed into a multi-objective optimization problem.By using the projection lemma and a linearizing change of variables,sufficient conditions for the existence of the robust fault estimator are derived on the basis of a set of linear matrix inequalities.Numerical examples are used to demonstrate the validity of the presented method.Chapter 6 concerns with the problem of robust fault-tolerant H∞ dynamic output feedback control for fractional-order linear uncertain systems with the order satisfying 0<α<1 in the presence of actuator faults.A new linear matrix inequality(LMI)formulation corresponding to the H∞ norm of fractional-order linear systems is proposed.Based on the new formulation and by introducing a new linearizing change of variables,sufficient conditions for robust fault-tolerant H∞ dynamic output feedback controller designs are derived in term of LMIs.Furthermore,the proposed controller not only enables the system to keep robust stabilization,but also achieves a better H∞ performance compared with the existing methods.Numerical examples are given to illustrate the design procedure and its effectiveness.Chapter 7 addresses the robust adaptive synchronization problem for a class of chaotic systems with unknown nonlinear uncertainty and actuator faults including loss of effectiveness,stuck,and outage.Since the knowledge of the accurate information of faults and upper bound of external disturbances is not necessary,the adaptive laws are proposed to estimate the unknown parameters online.Combined with the fractional Lyapunov direct method,a novel type of robust adaptive fault-tolerant controller is constructed,which can eliminate the effect of actuator fault and nonlinear uncertainty in the controlled systems.Furthermore,the designed controller with σ-modification adaptive schemes ensures that the synchronization error is uniformly ultimately bounded and can be reduced as small as possible,meanwhile,the issue of high gain can be avoided effectively.Simulation experiment on the fractional order Chua’s circuit system is given to confirm the efficacy of the proposed method.Chapter 8 summarizes the results of the dissertation and points out the future research topics.
Keywords/Search Tags:Fractional order systems, fault detection filters, fault estimation, robust fault-tolerant control, adaptive fault-tolerant control, linear matrix inequality(LMI)
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