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Research On Fault-tolerant Controller Design Method For Several Classes Of Linear Systems

Posted on:2013-11-24Degree:DoctorType:Dissertation
Country:ChinaCandidate:X P GongFull Text:PDF
GTID:1228330377459256Subject:Systems Engineering
Abstract/Summary:PDF Full Text Request
The reliability of the control system is a key to making systems run normally. However,in automated processes, the system may be broken which makes the system reach theundesired reactions. Fault tolerant control (FTC) schemes compensate influence of faultsautomatically in presence of faults such that stability can be guaranteed and dynamicperformance can be recovered as possible in the post-fault systems, and the systems run stable.Actuators are subject to be in presence of faults for consisting operation. Fault tolerance foractuators should be considered more carefully. Therefore, focus on actuator failure, in thispaper, firstly, the subject of discrete multi-time-delay systems’ fault-tolerant controller designproblem was systematically studied. Secondly, the subject of continuous multi-time-delaysystems’ fault-tolerant controller design problem was also systematically studied and relevantconclusions were obtained. Finally, a design method of step-by-step fault-tolerant controllerwas proposed and used to solve the fault-tolerant control problems in the four types ofsystems, linear continuous systems, continuous time-delay systems, linear discrete systemsand discrete time-delay systems, and some new research results was accessed.The main content and research works in this paper can be summarized as follows.1. For discrete multi-time-delay systems, Lyapunov stability theory and linear matrixinequality method were used to get the desigh method of discrete multi-time-delay systems’fault-tolerant controller. Firstly, for discrete systems with multi-time-delay in the state,immemorial and memorial state feedback control law were respectively used to get thesufficient condition that ensures systems have state feedback fault-tolerant controllers, statefeedback H∞fault-tolerant controllers, and immemorial state feedback guaranteed costfault-tolerant controllers. Secondly, for uncertain discrete systems with multi-time-delay inthe state, immemorial and memorial state feedback control law were respectively used to getthe sufficient condition that ensures systems have state feedback robust fault-tolerantcontrollers, state feedback robust H∞fault-tolerant controllers, and immemorial state feedbackrobust guaranteed cost fault-tolerant controllers. Finally, for discrete systems with multi-time-delay in the state and control input at the same time, by introducing immemorial statefeedback control law, get the sufficient condition that ensures systems have state feedbackfault-tolerant controllers, state feedback guaranteed cost fault-tolerant controllers, and statefeedback H∞fault-tolerant controllers, when circumstances that systems don’t existuncertainties and exist uncertainties are considered respectively. The correctness and effectiveness of conclusions above has been all verified bysimulation analysis. All the simulation results show that the fault-tolerant controller designednot only makes the fault closed-loop system asymptotically stable, but also allows the systemto meet some certain performance requirements.2. For continuous multi-time-delay systems, Lyapunov stability theory and linear matrixinequality method were used to get the desigh method of continuous multi-time-delaysystems’ fault-tolerant controller. Firstly, for continuous systems with multi-time-delay in thestate, immemorial and memorial state feedback control law were respectively used to get thesufficient condition that ensures systems have state feedback fault-tolerant controllers, statefeedback H∞fault-tolerant controllers, and immemorial state feedback guaranteed costfault-tolerant controllers, the corresponding design methods of optimal guaranteedcost fault-tolerant controller and optimal H∞fault-tolerant controller were also obtained.Secondly, for uncertain continuous systems with multi-time-delay in the state, immemorialand memorial state feedback control law were respectively used to get the sufficient conditionthat ensures systems have state feedback robust fault-tolerant controllers, state feedbackrobust H∞fault-tolerant controllers, and immemorial state feedback robust guaranteed costfault-tolerant controllers, the corresponding design methods of robust optimal guaranteed costfault-tolerant controller and robust optimal H∞fault-tolerant controller also were obtained.Finally, for continuous systems with multi-time-delay in the state and control inputat the same time, by introducing immemorial state feedback control law, get the sufficientcondition that ensures systems have state feedback fault-tolerant controllers, state feedbackguaranteed cost fault-tolerant controllers, and state feedback H∞fault-tolerant controllers,the corresponding design methods of optimal guaranteed cost fault-tolerant controller andoptimal H∞fault-tolerant controller also were obtained, when circumstances that systemsdon’t exist uncertainties and exist uncertainties were considered respectively.The correctness and effectiveness of conclusions above has been all verified bysimulation analysis. All the simulation results show that the fault-tolerant controller designednot only makes the fault closed-loop system stable gradually, but also allows the systemto meet certain property requirements. Compared to general guaranteed cost fault-tolerantcontroller, the optimal guaranteed cost fault-tolerant controller obtained make thecorresponding system performance upper bound smaller, that is, guaranteed cost optimizationproblem played a role of optimizing the upper bound of system performance. Theoptimal H∞fault-tolerant controller design can obtain systems’ minimum disturbancesuppressionγ min, which could be used to design general fault-tolerant controller more effectively, that is, as long as a given H∞performance index could meetγ> γmin, the linearmatrix inequality in the corresponding conclusions must be feasible, and the H∞fault-tolerantcontroller meet performance requirements must be able to obtain.3. For linear continuous systems, a step-by-step fault-tolerant controller design methodwas introduced to get the design method and design procedure of system’ step-by-stepH∞fault-tolerant controller and step-by-step guaranteed cost fault-tolerant controller. Whensystem has actuator failures that can’t be stabilized, effective fault-tolerant controller can’t beobtained by the existing fault-tolerant control methods. This problem can be effectivelysolved by step-by-step fault-tolerant controller design method. As long as these non-stabilityfaults did not occur in the actual-running system, a fault-tolerant controller can be designed tomake the system asymptotically stable and to maintain a certain performance. The mainline of step-by-step fault-tolerant controller design method is making systems’ performancesget better and better under the premise that makes systems asymptotically stable. In the studyof systems’ passive fault-tolerant control theory, this method has certain theoreticalinnovation and practical application.4. For continuous time-delay systems, discrete systems and discrete time-delay systems,by using the proposed step-by-step fault-tolerant controller design method, the design methodand design procedure of systems’ step-by-step guaranteed cost fault-tolerant controller andstep-by-step H∞fault-tolerant controller were obtained.The advantage of the step-by-step fault-tolerant controller design method obtained in thispaper lies in: when these above three types of linear systems exist non-stable actuator faults, itis not feasible to get system fault-tolerant controller design using the existing fault-tolerantcontroller design methods. But using the conclusions obtained in this paper, systems’ fault-tolerant controller design problem can be solved under the condition that the stabilization setisn’t empty. The fault-tolerant controller designed makes the system asymptotically stableand maintaining a certain performance. If the step method designed according to some knownlaw, it also makes system performance getting better gradually when actuator failure occurs.
Keywords/Search Tags:Linear Systems, Multi-time-delay, Linear Matrix Inequality, H∞Control andGuaranteed Cost Control, Fault-tolerant Control, Step-by-step Fault-tolerant Control
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