Studies On The Fault Detection Of Fractional-order Linear Systems

The description of some physical systems by the fractional-order model is more accurate than the integer-order.Therefore,the control problem of fractional-order systems is one of the hot research topics.With the further research on the control problem of fractional-order sys-tems,the problem of fault detection for them has received attention.However,the research results of fault detection methods for fractional-order systems are relatively few.Based on H_-and H_?norm performance indicators,this thesis studies the fault detection problem of nominal fractional-order systems,fractional-order systems with norm-bounded uncertainty and fractional-order systems with polytopic uncertainty.The specific contents include:1.The background of the research and related theoretical basis are introduced.First,the research status of fractional-order systems,intege-order systems fault detection and fractional-order systems fault detection is introduced.Then,the theoretical basis of fractional-order sys-tems and some lemmas in this thesis are introduced.2.Based on the H_-/H_?index,the fault detection problem of nominal fractional-order systems is studied.The fault detection problem is transformed into an observer design problem that satisfies the stability condition,the fault sensitivity condition and the disturbance robustness condition.The performance criteria for H_-norm and H_?norm are proposed.Based on this,the method of solving the fault detection observer and the corresponding threshold design method for nominal fractional-order systems are derived.3.Based on the H_-/H_?index,the fault detection problem of fractional-order systems with norm-bounded uncertainty is studied.Based on the H_-norm and the H_?norm index crite-rion,the method of solving the fault detection observer and the corresponding threshold design method for fractional-order systems with norm-bounded uncertainty are derived.4.Based on the H_?filtering method,the fault detection problem of fractional-order systems with norm-bounded uncertainty is studied.A fault detection observer is designed as a reference model for the parameter determination part,and then the fault detection problem is transformed into a standard H_?matching problem.Three methods of solving the fault detection observer and the corresponding threshold design method for fractional-order systems with norm-bounded uncertainty are proposed.5.Based on the H_?filter method,the fault detection problem of fractional-order systems with polytopic uncertainty is studied.A fault detection observer is designed as the reference model for the parameter determination part,and then the fault detection problem is transformed into the standard H_?matching problem.Three methods of solving the fault detection observer for the fractional-order systems with polytopic uncertainty are proposed.Then,a less conserva-tive H_?norm criterion for systems with polytopic uncertainty is derived,and the corresponding methods of solving the fault detection observer and threshold are given.