Unknown input observer for sensor fault detection in linear systems with unmatched uncertainties

Transcription

1 mme.modares.ac.ir * - - myazdi@ut.ac.ir *.). () : : : - Unknowninputobserverforsensorfaultdetectioninlinearsystemswith unmatcheduncertainties EsmaeelBagherpour-Ardakani,MohammadRezaHairi-Yazdi * MohammadMahjoob SchoolofMechanicalEngineering,UniversityofTehran,Tehran,Iran. P.O.B Tehran,Iran.myazdi@ut.ac.ir ARTICLEINFORMATION ABSTRACT OriginalResearchPaper Received3November4 AcceptedJanuary5 AvailableOnline7March5 Keywords: UnknownInputObserver ObserverMatchingCondition ResidualGeneration FaultDetection SensorFault Thispaperisdevotedtosensorfaultdetectioninlinearsystemswithobserver-basedapproach.It is assumed that the system has linear dynamics with the presence of uncertainties. The uncertainties are modeled as unknown input (disturbance), while it is assumed that the wellknownobservermatchingconditionisnot necessarilysatisfied.todecouplethe unknown-input effects, and distinguish their effects from the fault effects, an equivalent dynamic system is proposed thatis independentfrom the unknowninput.theequivalentsystemisconstructed by the use of unique integral filter. The introduced integral-filter, which is called buffer-based integral filter in this paper, has frequency response similar to the low-pass filter. Hence, the capability of noise filtration will also be provided. The construction of the equivalent dynamic systemis achievedfromtheuseofmultiple successivebuffer-basedintegratorsand the number of successive filters is related to relative degree between the unknown input and the sensor output.then,anunknowninputobserverisproposedfortheequivalentsystem,andtherefore, disturbance-decoupled and fault-sensitive with exponential-convergent toward-zero residual vector will be generated. Although the generated residual vector can be used for sensor and actuator fault diagnosis problems, the focus of this paper will be on the sensor fault detection. Finally, the applicability of the proposed method will be investigated via simulation of simple inverted-pendulumonhorizontal-movingcart. ().. -ResidualVector - () -FaultDetection Pleasecitethisarticleusing: : E. Bagherpour-Ardakani, M.R. Hairi-Yazdi, M. Mahjoob, Unknown input observer for sensor fault detection in linear systems with unmatched uncertainties, Modares MechanicalEngineering Vol.5,No.4,pp.9-3,5(InPersian)

2 [4].[5 ] [3]. 6 [3]. 7 [4]. ([6]) 8 ([7]) - [8] - [5].. [9].[ 9] [].. [] [] [].. -. () ) 7. ( -- 3.[] [3].[54] --. [98] [76].[] 4.((3) ).[3] - :. 5-AuxiliaryOutput 6-RelativeDegree 7-Higher-orderSlidingObserver 8-High-GainObserver -Threshold -UnknownInputObserver(UIO) 3-Reduced-Order 4-ObserverMatchingCondition

3 (4) () () = () + () + () (4) (5) () = () () () (5) (5).. () () () (3) () = () [() () ()] (6) 5. () - () (6) () (6) () () = () + () (7)» (7) (7). () «(8). = () () = (() ) () = (8). = 6 (, ). (, ) - (7) 7 () () () = () + () + (() ()) (9). () = () () (9) (7) () = () () = ( )() () ( ).( () - (9) :[7]. () Moore-PenrosePseudo-Inverse 6-Rank-Deficient 7-Luenberger-likeObserver () () = () + () + () = ( ) () = () ( () () ( ( (. (). (, ).( ) - : () () ) : 3 () rank( ) < + (,, ) () () = () 4 :[7] () rank() = rank() Low-passFilter -InvariantZero(TransmissionZero) 3-RosenbrockMatrix 4-Minimum-Phase (3) 94

4 . - - (6) (5) = + + ( ) =. (6) = [ ]. [] (7) = (7) ) ( (8) () () = () ( ) (8) ( ) [ 9]. [, ] [, ] (9). () = () (9) (8) (9). [], = () () () 3-PeakingPhenomenon [3]. (3). = :3, =,, ().[3] = = = :. = (6) () ().rank( ) = rank()3 =. (3) :(3) () () = () + () +(() ()) = ( ) (3) (4) = (4) ( )() 3 = = [ ]. =,, =,, = = =. = + + (, )..(, ) = + (5) = [ ] (, ) : [3]. [4]- -. -(, ). -RelativeDegree -CanonicalControllableForm

5 +-.. [], () [] = () [], = [],, (3) = =, (3) [], (). exp() [], = () () «-». ().. () ( ( - (.«-» (

6 (4) [], (7). () () () rank( ) = rank() (9) [], = [], + [], () = [], (9) - -4 :(3 (9) [], () = [], + [], +() [], (3) [],. [], (3) () = [], [], (3) [], = ( ) [], (3) (3) [], = [], [], (3) : (5).Rank( ) = Rank(). (, ). : () () (5) (3) (3).. () () < (5). [], = [], [], (4) [], = [], [], + [], [], = [], [], +() [] (), +() [], = () [], (4) =,,. = +. () (4) () - -r (5) [], =, = [], + [], + [], (5) (5) <. ().rank() rank() 3. (5), : = [ ], = [], + [], + [], + + [], (6) (5) (6) () = [], = () [], + + [], (7) (8) [ ], = [ ],, =,, =, (8)

7 + + + ( ) = sgn( ) + + ( ) = sg( ) (39) 3. = [ ]. () gn. ( = sgn( )) () (4) = / / / ( )/ / =, = / / / (4) = [.. ]. (4). = (4) (). / /5 ) :.. ( = 5s) 5. / ( () = [. ] ; 5s) 3 / < () () = () + () + () = ( ) () = () + () (33) () (33) < (). (34) () = [], + () = [], + + [], (34) (35), () =,, (35). ()- () (36) (9) [], = [], + [], () = [], +, (36) (3) (37) (3) [], = ( ) [],, (37) (38) () = [], [], +, (38) (39)

8 4 ( 4) ).(4) - - (6) (5) () [] C. Edwards, S. K. Spurgeon, Slidingmodecontrol:theoryandapplication vol.7.london:taylorfrancis, [4] -.(rank() rank()). = =. = (4).- = [ ] = [ ] = [ ] = [ ] () = [ ()], = () ( ) (4) :(43) = {5, 4, 3, } (43) ( ) () /99 /57)

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