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《航空器的稳定与控制》(英文版)Lecture 17 VALIDATION- DETAILS

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6-26 MODEL VALIDATION HoN WELL ARE WE DOING? A RIOUs CODES EXIST IN THE TOoL Box COM PARE CoMPARE MODEL'S SIMULATED O&PRE0cT日0 ITPUT WIT ACTUAL OUTPUT 导哥 N 工05M SIMULATE A叫00E PE COMPUTE PREOICTION ERRORs PREDICT PREDICT FUTURE OVTPUT RESID coM PUTE AND TEST RESI DUALS TRY AT LEAST 0JE工 F NoT. T00F THESE THE LoNGER THE PRE DICTION HoRIzoN, THE MORE DEMANDING THE TASK FOR MODEL

6-27 VALIDAT ION-DETAILS USUALLY WE 0o NoT Wow THEACTUAL SYSTEM DYNAMICS s。Hou0WE EsT丹BLsH工F∞ R MODEL工sGo0? vARIOUs TYPES OF TESTS CAN BE PERFORMED PREDICT(0心fN0s(MU升T10 eRRORS FREQUENCY RES fOWSE FIT MAKE SURE YOU USE DIFFERENT DATA To VALIOATE IF PossIBLE) CAN ALSO PERFoRM A VERY DETA(LED ANALYsIs of THE RESIOvALS L51 ECt)sy(t)-yltlt-1 yt)-(-))-Hk(t) lt)-G ulI CAUED THE 工AAov丹 TIONS PRoC∈s”AA0 CONTA WS A LOT oF INFORMATION AB0UT THE QUALITY OF OUR FIT

6-2 DESiR ABLE PRoPE RTIES FOR TME RESIDUALS O NoRAALLY OIsT &(BUTEO (AT LSAST SYMMETRIc) ZERD MEA O WHITE NOISE PRoCESS ④工DEED6er( UNcD RRE LATE)T PAST INPUTS 0-③: BASICALLY WANT Elt) K LIKE H55UME0F0Re(七 4: IF THERE ARE TRACES oF PAST IUPVT5 N THE RESI DUALS, THEN THERE fAT0Fy() THAT ORIGINATE5f川 T工PuA0 WAs NOT CAPTURE0LL IN OUR MODEL ANALYZE①WTM丹HsTo乐RAF(t) ANALYZE WITH(η:⊥上∈e(t-) 七= RESI DUAL AUTDCORRELATION DESIRED SMAPE ANALYZ④ ⊥e( cR0ss· CoRRELATIO T>0 coRRELATES ELt)WITH OLd u(t-r) DESIRED SHAPE 7

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633 MODEL SEL∈cod BE CAREFUL COMPARING MODELS USING THE SAME SET OF DATA USED TO MAKE THEM A LARGER M00∈ L WILL ALWAYs G叫E A68∈ TTER Fn( LDLER VN6) → MUST U5ENE小DAr千c。ARE GOOD MOOELS CIL STILL GIVE GooD PREDICT IONS ON THE NEW DATA AS WELL TY PICAL SCENARIO OLO DATA Ew OATA HIGHER ORo∈RAs GWE LOWER WN ON MODEL ORDER D DATA ACTUAL ORDER 4 BUT OVERF|T”TME DATA BY INCLVDING KNOWLEDGE OF PAKTICULAR NOISE MEASURED THIS EXTR"NosE"工川 Fo RMAT10A工 S NOT USEUL US SINCE WE PLAN TD USE工T DATA WITH DIfFERENT NOISE

PEo PLE HAVE DEVELOPED MODI FIED COST FUNCTIONS OF THE FoRM 0)(⊥+ FRsτTERA: STANDAR△cosT EcoNO TERM: PROVIDES A MEASORE OF THE DMPLEXITY OF THE mooEL s> TYPICALLY HAVE WITH MODEL SIZE INCREASE,6υ刂↑ 今 GIES Us A wAy7TA0工AN0 VEMENT5 TN VN AGAINST MoDEL COMPLEYITY ● STAND丹R0CRtT∈R升 AKAIKE INF. CRITERION (AIc) MIN DESCR\PTION LENGTH(MOL) UN: LOGN d0wENS(o小0Fe 83 ECTIVE Now:AN了 d, e →FRF1以ED MN了 PLOT J Vs. d AND SELECT LOWESTVALVE 丹cEss1 BLE FoR ARX MODELS工 N ARX STRUC.A

2 STATE SPACE foRM DISCRETE TIME MODELS WRITTEN IN TERMS 0FSτ ATE SPACE0 FFERENCE ERUATIo心 k升xk+Buk K20 K K A55MEX。=0 CONSIDER RESPONSE TD A UNIT DISCRETE 工MULE(工E. k·1 工FFK=0 RESPONSE Y。CX。- ·CX、=cB x,=A6 Y2·C2cA8×z=8 YK Cab K> THE TERMS h=CAB ARE CALLED THE MARKoV PARAMETERS OF THE SYSTEM 今 THE MARKOV PARA飞 ERs ARE THE VALvE OF THE 0ISCRETE-TIME IMPULSE RESPDNSE SEE KAILATH CHEN

HANKEL MATRiX AN IMPORTANT MATR升 SSoCIAT∈0mH MARKov PA RAME TE Rs ELE比 ENTs oF THE HAAKEL MATRIX At毛 THE MARK0 N PARAMETERS-Co小sTNT什LG ANTI-D,AGoNALS R∈ALL工 MPoRTANT1 NoTE THAT8 [8A6] B AB CAB CAB MC - CONTROLLABILITY MATRIX OBSERVABILTf MATRIX CLOSE CONNECTION BETWEEN 8ETEE小 HANKEL MATR AND M。,A

2-·5 INTERESTING CONNECTION BUT How USE THs?.Nov∈wAT 8A8…8 CA CA →THE5∈Tu6LE4T弃N升 URAL sY5EM REALIZAT (ON PRoce5s(地 wTo GET ,6 PRoN1DED THAT WE CAA FIND THE MARKO PA RAMETERS FRoM THE MEASURED OfT

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