ERRATA. Aircraft System Identification: Theory and Practice by Vladislav Klein and Eugene A. Morelli

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1 ERRAA Aircraft System Identificatin: hery and Practice by Vladislav Klein and Euene A. Mrelli Knwn errrs are listed belw. Please reprt any ther errrs t e.a.mrelli@nasa.v. his list was last updated n Sunday, January 7, 06. Pae x Line 5, (GLS) shuld be deleted. 3 he expressins fr bdy-axis inertia elements in Eq. (3.6) are incrrect. Eq. (3.6) shuld be: I y + z dm I x + z dm I x + y dm x y z Vlume Vlume Vlume I xy dm = I I yz dm = I I xz dm = I xy yx yz zy xz zx Vlume Vlume Vlume 37 he rtatin matrices in Eq. (3.7) are incrrect. Eq. (3.7) shuld be: x E csψ sinψ 0 csθ 0 sinθ 0 0 u y E = sinψ csψ csφ sinφ v z E 0 0 sinθ 0 csθ 0 sinφ csφ w 39 he sin f the thrust term in Eq. (3.34c) shuld be neative, nt psitive. Eq. (3.34c) shuld be: qs β = CY W + p sinα r csα + cs β sinφ csθ mv V sin β csα + csα sinθ sinα csφ csθ V m 4 he sin f the I xz term in the expressin fr c 8 in Eq. (3.4) shuld be psitive, nt neative. he expressin fr c 8 in Eq. (3.4) shuld be: c8 = Ix Iy Ix + I xz Γ f 7

2 4 he sin f the thrust term in Eq. (3.39c) shuld be neative, nt psitive. Eq. (3.39c) shuld be: qs β = CY W + p sinα r csα + cs β sinφ csθ mv V sin β csα + csα sinθ sinα csφ csθ V m 4 he first term inside the secnd set f parentheses in Eq. (3.43b) cntains a typraphical errr. Eq. (3.43b) shuld be: y E = V csα cs β sinψ csθ + V sinβ ( sinψ sinθ sinφ+ csψ csφ) + V sinα cs β ( sinψ sinθ csφ csψ sinφ) 50 In the first line f Eq. (3.6), in the first term after the secnd equals sin, the factr f shuld be deleted. Eq. (3.6) shuld be: C L V SC V SC V S V V = ρ L = ρ L + ρ V C C L V S L V S L α = ρ = α L α ρ α C C L V S L V S L δ L q = ρ δ = ρ q L 63 At the far riht f the first line in Eq. (3.0a), C D shuld be deleted. Eq. (3.0a) shuld be: qs V qc V = C + C α + C + C V α q m V V D D D Dδ sinα csγ ( θ α ) α m δ 70 he sin f the thrust term in Eq. (3.37a) shuld be neative, nt psitive. Eq. (3.37a) shuld be: qes β = CY + p sinα W E r csαe + cs βe sinφe csθe mve cs βe VE sin βe E csαe + csαe sinθe sinαe csφe csθe V m E f 7

3 85 here shuld be a transpse n the secnd Φ n the riht side f Eq. (4.47). Eq. (4.47) shuld be: P Τ Τ ( i i ) = Φ ( i ) P( i i ) Φ ( i ) + Γ ( i ) Q( i ) Γ ( i ) w w 4 here shuld be an asterisk added t the z variable n the left side f Eq. (5.78), and the z variable in the first line f pae 5 shuld als have an asterisk added. Eq. (5.78) shuld be: X * * z = rz rz rnz 7 In the first sentence f the last pararaph, the wrd variables shuld be inserted after independent. he first sentence f the last pararaph shuld be: Fr all fliht test data sets and many wind tunnel data sets, the measured values f the independent variables are nt unifrmly spaced ver an interval. 6 he element in the secnd rw, secnd clumn f the X matrix shuld have index instead f. he equatin in the middle f pae 6 shuld be: b b β p r δa δr V V b b β p r δa δr X = V V b b β( N) p( N) r( N) δa( N) δr ( N) V V 44 he subscript fr υ n the left side f Eq. (5.35) shuld be z, nt. Eq. (5.35) shuld be: z ˆ ˆ υ i = z i θ θ ξ i i =,,,N 0 3 f 7

4 6 he quantity t kj in the numeratrs f Eq. (5.6) shuld be squared. Eq. (5.6) shuld be: t n n kj tkj kj and k = kj λj λ j= j j= φ φ φ 64 he strict inequality m< np after Eq. (5.69) shuld be m np. 65 he inverse f B in Eq. (5.73) shuld be the pseud-inverse. Eq. (5.73) and the fllwin text shuld be: J ME ( ) z Xθ I 0 ( z Xθ ) = ( d Bθ ) 0 V ( d Bθ ) = + ( z Xθ ) ( z Xθ ) ( d Bθ ) V ( d Bθ ) = z Xθ z Xθ + θ B BB d B V B θ B BB d (5-73) which is the frm f the cst functin fr the Bayesian estimatr, cf. Eq. (4-8) with θ = B BB d and Σ = BV B. p p 85 here shuld be a factr f ½ in frnt f the secnd derivative term in Eq. (6.3). Eq. (6.3) shuld be: J J J ( θ + θ) = J ( θ) + θ + θ θ + θ θ θ θ= θ θ= θ 86 here shuld be a factr f ½ in frnt f the secnd derivative term in Eq. (6.4). Eq. (6.4) shuld be: J J J ( θ + θ) J ( θ) + θ + θ θ θ θ θ θ= θ θ= θ 4 f 7

5 9 he transpse in Eq. (6.30) shuld be applied t the residual vectr n the left, nt the ne n the riht. Eq. (6.30) shuld be: N J i i ˆ θ = v R v i= N ˆ = i i ( i) ( i) z y R z y i= 50 Sme f the numbers in able 7.3 are incrrect. able 7.3 shuld be: able 7.3 Parameter estimatin results fr Schreder sweep frced scillatin n an F-6XL.5 percent mdel Frequency-dmain equatin-errr Frequency-dmain utput-errr Parameter ˆθ s ( ˆ θ ) ˆθ s ( ˆ θ ) A 8.58 x x x x 0 B 3. x x 0 3. x x 0 C.8 x x 0.95 x 0.80 x 0 b.46 x 0.64 x 0.55 x 0.9 x 0 59 he year f publicatin fr Reference 4 shuld be 997, nt he inequality in the cnditin fr Eq. (8.9a) shuld be <, nt. he inequality in the cnditin fr Eq. (8.9a) shuld be: k < 5n p 34 he subscript fr λ in Eq. (0.5b) shuld be β f Eq. (0.5b) shuld be: ( ), nt b f. v i f E i = + f tan + b f + v f i u i β λ β β β 5 f 7

6 343 Eq. (0.6) shuld be the same as Eq. (3.49). Eq. (0.6) shuld be: ( f ) β = tan tan β csα 347 he subscript fr λ in Eq. (0.4b) shuld be β f Eq. (0.4b) shuld be: ( ), nt b f. v i β f i = + λ tan E β f β f β 0 + f + b v i 0 β + f β f u i 354 After Eq. (.3), replace the material up t and includin Eq. (.4) with: he value f ( t ) when t = 0 can be btained usin L'Hpital ˆ s rule, In discrete-time frm, fr t k ( 0) = = k t, ( ω + ω ) t π c k π sinωtk t + sinωck t k 0 k t π ( ωt ωc) ( k t) = ( ωt + ωc) k = 0 π (.4) 356 Eqs. (.) shuld be: i+ ( ) 5a + 0 t a = z k 0 i+ k= i k= i 0 ta = k i z k i+ ( ) 0a + 34 t a = k i z k 0 k= i 6 f 7

7 356 Eq. (.3) shuld be: i+ i+ 34 ˆyi = aˆ0 = z k k i z k 70 7 k= i k= i 379 here shuld nt be a pwer f applied t N in the denminatr n the riht side f Eq. (.66). Eq. (.66) shuld be: N N = N i= 0 k= 0 u i Uw k Uw k N N w i i= 0 * 4 In sectin.8., all instances f the text cmpat_ln_dem and cmpat_lat_dem in any fnt shuld be dca_ln_dem and dca_lat_dem, respectively, in the same fnt as the riinal. 7 f 7