Department of Automotive, Combustion Engine and Railway Engineering
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(3) MASTER‘S THESIS ASSIGNMENT I. Personal and study details Student's name:. Soukup Jan. Faculty / Institute:. Faculty of Mechanical Engineering. Department / Institute:. Personal ID number:. 459619. Department of Automotive, Combustion Engine and Railway Engineering. Study program:. Mechanical Engineering. Branch of study:. Transportation, Aerospace and Handling Technology. II. Master’s thesis details Master’s thesis title in English: Two-Level Energy Management Strategy for Hybrid Electric Vehicle Using Planned-Trip Information Master’s thesis title in Czech: Dvouúrovňová řídící strategie pro hybridní vozidlo s využitím informací o plánované trase Guidelines: 1. Analyse the current state of hybrid electric vehicle control and energy management strategies. 2. Focus on parallel HEV configuration. 3. Design an energy management strategy with close-to-optimal results using trip information. 4. Validate the strategy on a created vehicle model. (Thesis will be submitted in English language). Bibliography / sources:. Name and workplace of master’s thesis supervisor: Ing. Rastislav Toman, FME. Department of Automotive, Combustion Engine and Railway Engineering,. Name and workplace of second master’s thesis supervisor or consultant:. Date of master’s thesis assignment: 14.04.2021. Deadline for master's thesis submission: 14.07.2021. Assignment valid until: 19.09.2021 ___________________________. ___________________________. ___________________________. Ing. Rastislav Toman. doc. Ing. Oldřich Vítek, Ph.D.. prof. Ing. Michael Valášek, DrSc.. Supervisor’s signature. Head of department’s signature. Dean’s signature. III. Assignment receipt The student acknowledges that the master’s thesis is an individual work. The student must produce his thesis without the assistance of others, with the exception of provided consultations. Within the master’s thesis, the author must state the names of consultants and include a list of references.. . Date of assignment receipt. CVUT-CZ-ZDP-2015.1. Student’s signature. © ČVUT v Praze, Design: ČVUT v Praze, VIC.
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(20) 0. t. tf. 0. t. tf.
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(23) Td x u.
(24) T. u. x. x.
(25) x1 xi B. A1 Ai. x2. A2 ,. u u. B..
(26) µ µ. 0. 1. ξ1. µ ξ1. J J( ) = g. !. tf. g( (t), (t), t) t t0.
(27) ṁf. t0 tf t0. tf.
(28) uk Jk,k+1 ∗ u∗k+1 Jk+1,n. x. x. x(n). x(0). x(n). t. t. n×m. m. n x(n). u u u∗ Jk,k+1. ∗ Jk+1,n. k+1 k+1. x(n) u∗k (k) =. ∗ Jk,n =. ". u. #. n×m. ∗ Jk,k+1 (x(k), u(k)) + Jk+1,n (x(k + 1)). $%.
(29) x(n) k. x∗. H ( (t), (t), (t), t) ! g( (t), (t), t) +. T. x. (t)[ ( (t), (t), t)]. g. ˙ (t) = ( (t), (t), t) .. H ( (t),. (t),. (t), t) ≤ H ( (t), (t),. t ∈ [t0 , tf ]. H ( (t),. (t),. ∂H ˙ (t) = ( (t), (t), (t), t) ∂ ∂H ˙ (t) = − ( (t), (t), (t), t) ∂ (t), t) ≤ H ( (t), (t), (t), t). (t), t) ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭. ∀t ∈ [t0 , tf ].
(30) *. ∂h ( (tf ), tf ) − ∂. (tf ). +T. δ. f. *. + H ( (tf ),. (tf ),. + ∂h (tf ), tf ) + ( (tf ), tf ) δtf = 0 ∂t. h. δ. f. δtf. ˙ H (x(t), u(t), p, t) = ṁ (u(t), t) + p ξ(u(t), t) ξ˙. ṁ. p p. p1.
(31) p1 > p. p. p2 < p. 0. t. tf.
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(36) T. u.
(37) m .. C. .. .. .. V P i η. . .. f. . .. cx Ax δ η i i η r g ρ ξ0 ξf ξ ξ. . . 3.78, 2.05, 1.28, 0.94, 0.78, 0.67 . . . − . − . . . . .. . . . .. . . . ..
(38) R. Rα. G Fx. R. α. R Fx. R. v̇(t) =. Rα. G. α. 1 (Fx (t) − Rα (t) − R (t) − R (v(t))) mδ. m. δ. Fx G R. Rα R 1 ρ cx Ax v 2 (t) 2 Rα (t) = mgf (α(t)) R (t) =. R (t) = mgf cx f. (α(t)). Ax. g α. ∆t ∆v(t) 1 = (Fx (t) − Rα (t) − R (t) − R (v(t))) ∆t mδ. Fx (t) = mδ. ∆v(t) + Rα (t) + R (t) + R (v(t)) ∆t. Fx Fx (t) = (T (t) + T (t)i η ) i (t) i η r i. i. η =η η r. i. η.
(39) Fx /2 i ,η. T. T ,i ,η. i ,η r. Fx /2. ω (t) =. ω (t) = ω(t) i. ω ω ω(t) =. T. (t) = T (t) + T (t)i η =. v(t) i (t) i r. mδ ∆v(t) ∆t + Rα (t) + R (t) + R (v(t)) i (t) i η r. ˙ = − I(t) ξ(t) C I C. R(ξ) I V0 (ξ) +. P. −. V0 P. R.
(40) P R(ξ(t))I(t)2 − V0 (ξ(t))I(t) + P (t) = 0 R. V0. RI 2. I(t) =. P. V0 (ξ(t)) ±. , V02 (ξ(t)) − 4R(ξ(t))P (t) 2R(ξ(t)). (ξ(t)) ≤ P (t) ≤ P. ,. (ξ(t)). 1.4 R ( Ω). 4 V0 ( ). ,. 3.8. 1.2. 3.6 0.2. 0.4. 0.6. 0.2. 0.8. 0.4. 0.6. 0.8. ξ (−). ξ (−). ). V0 = s V 0 s R = R p s. p. R∗ = R c. C C∗ ∗.
(41) P P (t). P (t) =. P (t). η. =. T (t) ω (t) (η η (T (t), ω (t))). η. T (t). η T ω T. ,. (ω (t)) ≤ T (t) ≤ T. 0 ≤ ω (t) ≤ ω. ,. (ω (t)). ,. 40. 200. ) 0. 0. T (. T (. ). 20. −20 −200. 0. 2,000. 4,000 (. 6,000 −. 8,000. −40. 0. 4,000. 8,000 (. ). T. ω. ω. 0 ≤ T (t) ≤ T ,. ≤ ω (t) ≤ ω. ṁ (t) = T (t) ω (t). ,. (ω (t)). ,. (T (t), ω (t)). 12,000 −. ). 16,000.
(42) ). 150. T (. 100. 50. 2,000. 4,000 (. −. 6,000 ). /. ∗. J( ) =. !. tf. ṁf ( (t), t) t t0.
(43) ≤ ξ(t) ≤ ξ. ξ P T. ,. ,. (ξ(t)) ≤ P (t) ≤ P. ,. (ξ(t)). ,. (ω (t)). (ω (t)) ≤ T (t) ≤ T. 0 ≤ ω (t) ≤ ω. ω. ,. 0 ≤ T (t) ≤ T. ,. ≤ ω (t) ≤ ω. ,. (ω (t)). ,. t0 = 0, tf = T ξ(t0 ) = ξ0 , ξ(tf ) = ξf T ξ ˙ ˙ (t) = [ξ(t)]. (t) = [T (t)]. T (t) = T. J(T ) =. !. (t) − T (t) i η. T. T (T (t), t) ω(t) 0. (T (T (t), t), ω(t)) t.
(44) T. T. J( ) =. !. tf. g( (t), (t), t) t t0. ˙ (t) = ( (t), (t), t). ∗. ∗. ∂H ( (t), (t), (t), t) ∂ ∂H ˙ (t) = − ( (t), (t), (t), t) ∂ (t), t) ≤ H ( (t), (t), (t), t) ˙ (t) =. H ( (t),. (t),. H. H ( (t), (t), (t), t) ! g( (t), (t), t) +. T. ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭. ∀t ∈ [t0 , tf ]. (t)[ ( (t), (t), t)] t ∈ [t0 , tf ]. ˙ = − I(t) ˙ (t) = ξ(t) C.
(45) (t) = T (t). J(T ) =. !. tf. ṁf (T (t), t) t t0. ˙ H (ξ(t), T (t), p(t), t) = ṁf (T (t), t) + p(t)[ξ(ξ(t), T (t), t)] p ṗ(t) = −. ∂H (ξ(t), T (t), p(t), t) ∂ξ p. (T (T (t), t), ω(t)) − , 2 V0 (ξ(t)) − V0 (ξ(t)) − 4R(ξ(t))P (T (t)) − p(t) 2R(ξ(t))C. H (ξ(t), T (t), p(t), t) = T (T (t), t) ω(t). p. H (T (t), p(t), t) = T (T (t), t) ω(t) (T (T (t), t), ω(t))− , 2 V0 − V0 − 4RP (T (t)) − p(t) 2RC. ṗ(t) = −. ∂H (T (t), p(t), t) = 0 ∂ξ.
(46) 1.5. 4. R ( Ω). V0 ( ). 3 2. 1. 0.5 1 0. 0.2. 0.4. 0.6. 0. 0.8. 0.2. ξ (−). 0.4. 0.6. 0.8. ξ (−). p. p. p. p. H η̄ ṁ = C V η̄ η η̄ ξ˙. ṁ =. C V η̄ η η̄ ˙ ξ = p0 ξ˙ H η̄. p0. T.
(47) T p. p. ·10−4. p = −0.3 p = −0.35 p = −0.4. H. 6. H. 8. 8. p = −0.3 p = −0.35 p = −0.4. ·10−4. 7 4 6 0. 50 T ( T. −100. T. ). =. −50. 0. T (. T. T. ). = p. p∗ = −0.35. ξ(tf ). ξf p ξ(tf ). ξ0 =. ξf. ξ ±. ξ ξ. ∆ξf = 0.003.
(48) 0.8. p0 p1 p2 p3 p4 p5 p6. ξ (−). 0.75. 0.7. = −0.393 = −0.202 = −0.249 = −0.281 = −0.301 = −0.286 = −0.289. 0.65. 0.6. 0. 200. 400. T. t( ) p. ξ (−). 0.9 ξ. 0.8. 0.7 ξ. 0.6 0. 200. 400 t( ). (t) ≥ h1 (t) = ξ. − ξ(t) ≥ 0. h2 (t) = ξ(t) − ξ. ≥0. ν L. ˙ h11 (t) = −ξ(T (t)) ˙ h1 (t) = ξ(T (t)) 2. T H.
(49) L (T (t), p(t), ν(t), t) = H (T (t), p(t), t) + ν(t). 1. (T (t)) =. ˙ = ṁ (T (t), t) + (p(t) − ν1 (t) + ν2 (t)) ξ(T (t)) 1. ≥. ξ˙ ≤ 0. ṗ(t) = −. ∂L (T (t), p(t), ν(t), t) = 0 ∂ξ ξ. L ν τ p(τ + ) = p(τ − ) − η(τ ) τ+. ∂ (τ ) ∂ξ. τ−. η. τi. p. p(τ + ) = p(τ − ) ± η(τ ) ξ ξ. ξ. η(τi ) 1. τi. ≥. p. [0, T ]. pi. τi p. τi p 1. ξ(τi ). ≥. τi [0, τi ]. t10 = 0, t1f = τi , ξ(t10 ) = ξ0 , ξ(t1f ) = ξ t20 = τi , t2f = T, pi. ξ. ξ(t20 ) = ξ. , ξ(t1f ) = ξf. [τi , T ].
(50) 0.9 ξ. ξ (−). 0.8. 0.7 ξ. 0.6. 0.5. −0.1. τ1. τ0 τ2. T. t( ) p. ξ. ξ. 0.8. ξ (−). p. 0 −0.05. 0.7. ξ. 0.6 0. 200. 400 t( ).
(51) T T. T. ω f (x, y) = a00 + a10 x + a01 y + a20 x2 + a11 xy + a02 y 2 + + a30 x3 + a21 x2 y + a12 xy 2 + a03 y 3 x. y. aij x y. f (x, y) = a00 + a10 x + a01 y + a20 x2 + a11 xy + a02 y 2 + a21 x2 y + a12 xy 2 + a03 y 3 + + a22 x2 y 2 + a13 xy 3 + a04 y 4 + a23 x2 y 3 + a14 xy 4 + a05 y 5. 200. R2 = 0.836. ) 0. −200. T (. T (. ). 200. 0. 2,000. 4,000 (. 6,000 −. ). 8,000. 0. −200. 0. 2,000. 4,000 (. 6,000 −. ). 8,000.
(52) 20. 20. 0. T (. T (. R2 = 0.683. ). 40. ). 40. −20 −40. 0 −20. 0. 4,000. 8,000 (. 12,000 −. −40. 16,000. 0. 4,000. ). 8,000 (. 16,000. ). R2 = 0.997. ). 150. ). 150. 12,000 −. T (. 100. T (. 100. 50. 50. 2,000. 4,000 (. −. 6,000. 2,000. ). 4,000 (. −. 6,000 ). −. .. ∆ξ = 0.001.
(53) 4 250 700 1,600 3,700 / ∆ξ = 0.001. T. = 0. T. p. p.
(54) ξ (−). 0.7. 0.65. 0.6 0. 2. 4 s(. 6. ) p. p. ξ T. ξ. T. ξ. p p(t) = p (t) + K (ξ (t) − ξ(t)) + K. !. (ξ (t) − ξ(t)) t ξ ξ. p.
(55) p ξ. e. +. +. +. p ξ. T. −. T ξ. K. K. K. K. p. ξf.
(56) ξ (−). 0.7. p. 0.65. −0.34 −0.34 −0.35 0. 2. 4. 6. t( ). T. p.
(57) 150. ). 100. 100. T(. T(. ). 150. 50. 50. 2,000. 4,000 (. −. 6,000. ). 2,000. 4,000 (. −. 6,000. ) 4.88. 4.88 3.92. 3.85 /. / y. y.
(58) T. ξ. ( ( R V0 f rd cx. ,T) ,T) ξ ξ. f( f(. ,T) ,T).
(59) ←#. ∆. ←# ←# ←# ←#. 3.85 3.62 6.26 6.24 44.4 47.1 55.5 122.4 123.9. 14 117 121 63 600 609 537 1486 1384. −116 −15 −67 −117 −777 −464 −614 −1163 −1718. −102 102 54 54 −177 145 −77 323 −334. −. / 26.8 30.3 35.4 40.4 63.9 69.2 74.2 79.6 81.1. 33.2 32.0 33.5 36.0 60.4 73.7 78.1 80.9 77.9. 30.6 29.6 33.8 36.7 66.9 63.8 74.3 80.5 82.7. 29.9 29.9 34.4 42.4. −.
(60) / ). 40. v(. 60. 20. h( ). 0 300 250 200 0. 1. 2. / ). 40. v(. s(. 20. 3. 4. ). h( ). 0 300 250 200 0. 1. 2 s(. ). s(. ). 3. / ). 80 60. v(. 40 20. h( ). 0 360 320 280 0. 2. 4. 6.
(61) / ). 80 60. v(. 40 20. h( ). 0 360 320 280 0. 1. 2. 3 s(. 4. 5. 6. ). v(. / ). 100 50. h( ). 0 600 500 0. 10. 20. / ). 100. v(. 50. h( ). s(. 0 350 300 250 0. 10. 30. 20 s(. 40. ). 30 ). 40. 50.
(62) / ) v(. 50. h( ). 100. 0 400 350 300 250 0. 10. 20. 30 s(. 40. 50. ). / ). 100. v(. 150. 50. h( ). 0 600 400 200 0. 20. 40. 60 s(. 80. 100. 120. 80. 100. 120. ). / ). 50. h( ). 100. v(. 150. 0 600 400 200 0. 20. 40. 60 s(. ). 60.
(63) T. m = −(ξ(tf ) − ξf ) C V. η η̄ η̄ η H η̄. ξf. m = −(ξ(tf ) − ξf ) C V. ξf. 1 η η̄ η̄ η H η̄. ξ. ξ T. ξf.
(64) T. T. T. >0. < C1 T ξ(t) > ξ. ξ(t) < ξ. T =T. T =T. T =0. ξ(t) < ξf. ξ(t) < ξ. ξ(t) > ξ. T =0. T = (ξ(t) − ξf ) T. T = C2 T. T = C3 T. C1 C2 T. C2.
(65) 0.8 ξ (−). ξ (−). 0.8 0.7. / ). 0.6. 100 50 0. v(. v(. / ). 0.6. 0.7. 0. 500. 1,000. 1,500. t( ). 100 50 0. 0. 500. 1,000. 1,500. t( ) 5.26 4.77 4.71. 5.26 4.61 4.5 /. /.
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(67) ∆. =. −. − ∆. −. =. −.
(68) ←* ←* ←* ←*. ←* ←* ←* ←*. 19.6 (21.3) 2.1 (1.7) 4.4 (4.2) 7.3 (6.9) 4.4 (4.2) 1.6 (1) 1.4 (1) 1.7 (1.7) 1.5 (1.9). 12.6 (13.7) 0.2 (0.4) 1.8 (2.3) 3.1 (3.7) 1.7 (2.1) 0.4 (0.6) 0.1 (0.4) 0.6 (0.8) 0.7 (1). ←* ←*. 17 (17.6) 1.3 (1.7) 3.6 (4.7) 6.1 (6.1) 4 (4.4) 1 (0.9) 1.3 (1) 1.1 (1.3) 2.1 (1.9). 11.2 (12.9) −0.5 (0.2) 1.2 (2.4) 1.1 (3.1) 1.3 (2.1) 0.3 (0.6) 0.1 (0.5) 0.3 (0.7) 0.6 (1). 4.1 (4) 4.6 (4.6) 3 (3.4). 18.6 (21) 0.3 (2.1) 2.3 (4.9) 7 (7.2) 3.9 (3.8) 1 (1.5) 1.6 (1.4) 1.1 (1.2) 2.1 (2). 9.9 (11.3) 0.3 (1.3) 1 (2.1) 3.5 (4.8) 1.3 (1.9) 0.2 (0.9) 0.1 (0.7) 0.1 (0.6) 0.6 (1). 3.7 (3.7) 4.2 (3.9) 3.3 (3.1). 19.9 (19.8) 3.5 (5.7) 1.2 (3.6) 5.3 (5.9). . . . .. . . .. 12.1 (14.6) 0.9 (2) 0.7 (1.8) 2.6 (3.4). 3.8 (3.8) 4.3 (4) 3.3 (3.2). . . .. . . . . . . . ..
(69) ..
(70) ξ (−). 0.8. 0.7 0.6 60 40 20 0 300. 0.7. / ). 0.6 100. v(. 50. h( ). h( ). v(. / ). ξ (−). 0.8. 250 200 0. 1. 2 s(. 3. 0 600 500. 4. 0. 10. ). 20 s(. 30. 40. ). 4.21. 4.88. 2.04. 4.13 3.94 3.92. 1.32 1.3 /. /. 0.8 ξ (−). ξ (−). 0.8 0.7. / ). 100. v(. 50 0 350 300 250. h( ). h( ). v(. / ). 0.6. 0.7 0.6 150 100 50 0 600 400 200. 0. 15. 30 s(. 45. 0. 30. 60 s(. ). 90. 5.28 5.03 4.98 4.98 /. 120. ) 5.68 5.43 5.37 5.36 /.
(71) p. p. p. ξ (−). 0.8. 0.7 0.6 80 60 40 20 0 360 340 320 300 280. 0.7. v(. / ). 0.6. h( ). h( ). v(. / ). ξ (−). 0.8. 40 20 0 300 250 200. 0. 2. 4 s(. 6. 0. ). 1. 2 s(. 3 ). 4.26. 8.02 7.27 6.99 6.81. 3.04 2.81 2.78 /. /. p.
(72) 0.8 ξ (−). 0.7. v(. / ). 0.6 60 40 20 0 300. h( ). h( ). v(. / ). ξ (−). 0.8. 250 200. 0.7 0.6 150 100 50 0 600 400 200. 0. 1. 2 s(. 3. 4. 0. 30. 60 s(. ). 90. 4.21. 5.37 5.04 4.93 4.94. 2.04 1.32 1.3 /. 120. ). /.
(73) 0.8 ξ (−). 0.7. 0.7 0.6. v(. / ). 0.6 80 60 40 20 0 360 340 320 300 280. h( ). h( ). v(. / ). ξ (−). 0.8. 0. 2. 4 s(. 100 50 0 350 300 250 0. 6. 15. 30 s(. ). 45. ). 6.5. 5.37 5.04 4.99 4.96. 5.19 5.11 4.95 /. /.
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(75) 0.8 ξ (−). ξ (−). 0.8 0.6. 0.6 0.4. / ). 100. v(. 50. h( ). 0 400 350 300 250. 150 100 50 0 600 400 200. 40. 60. s(. 80. 0. 100. 30. 60 s(. ). 90. 5.68 4.18 3.93 3.95. /. /. ξ (−). 0.8 0.6 0.4 150 100 50 0 600 400 200 0. 30. 120. ). 5.23 3.26 3.06 3.07. / ). 20. v(. 0. h( ). h( ). v(. / ). 0.4. 60 s(. 90. 120. ) 5.37 3.62 3.45 3.45 /.
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(80) Ax C cx f Fx g h H H i I J K K L m m p P rd R R R Rα s t T u v V V0. x α δ η ν ξ ρ τ ω.
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(90) 0.8 ξ (−). ξ (−). 0.8 0.7. / ). 40. v(. 20 0 300. h( ). h( ). v(. / ). 0.6. 250 200 0. 1. 2 s(. 3. 0.7 0.6 60 40 20 0 300 250 200. 4. 0. 1. ). 2 s(. 3 ). 4.21. 4.11. 2.04. 1.71. 1.32 1.3. 0.9 0.83. /. /. ξ (−). 0.8. 0.7 0.6 60 40 20 0 300. 0.7. v(. / ). 0.6. h( ). v(. / ). ξ (−). 0.8. h( ). 4. 250 200 0. 1. 2 s(. 3. 4. 40 20 0 300 250 200 0. 1. ). 2 s( 1.75. 0.96 0.96. 1.19 1.09 /. 4 3.99. 4.1 1.95. 3 ). /.
(91) 0.8 ξ (−). ξ (−). 0.8 0.7. / ). 0.6. 40. v(. 20 0 300. h( ). h( ). v(. / ). 0.6. 0.7. 250 200. 40 20 0 300 250 200. 0. 1. 2 s(. 3. 0. 1. ). 2 s(. 3 ) 8.18. 8.13. 7.05 6.95 6.91. 7.05 6.88 6.91 /. /. 0.8 ξ (−). ξ (−). 0.8 0.7. / ). 0.6. 40. v(. 20 0 300. h( ). h( ). v(. / ). 0.6. 0.7. 250 200. 40 20 0 300 250 200. 0. 1. 2 s(. 3. 0. ). 1. 2 s(. 3 ) 8.02 7.27 6.99 6.81. 8.4 7.21 7.19 7.04 /. /.
(92) 0.8 ξ (−). ξ (−). 0.8 0.7. / ). 0.6. v(. 60 40 20 0 360 340 320 300 280. h( ). h( ). v(. / ). 0.6. 0.7. 0. 2. 4 s(. 6. 60 40 20 0 360 340 320 300 280 0. 2. ). 4 s(. 6. ) 6.42. 6.22. 5.06 4.83 4.76. 5.02 4.75 4.76 /. /. 0.8 ξ (−). ξ (−). 0.8 0.7. / ) v(. 60 40 20 0 360 340 320 300 280. h( ). h( ). v(. / ). 0.6. 0. 2. 4 s(. 6. 0.7 0.6 80 60 40 20 0 360 340 320 300 280 0. ). 2. 4 s(. 6. ) 6.5. 6.51. 5.19 5.11 4.95. 5.11 4.96 4.79 /. /.
(93) 0.8 ξ (−). ξ (−). 0.8 0.7. / ). 0.6. v(. 60 40 20 0 360 340 320 300 280. h( ). h( ). v(. / ). 0.6. 0.7. 0. 2. 4 s(. 6. 60 40 20 0 360 340 320 300 280 0. 2. ). 4 s(. 3.25 2.91 2.93. 3.06 2.78 2.78. /. /. ξ (−). 0.8. 0.7. v(. / ). 0.6 80 60 40 20 0 360 340 320 300 280. h( ). / ). ξ (−). 0.8. v(. ) 4.56. 4.65. h( ). 6. 0. 2. 4 s(. 6. 0.7 0.6 80 60 40 20 0 360 340 320 300 280 0. ). 2. 4 s(. 4.61 3.17 2.85 2.84 /. 6. ) 4.26 3.04 2.81 2.78 /.
(94) ξ (−). 0.8. 0.7. 0.7. 0.6. 0.6. 100. 100. / ). / ). ξ (−). 0.8. v(. 50. 0. h( ). 600 500 20 s(. 30. 0 600 500. 40. 0. 10. ). 20 s(. 30. 4.88. 5.1. 4.13 3.94 3.92 /. /. ξ (−). 0.8 0.7 0.6 100 50 0 600 500 0. 10. 40. ). 4.36 4.14 4.15. / ). 10. v(. 0. h( ). h( ). v(. 50. 20 s(. 30. 40. ) 5 4.34 4.14 4.15 /.
(95) 0.8 ξ (−). ξ (−). 0.8 0.7. 0.7. / ). 0.6. 100. 100. v(. 50. h( ). 0 350 300 250 15. 30 s(. 50 0 350 300 250. 45. 0. 15. ). 30 s(. 45. ) 5.28 5.03 4.98 4.98. 5.21 4.95 4.86 4.89 /. /. ξ (−). 0.8 0.7. / ). 0.6. v(. 0. h( ). h( ). v(. / ). 0.6. 100 50 0 350 300 250 0. 15. 30 s(. 45. ) 5.37 5.04 4.99 4.96 /.
(96) 0.8 ξ (−). ξ (−). 0.8 0.7. 0.7. / ). 0.6. 100. v(. 50. h( ). 0 400 350 300 250 20. 40. s(. 100 50 0 400 350 300 250. 60. 0. 20. ). s(. 40. 5.19 4.83 4.76 4.78 /. /. / ). ξ (−). 0.8 0.7 0.6 150 100 50 0 400 350 300 250 0. 60. ). 5.05 4.7 4.63 4.65. v(. 0. h( ). h( ). v(. / ). 0.6. 20 s(. 40. 60. ) 5.26 4.9 4.82 4.82 /.
(97) 0.8 ξ (−). ξ (−). 0.8 0.7. 0.7. / ). 0.6. 100. v(. 50 0. h( ). 600 400 200 60 s(. 90. 100 50 0 600 400 200. 120. 0. 30. ). 60 s(. 90. 5.65 5.42 5.36 5.34 /. /. ξ (−). 0.8 0.7 0.6 150 100 50 0 600 400 200 0. 30. 120. ). 5.73 5.44 5.34 5.34. / ). 30. v(. 0. h( ). h( ). v(. / ). 0.6. 60 s(. 90. 120. ) 5.68 5.43 5.37 5.36 /.
(98) ξ (−). 0.8. 0.7. h( ). v(. / ). 0.6 150 100 50 0 600 400 200. 0.7 0.6 150 100 50 0 600 400 200. 60 s(. 90. 120. 0. 30. ). 60 s(. 90. 5.32 4.93 4.82 4.83 /. /. ξ (−). 0.8 0.7 0.6 150 100 50 0 600 400 200 0. 30. 120. ). 5.6 5.18 5.1 5.08. / ). 30. v(. 0. h( ). h( ). v(. / ). ξ (−). 0.8. 60 s(. 90. 120. ) 5.37 5.04 4.93 4.94 /.
(99) 0.8 ξ (−). ξ (−). 0.8 0.7. / ). 40. v(. 20 0 300. h( ). h( ). v(. / ). 0.6. 250 200 0. 1. 2 s(. 3. 0.7 0.6 60 40 20 0 300 250 200. 4. 0. 1. ). 2 s(. 3 ). 4.21. 4.11. 3.2 2.72 2.65. 2.83 2.31 2.27. /. /. ξ (−). 0.8. 0.7 0.6 60 40 20 0 300. 0.7. v(. / ). 0.6. h( ). v(. / ). ξ (−). 0.8. h( ). 4. 250 200 0. 1. 2 s(. 3. 4. ). 40 20 0 300 250 200 0. 1. 2 s(. 4.1. 3. 4. ) 4. 2.97 2.56 2.51. 2.95 2.47 2.37. /. /.
(100) 0.8 ξ (−). ξ (−). 0.8 0.7. / ). 0.6. 40. v(. 20 0 300. h( ). h( ). v(. / ). 0.6. 0.7. 250 200. 40 20 0 300 250 200. 0. 1. 2 s(. 3. 0. 1. ). 2 s(. 3 ) 8.18 7.24 7.27 7.22. 8.13 7.21 7.19 7.17 /. /. 0.8 ξ (−). ξ (−). 0.8 0.7. / ). 0.6. 40. v(. 20 0 300. h( ). h( ). v(. / ). 0.6. 0.7. 250 200. 40 20 0 300 250 200. 0. 1. 2 s(. 3. 0. ). 1. 2 s(. 3 ) 8.02 7.23 7.16 7.07. 8.41 7.52 7.5 7.41 /. /.
(101) 0.8 ξ (−). ξ (−). 0.8 0.7. / ). 0.6. v(. 60 40 20 0 360 340 320 300 280. h( ). h( ). v(. / ). 0.6. 0.7. 0. 2. 4 s(. 6. 60 40 20 0 360 340 320 300 280 0. 2. ). 4 s(. 6. ) 6.42. 6.23. 5.46 5.39 5.31. 5.4 5.29 5.26 /. /. 0.8 ξ (−). ξ (−). 0.8 0.7. / ) v(. 60 40 20 0 360 340 320 300 280. h( ). h( ). v(. / ). 0.6. 0. 2. 4 s(. 6. 0.7 0.6 80 60 40 20 0 360 340 320 300 280 0. ). 2. 4 s(. 6. ) 6.5. 6.51. 5.58 5.53 5.46. 5.52 5.46 5.38 /. /.
(102) 0.8 ξ (−). ξ (−). 0.8 0.7. / ). 0.6. v(. 60 40 20 0 360 340 320 300 280. h( ). h( ). v(. / ). 0.6. 0.7. 0. 2. 4 s(. 6. 60 40 20 0 360 340 320 300 280 0. 2. ). 4 s(. 6. ) 4.56. 4.65. 3.57 3.52 3.43. 3.74 3.6 3.57 /. /. ξ (−). 0.8. 0.7. v(. / ). 0.6 80 60 40 20 0 360 340 320 300 280. h( ). h( ). v(. / ). ξ (−). 0.8. 0. 2. 4 s(. 6. 0.7 0.6 80 60 40 20 0 360 340 320 300 280 0. ). 2. 4 s(. 6. ) 4.27. 4.61. 3.47 3.36 3.33. 3.67 3.51 3.45 /. /.
(103) ξ (−). 0.8. 0.7. 0.7. 0.6. 0.6. 100. 100. / ). / ). ξ (−). 0.8. v(. 50. 0. h( ). 600 500 20 s(. 30. 0 600 500. 40. 0. 10. ). 20 s(. 30. 4.88 4.42 4.35 4.31 /. /. ξ (−). 0.8 0.7 0.6 100 50 0 600 500 0. 10. 40. ). 5.1 4.65 4.56 4.54. / ). 10. v(. 0. h( ). h( ). v(. 50. 20 s(. 30. 40. ) 5 4.6 4.54 4.51 /.
(104) 0.8 ξ (−). ξ (−). 0.8 0.7. 0.7. / ). 0.6. 100. 100. v(. 50. h( ). 0 350 300 250 15. 30 s(. 50 0 350 300 250. 45. 0. 15. ). 30 s(. 45. ) 5.28 5.06 5.05 5.03. 5.21 4.98 4.96 4.95 /. /. ξ (−). 0.8 0.7. / ). 0.6. v(. 0. h( ). h( ). v(. / ). 0.6. 100 50 0 350 300 250 0. 15. 30 s(. 45. ) 5.37 5.13 5.12 5.08 /.
(105) 0.8 ξ (−). ξ (−). 0.8 0.7. 0.7. / ). 0.6. 100. v(. 50. h( ). 0 400 350 300 250 20. 40. s(. 100 50 0 400 350 300 250. 60. 0. 20. ). s(. 40. 5.19 4.92 4.92 4.89 /. /. / ). ξ (−). 0.8 0.7 0.6 150 100 50 0 400 350 300 250 0. 60. ). 5.06 4.78 4.78 4.76. v(. 0. h( ). h( ). v(. / ). 0.6. 20 s(. 40. 60. ) 5.27 5 4.99 4.96 /.
(106) 0.8 ξ (−). ξ (−). 0.8 0.7. 0.7. / ). 0.6. 100. v(. 50 0. h( ). 600 400 200 60 s(. 90. 100 50 0 600 400 200. 120. 0. 30. ). 60 s(. 90. 5.65 5.47 5.45 5.42 /. /. ξ (−). 0.8 0.7 0.6 150 100 50 0 600 400 200 0. 30. 120. ). 5.73 5.52 5.48 5.47. / ). 30. v(. 0. h( ). h( ). v(. / ). 0.6. 60 s(. 90. 120. ) 5.68 5.48 5.48 5.44 /.
(107) ξ (−). 0.8. 0.7. h( ). v(. / ). 0.6 150 100 50 0 600 400 200. 0.7 0.6 150 100 50 0 600 400 200. 60 s(. 90. 120. 0. 30. ). 60 s(. 90. 5.32 5.05 5.02 5 /. /. ξ (−). 0.8 0.7 0.6 150 100 50 0 600 400 200 0. 30. 120. ). 5.6 5.33 5.29 5.27. / ). 30. v(. 0. h( ). h( ). v(. / ). ξ (−). 0.8. 60 s(. 90. 120. ) 5.37 5.15 5.12 5.09 /.
(108) 0.8 ξ (−). ξ (−). 0.8 0.6. 0.6. / ). 0.4. 100. v(. 50. h( ). 0 400 350 300 250 40. 60. s(. 80. 100 50 0 400 350 300 250. 100. 0. 20. ). 60. 80. ) 3.26 3.06 3.07 /. /. 0.8 0.6 0.4. 100 50 0 400 350 300 250 0. 20. 100 5.23. 5.13. ξ (−). 40 s(. 3.15 2.93 2.94. / ). 20. v(. 0. h( ). h( ). v(. / ). 0.4. 40 s(. 60. 80. 100. ) 5.31 3.27 3.06 3.07 /.
(109) 0.8 ξ (−). ξ (−). 0.8 0.6. 0.6. / ). 0.4. 100. v(. 50 0. h( ). 600 400 200 60 s(. 90. 100 50 0 600 400 200. 120. 0. 30. ). 90. 5.65 4.15 3.91 3.93. /. /. 0.6 0.4 150 100 50 0 600 400 200 0. 30. 120. ). 4.21 3.94 3.94. 0.8 ξ (−). 60 s(. 5.73. / ). 30. v(. 0. h( ). h( ). v(. / ). 0.4. 60 s(. 90. 120. ) 5.68 4.18 3.93 3.95 /.
(110) ξ (−). 0.8. 0.6. 0.6 0.4. 150 100 50 0 600. 150 100 50 0 600. h( ). v(. / ). 0.4. 400 200. 400 200. 60 s(. 90. 120. 0. 30. ). 90. 5.32 3.51 3.34 3.35. /. /. 0.6 0.4 150 100 50 0 600 400 200 0. 30. 120. ). 3.8 3.63 3.61. 0.8 ξ (−). 60 s(. 5.6. / ). 30. v(. 0. h( ). h( ). v(. / ). ξ (−). 0.8. 60 s(. 90. 120. ) 5.37 3.62 3.45 3.45 /.
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