Examen de Conduite des procédés
Transcription
Examen de Conduite des procédés
→ → ") * * + ! , - * - ! 0 /= • • 2 2 * + * * % * ! * % % 0 /= 0 / = 0 / ** - 7 +6 − ! #" • # 5 * * , $ - * ' +. + * 80 / • + . 4 !2 * +. , 3 ") * * 1 ε0 / : 0/ 90 / 0/ 0/ * , 0/ - 4 ;3 /# " % 5 0- 4 # < , 5 - 3# #= * > • * • A - * 3 - * - .# > * • • • * * * ! 0 /? # * - * -- @ 0 / ? 90 / ; 80 /# 5 - 3# ' * * * 0/?' # * 2 - 3 - * 3 * - * ' @ 0 / ? 90 / ; 80 / , - * '# * # * 3 0 ' /# > - ) ! "# $ % * * % B & * # ! '# ' % ($ # ' # • 2 • > • 3 0 % C • * • + * .#7( # ") 3* B * 3 - * , 0/ 3 ) # • + * * % - * ' C 2 3 % % - * % ( * * # 1# * '2 B * , # @.0 /? 0 /;80 / % * % # - * C * 3 * ( * ! "# $ % 3 * % # ' * ' % '2 ! 0 / ? ' 0 : / * @10 / ? 90 / ; 80 / B* '# % ( * * * 3 # - * 4 # ") - * ' #$ 3 % / C % * #D # - * % * * - 3# / % 52 3 % % 5+ * #+ ) * * D '# '2 > * * * * • * 3 - * # • 2 ( -) B - * * - * • A ' 0 5 - 3# • A % % * C E * * * • > - ) ' B1#1 0 B * ? # AC * • / # * # ( * * 5+ (* 3 # & ! '# ' % ($ # ' # ! " → ε " ε# $ %& ε ' ! ! ( ) ( ) ! " " / . ) , "* , % , / , ## $$ ##%# #$ 1) Boucle ouverte 2 1" % 3 ( − )( + ) %. , 0 % $ " 0 ε * % ) + + , % ) " 0 % # ' % - " / " - % # " ' / /, 2) Boucle fermée 2 " % " % " % " % +4 − " %= = = = = 2 " % + " % " % + " % + +4 − 5 0 6 + / + , ) 7 /, 0 * / 5 # , % 2 +4 −2 - /" ) " - 7 / 2 % /, / 8 0 3) Correction Proportionnelle " %= 9 2 " % " % " % " % +4 − = = = 2 " % + " % " % + " % + +4 − / -* ) :) %. < * = /, / 2 +4 +2 − / "2 # */ %! + . , " ω + ξω + ω " %= ;"% = 0 ω =2 ξω = 4 ω =2 − ) 4≥ 4 ≥ 2 − "2 # % ⇔ ξ≥ . 2 = 2 − 4 ξ= = ω ω = 2 − 4 2 − ' ξ= 4 2 − ≥ > & ≥2 # > + ≤ = 2× 0 /, %. = - = ?. 2 ≈ ? / , /, /, / 0 ! !? 0 " / 7 / % #A #B2 & "2 # %C # & "2 # % 0 , , 0 A ? # & "2$?# % # & # # & 2 D " % " % " % " +4 − % " %= = = = = " % + " % " % + " % + 2 &" + 4 − % +4 +2 − " % 0 B# .2 ' .2C "% " % $1" % /, "% " % $"#2& % -E " % 0 B#F ' FC / 0 " @ 9 ε"∞% 5 ε"∞% G" % ; " %H" % − > −F 2 − − <F 2 − 5 , @ / B# & "2 # − > −F(2 − − " % 0 B#F ' FC %C$:" % < F(2 − ) ) /* ' ' " % $# & */ − >− 2 +F − < 2 −F ' − + 2 >F > F − − 2 < −F < F 2 2 = .> = .2? .> , .> ! !? 4) Correction PD et PID " %= " + % " % " % " % = + " % " % + " + % " % " " %= &8/ % 2 " + % 2 " + % +4 − = = = 2 " + % +4 +2 " + %− + +4 − B2 " + %C &" − %" + % 2 " + = + B2 " + %C &" − %" + % " + %" − % + 2 2 " + . % = = + . % " . + %" − % + 2 " + . % " 2 " + . % " + %" − % + 2 " # % 2 2 2 &"2 − % " %= = = = " − %+2 +2 − + B &"2 − %C 9 0 , 0 A 5/ */ "I % , 0 , / " * = 6 J = /, ) " 9 =K ) / 2 " + %" + % " − %" + % 2 " + % 2 " " %= = = 2 " + %" + % " − %+2 " + % + B"2 − + " − %" + % I ξ= 9 " %= . "2 − % ≥ ' 2 / ) " / */ I ≥ .F> , * ' / / L , #M / 0 ' 2 " + % + "4 + 2 % +2 − % " + % 2 " − %+2 + I. " 0 0 %' / 7 / * + %& % & C + "2 & * 0 %. =K%. % * ξ B"2 # %& ω C≥ . / 6 ...%. = ' 9 # # /, / 0 * N O " ) .< 0 " / / 0 / / 0 0 / %. % /, , → #+ ,, - " ! . / , / " 1 0= • • ( ( , . - "- ( ( > . / 3$ #+ ,, "* / + + + ! !, ! 5 / 3$ ! 6 $ . ε1 0 9 , 6 , ! + 81 0 1 0 1 0 1 0 $ 1 0 :; : $ + + ! ! ! 6 1 <0$ = ! ! ! 6 1 <0$ ,! / ! !$ ? , > ? , " 71 0 , 1 0= • • • • 4! ! ! . 2 ! 3! #+ ,, + ! θ1 0 ! θ1 0 " , + 12 + 0 @ A B 10 ! ! + 2 θ1 0 = 2 1 0 , ! . $# θ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θ0 1 $ 0τ 1 τ 0 13 θ0 1 %:1 1 ! , - / , %0 > .? 1 ' -1 + > ( 3 @ , 0 !" # $ 3 θ% 0 1 5 01 (θ%0 1 .- $ 70 1(80 1(θ%0 1 θ0 1" / " / λ 3 × " + ")" "( 3 "% ")" " - + θ . - "/ θ0 1 0 1= = 0 1 ? ;, ,$ ,0 % λ 0 1= - "# $ 0 1= θ0 1 θ0 1 θ ,0 1 0 1 2 = ; - 1 θ 0 11 " θ ,0 1 ,$ = 00 1 , (% + τ% )(% + τ ) % #$ , θ0 1 - 01 ! θ0 1 θ% 0 1 <% - , =( 0 1= 0 1= 13= 013=0θ 6 -" 6 - , θ0 1 < , θ ,0 1 1 ' θ 0 14τ -" / - ); , $ 6 (τ 3 9 , - :1 .- ,,$ θ0 1 0 1 ( %0 1 = % 0 1 0 1 ; (; 70 1 , 0 1( %0 1( 0 1" , - 1 + 2- 3 01 , ; - - θ% 0 1 θ% 0 14τ% (01 "6 τ% 3 9 ( . λ (% + τ ) - θ ,0 1 $ θ0 1 , - =(λ(τ% τ" 1" - - - " !? - , ? - - 1" % & #" ' (# " ) * " 1 - , - , A0 1 - τ 0. $ ; , , =(λ 1 / ,1 + - $1 + - , - A 0 1= - , " !? 0$ θ0 1 θ ,0 1 A0 10 (,. 1 . -0 , 2 0 , , - ( B" - >= . " C 0 ω -- 2CD 0 ,$ ω1 1" =( =( , , 1" ,- 2 ; - =(λ(τ " 7 , - 0 :1 :" . θ , (- = CD 11" ? . ( ; ( ( 1" 1 & -- ; - G:1 / - & . > .? 0 A0 1 1" 1 & -- - 6 - - ( , + 0 1 3 = 0%4 -" / ' - , 1 - =. = !" # $ 0 1 - ' - ; < ,0 $ + ' H- - 1 θ%0 11 " θ% ,0 1 - K0 1 3 ,0 - θ0 11 " θ ,0 1 1 3 τ% - - - - ? , E0 -- 1 I <9 - -θ% - 0 1= ! ,J 1" 0 0 1" / 0 1 ' %0 1 -- 1 ' "/ θ . 0 1 3 = 0%4 ' 1 0 θ 6 -" , ( 1 0 θ% + @ ; 1 - 0 A0 1 ; & θ% - - , 2 ,,- ' / - - 0 1" / 0 1 3 = 0%4 ' 1 $ θ ,0 1 , - &$' , - ? ; :1 ( EF , , 1 ' @ 8 0 1 θ% 0 1 θ% ,0 1 . ( %0 1= +' 0 1 3 = 0%4 ' 1 - $ θ% ,0 1 , % ( % + τ% %0 1 " 0 1= " %+τ θ θ% 0 1 ; ? , = "/ θ%0 1 $ 2τ% θ% ,0 1 & $ " - " #" ' (# " ) * " &$'( / , ? %4 θ% ,0 13= 6 θ , - (θ - - - - + $ G 0 13= %4 0 1 −θ 0 1) , . . ! G0 1 θ% , ! θ% 8 0 1 0 1 %0 θ 1 0 1 θ ! , G0 3τ"# -1 / - 0 - = " 1 - 0$ θ% 1 , 1" 6 (,. = ( ; L ,1 6 $ - " C = 1 ω - 0 1= , , - M EF ; % θ0 1 θ ,0 1 =.( .( ( B" CD - - 1" ' ( - , ω1 2CD 0 + θ 0 1 , ,- θ% ," 6 @ ; 0 - + EF , θ% K0 1 , - 1 ' $1 + , " , - " 2 - - ( , - E) ( - θ% θ - !" # $ $ - G & #" ' (# " ) * " = π ω %−ξ "" # "! $%&" '! (( ! ! ) , * * $ 1 -. 2 + 6 + + * / θ, . + 7" θ, . / 7, . : 9 + * ,.: 9 + 8, . *+ , + 3, .1 = 3, . " 9 3, ." 9 + + $ "0 # , *+ , . : 1.* + $ + 7 !3, !" # $ 5 .1 5/ / + 5 $ /$ / , . , .= = , . @ " + " / 5 + + . ? 4 6 " +. ' , . : = , + * . 9 + , . + + 5 / ." 0 $4 .+ + *+ ,. ; θ, .13, .17, .1 , .1 <, ." ) + 1 : %=& : %=>" - . # . ' + , $ ' ) + + * / 3 /+ # () $ <, ." " $ <, . *2 A+ $ -71 <" , . , .= , / + , . 5, . @ " 0 + < .@ -/0 . 7, ." ) %, . : B% / 9 + / + 5 , . : B% , 7 !3 , . 7 , .. " 7 !3, . +" 9 + + /$ % & #" ' ( " 7 . ? !3, . 1 4 *- . !/+ +. + 5 . C * 0 . / 6 %, . % * "? + 4 * + + ' , . /+ . ? * .,7 ? , .= + ,$ /$ , . : B ,%D , ." # , . *+ / + + ω. B + @ + * ?%F G % F $ A " + ") + - + / + ? , + "9 + ?%F : H" F , + -." ! + $ + + ξ : "I. , 5 ; 0 : " " 1 $ 2 + A+ $ 7 , ++ , + + 1+ 3 + $ + "9 5 " + @0 + 4 , .1 /+ M, . <, .." ' * + → /. & ++ + + + + * + & * + E1 ?" ω / + ω B 0 1+ + 0 "? ?" 4 * ε%,∞. / + B & 7 !3 %." + 4+ , F." , 2 + - * + / J E K L. . ? 4*/ + * < + ,<, . : %=. 7 !3 : . / + B &" 0 + 1 4 ,∞ . = [ , .] = [ , . , .] + / + , F." 4* / B 1&1 A % F " . ? ,$ +. !ξ . ? , * → 1 - @ !3, . 7, .. " + / ω ,% + . + ξω + ω ξ ++ 5 &" + + &" + + 5 / B% B% ω. / + + 5 + + + " + . / + 3 , . : B ,%D . ? 4 *- A 7, . 2 , . , . , .= ) ) 5 <, . 1 + / %, 1 ,. / 5 6 1 + + 7 $ * $ + + + J +5 σ" ) //+ K" ) + !" # $ & #" ' ( " < 7 !3 ε% 1 N, ) N, 1 ' . O, . : BO 1 / % , .= σ, . , . ") + 7 !3 . 1 , .= / + / + P, . N ?1/+ ) + , .= , . 7 M, . , . %, . = %+ O , . %, . O + + + . ! +. ! /+ O + O , .= / ξ * + σ P, . ω + ξω + ω , .= P, . + σ, . N 7 M, . , . % = " ) σ, . , . , . , . N , . N , . = N, . = %+ N , . , . + N , . / + &1BN N, . / / , .= ' ' <: 1 / + . σ M%, . = N, . 9 / + ε 1 . : BN / + O, 1 ω. * N, + + / + 0? + + + ξ : "I 0 : " " BO " # BN1BO J +5 . ,$ &" K" ) 1- ; BN BO " BN BO +, 0 . 1 4 BN BO " . ? 4* ε%,∞. / + BN1BO & 7 !3 + , * %." + 4+ , F." , 2 + - * + / J ? K L. . ? 4*/ + * < + ,<, . : %=. 7 !3 : . / + BN 1 BO &" " 0 + 1 [ , .] = [ , . , .] ,∞ . = + / + , F." + → /. & ++ + + + N, . $. 0 / + + + " $ 7 , ++ → + 1 , N, . O, . + , !" # $ + 2 , . @. O * + + 0 1 2 + A+ ? N , <, .." + . @ / @0 4 + + 1+ /+ + 1 + 5 & #" ' ( " ) 0 8* ' 6 - + + 1 <, ." + J 0? K 9 % +J K , + , + 7 . !3, . : */ + '+ <, . 7, . 1 2 ,. 0. 3 + + / <, . J +5 K = 7, . = %+ '+ 1 < ε 1 O, ) = σ = % ε = ε = + = + O = − ,σ + N . σ M%, . M, . . N, 7 . ε ? + ε = = + ε = O = − − O O ,σ + + N .= N − = + O − O ( N % = + % − N + O N ) & = !" # $ = O %+ O ( % + N ) & #" ' ( " − π # #− = ( -. * / ) 01 * + * ! 2 3 4,0ω 1 *$) #$%& '() 5 * + .' " * 7 .' "* .' .' * ) . *. - . ,% 2 ) 8* 7 -'. /%'0' '.* * > θ2 "* ;< - . * *. * , 44 * *. * > * * , 6 " , # . .* . .* 1) 8* * . 1 ! " *. *. ( .' .' 6 @< - . - . " 9 = #+ 9 : : ;2% * 6. * . *6 - , . , . # θ - . * * .* . . 1 , 1 #, 1 = - = . * * • • • 7 - . " 2 04ω +,&% $ . .* * , . 8* 7 • • +,&)# $ *( " *. - # = θ = ) 1 # ,# + ? 1 @2θ * , A 1 .' .' 6 - 1 : 1 : $ ! % &' /& ' 1 2($+% ') ) & 3 3 θ 4 # , 1 #, 1 @ #B1 * C *. A* A * / *. * 1 5 8* # , 1 D 5 * D * -0 . 1 % * . *, * *. * 1 D .1 % .' 8* . " * "* D B1 .* * * 1 5 ) 8* . /* ) . 5 7 * . # 6 H # ,# + 5 ,# + θ 1 * 5 8*/* .' ( A . .* 8* I , 1 /. . . - . * . "* .* * * * /* * ω1 H# 5#J , * * - . * H# * . . - . * 8* I# , 1 /. - .. * 8* ," 8* J1 * * - . * . .* 5 - A * θ2 H# 2 ? θ, 1 #, 1 I , 1. 5 4# /. 5 * 8* ," - 1 I , 1= , . . - . 7 I , 1= *. - .1 ! 1 ; 1 *. * θ, 1 ! I# , 1 = #, 1 , * B1 . 1 0 /( 1 ! #, F 5G . * , 1= 1 5 ). * ./ * $ω 1 I# , 1 = .* - - / " * / ) + ξω + ω $) -. * / ξ * 1 A -( H# 2 ? .* 0 * ξ * .1 .* 0 * * A *- *. - , 3B1 . - . *. * E #; " * #, 1 0 /( - *. * ) E 7 * F G - . /* 5 , 1 2 H# - / 0 . * * + Cω 8* C) -. * / - -. * *( + ξω + ω ξ * ω1 5 - 8* I , 1 1 K* .* 0 -1 "1 K* - ! " * * * * * . * - I , 1= 5#J , * # ,# + )# 1 J1 , . .*1 D $ ! % &' A * .. .* * * , * 2 #1 * , * 2 #1 * . '1 A ( D 8* 0 * 8* 0 . /& ' 51 2($+% -( M, 1 = L * 6 2 ? . 6 2# . *. 6 ) . . ." 8* * * & * + + .' * .' * . L *+ 7 .' ,# + )# 1 7 * *. # A * * * 8* . . .* 3 7 . * . .* . 6. / * - * 8 # 4 , 1 #, 1 θ 4 # #, 1 @ θ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ξ * * * * * 1 F 5G I9 , 1 = *. 5 ω1 * 5 0 /( 1 A .' * * * . - + ξω + ω 8* ) -. * / ξ * 6?J , * .. * * . H 8* / .* / ω 1 I3 , 1 = , * H ) . .* 0 / * * .* * - L * * 9 *. K, 1 , 1 . 5ω - * * *. 5 " 1 . , - , 1 A -. . , 1 , 1 ω1 - . H9 8* 51 * ) 5#J) 8* * + .' * -"* . * 5 # M, 1 A .* .* * + ξω + ω ξ * D J ,* * *" * * , 1 . 1 ,# + 1D * + * .' . * 6 *( L # $ ! % &' D − π " = ) "− * + , !" 0 -' % %-&% ' $ #$%& ' ( )'*+%',' -$( * ( # %,' !% 1 % .!% , % 4% % - ./ 1% , !% % -' % 2 ) ! . 3 1 .% - θ % 8 ' % 1 % -' % - ! 5 1 -' % , 1 6'7 + 1 -' % 2 3 1 % %' + %2 3 %* % % 1 . 2 ) %6 5 θ2 3 % 3 7 # θ2 3 = 2 3 ,- . - 2 3= - / 3 ) * + "2 ( # 3= :2 3 = θ2 3 + 0 1 . - . %- 2 % -' %.. 6 % 7* 6 8 7 2 % 6 % 73 6θ7 0 -' 23 '2 3 #. ;2 3 " = + :2 3 < =* " < "* < " "<= 2 3= " . * - " % 3 2 3= . . 6' 97 -% % 4% ≈4-5 . .4 - ;2 3 2 3 2 3 2 3 2 3 θ2 3 = " = × × = = 2 3 2 3 θ2 3 2 3 2 + 32 + " 3 2 + =32 + "3 3 > ( % ? + 5 @ % 4% @ ≡ ℜ 2 3 A 1B < 2 3* " < " 2 3 < =2 3 5 -3 0 %' 1 ,% % & 2 2 3 < C * -' 1 % 3* 4% % 2 ! '2 33 1 %- % @ D5 4% 4% % 1 % * E∞ 2 5 2 3= ./ 0 % )0 1 % - 2 -% .!% % ! 35 + 3 1 464 % '2 3 0 "2 3 < F" 0 " ; 9 1 % . - ! # + 3 ≈ -5 4- % 5 -' $ $ %&' (( - ; 9 7 ; "2 3 > ( 1) 3 % ;2 3 . F" ; 92 3 2 3 = " "2 3 2 3 = = G 2 3 "+ "2 3 2 3 +H += += " ' ! 4% %' > 2 3= !3 F+ 2 G ..-3 % - % F+ * %) 1 % 4% 3 > ! D F" < F+ % % / 3 + % 1 & 2 3 1 % 3 " = H =F" 2=F" G 3 C 2 H3 =F" I ! 1 B A F" A H* % 14% %) % % + H < ± J√=* + < π C √= ≈ F" < F+ % 26 1 73 @ * 3 + %' * 1B 6 1 7/ EG < ! 2 - ! ⇔ 8 ' 2 3 < F 2"E % 3 0 % L ! 3 + F < F %- 2 3 9" 2 3 = %- . " 3 M -' + 5 % F" 0 -F+ < H % % K" 2 -3 4% * - 3 % F 1% F+ -% % , % "×F+ < "=× + -% F < "×H < N H < "=× K" < N "= 2 -3 - 2 . 3 - - % "2 3 2 3 % 4% 15 @ + . % ( ! ! ' 4% % ! ! * % % . % , =O -% + ! . % ! @ " 15 1 % % % -' ε 2∞ 3 = → ε 2 3 -ε 2 3 = 2 3− 2 3= 2 3 "− ≈ 4- . 64 2 3 2 3 "+ 2 3 2 3 ; > + 1 % % % 2- 9 ! < "C 2 + "32 + =3 " = ≈ GO 0 -2 J% /3 ! → 2 + "32 + =3 + = 2" + 3 -3 + % 2 -' 1 % "3 % .!% % ) 4% ( % . 4%1% % 2 1 % "3 4% % % 21 % % - 1 % . %' 3@ 4% . - -% 2( % 5 %- - % 3 + - -% 1! 1 % 2 * - -% 5 3 % J % % 5 -' 2"3 -% % 4% 2 G O3 ε 2∞ 3 = ! # $ $ %&' (( 9/ 0 1 & 8 -' -' 1% - %) 6 -'5 , % 5 !% % - 5 : J * %2 % 3 ; < ≈94- =.4 % - % 2 3P "2 3 2% 2 3P "2 33 5 -' 2 + 0 6 1 !% # 7* - 4% % 2 33 0 ..-% % %- - 4% 7 0 -' - % > ;" 7 G2 : 3 "2 3× 2 3 ; 7 9 ;" N2 3 $0 # 0 % % . 3 > % - ? 2 - ( 1) > % ! %- . . - M 2CN M 3 = F G 2" + 2 3× 3 2 3 2 3= "2 3 G2 G ; 23 D3 3 0 -' "2 3 > - , G G < " 2 -3 % . .- FG 2 3= 3 -% + : L2 3 4% - -' ) ) - G 2 3 "2 3 2 3 G2 3 G = = 2 3 " + 2 3 2 3 2 3 + = 2 " + G3 " G " 1 % . . % 26 173 ! 4% 26 F173 . - % L2 3 FG G 2 3= -3 0 % %' . % % 4% - % ε 2∞ 3 ≤ " * 0 ! G + =2" + ! G 3 = 2" + "+ G =2" + ," O > % % 4% ε 2∞ 3 = " − ′ = G 3 = G FG % " "+ * ′ "+ ′ 3 % % -FG ≥ Q - J- . ) 2 3= G # ( L2 3 N= += $ $ %&' (( D 0 N2 3 > 3 < FN % ( 1) 2 3= N= += R ;2 3 ; 92 3 9G 2 3 = + (ω ( .- N " ω = ′ * ω = 3 S% % 1 % $ < " 2! 4% %' -3 0 - -' 3 S% N -% 2 1 = N= FN 9G2 3 - - . - FN N ′ N = ′ " = " + ′ ′ N ′ ω = ′ N ′ ′ = N= = = N= ( % 4% 2! ′ ′ + N = ′ ′ N= N + = + N= N N N % % $3 @ - =" 2 S% 3 1B N N % % . ′ - -% * % 3 - % % %- . . - =" ⇔ 2 = ′ D3 . +ω ω3 % ω = 2 C =* = M ′ 2 3 2 3 N2 3 2 3 N = = 2 3 "+ N 2 3 2 3 2 3 2" + ′ 3 + 2 3= % % + $ω 9G 2 3 = 4% $* 0 $0 %- . . G # 0M> J - < "3 % % , <" - - 5 = % FN @ = ≈ "G Q N= 2 + - I -3 0 % - - 4% % % - .!% @ 4% 5 4% 2 J % 3 S% 5 - -% % J 2 % - - % N2 3 > - N2 3 % ! 3 % 1 N2 % 3 3* N % J .% J% % % # @2 ! - -% 3 $ $ %&' ((