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12.ఏ㐩㛵ᩘ䛻䜘䜛䝣䜱䞊䝗䝞䝑䜽

ᩍ⛉᭩

6.4, 7.4, 7.5

ྜᡂఏ㐩㛵ᩘ䛾ồ䜑᪉

₍₁₎

z 䛂┤ิ⤖ྜ = ఏ㐩㛵ᩘ䛾᥃䛡⟬䛃, 䛂୪ิ⤖ྜ = ఏ㐩㛵ᩘ䛾㊊䛧⟬䛃䛷䛒䛳䛯䚹 䛷䛿䚸䜒䛳䛸」㞧䛺ሙྜ䛿䛹䛖䛷䛒䜝䛖䛛? z ౛䛘䜀䚸௨ୗ䛾ሙྜ䛷G(s) = Y(s) / R(s) 䜢ồ䜑䜛䛣䛸䜢⪃䛘䜘䛖䚹

z 㛵ಀᘧ䜢᭩䛝ฟ䛩䛸䚸U(s) = R(s) – Y(s), Y(s) = G₀(s)U(s) 䛾2䛴䚹ồ䜑䛯䛔䛾䛿䚸

R(s) 䛸 Y(s) 䛾㛵ಀ䛷䛒䜛䛛䜙䚸↓㛵ಀ䛺 U(s) 䜢ᾘཤ䛧䜘䛖䚹 Y(s) = G₀(s)(R(s) – Y(s)) z ⛣㡯䛩䜛䛸䚸(1 + G₀(s))Y(s) = G₀(s)R(s) 䛸䛺䜛䛾䛷䚸R(s) 䛸 Y(s) 䛾ẚ䜢ồ䜑䜛䛸䚸 G₀(s) – + R(s) U(s) Y(s) ) ( 1 ) ( ) ( ) ( ) ( 0 0 s G s G s R s Y s G 

ྜᡂఏ㐩㛵ᩘ䛾ồ䜑᪉

_(䠎)

z 䜘䜚」㞧䛺ሙྜ䜒ྠᵝ䛻ྜᡂఏ㐩㛵ᩘ䜢ồ䜑䜛䛣䛸䛜䛷䛝䜛䚹 z [౛]

z 㛵ಀᘧ: U₁(s) = U(s) – Y₂(s), U₂(s) = Y₁(s) – Y₃(s), U₃(s) = Y₂(s), Y(s) = Y₃(s),

Y₁(s) = G₁(s)U₁(s), Y₂(s) = G₂(s)U₂(s), Y₃(s) = G₃(s)U₃(s) z U₁(s), U₂(s), U₃(s), Y₁(s), Y₂(s), Y₃(s) 䜢ᾘཤ䚹 z Y (s) = G₃(s)G₂(s)(G₁(s)(U (s) – G₃(s)–1_{Y (s)) – Y (s))} G₁(s) G₂(s) G₃(s) U₁(s) Y₁(s) U₂(s) U (s) Y₂(s) U₃(s) Y₃(s) Y(s) – – + + ) ( ) ( ) ( ) ( 1 ) ( ) ( ) ( ) ( ) ( ) ( 3 2 2 1 3 2 1 s G s G s G s G s G s G s G s U s Y s G  

䝣䜱䞊䝗䝞䝑䜽⣔䛾ఏ㐩㛵ᩘ

₍₁₎

_(㔜せ)

z ༢⣧䝣䜱䞊䝗䝞䝑䜽䛾ሙྜ: z ⿵ൾჾ C(s) 䜢ධ䜜䛯䝣䜱䞊䝗䝞䝑䜽䛾ሙྜ: G₀(s) – +

U(s) E(s) Y(s)

) ( 1 1 ) ( ) ( ) ( , ) ( 1 ) ( ) ( ) ( ) ( 0 0 0 s G s U s E s G s G s U s Y s G   ධຊ䛛䜙㏣ᚑㄗᕪ䜎䛷䛾ఏ㐩㛵ᩘ G_P(s) – +

U(s) _{E(s) Y(s)}

C(s) ) ( ) ( 1 1 ) ( ) ( ) ( , ) ( ) ( 1 ) ( ) ( ) ( ) ( ) ( s G s C s U s E s G s C s G s C s U s Y s G P P P   䛾ఏ㐩㛵ᩘ ධຊ䛛䜙㏣ᚑㄗᕪ䜎䛷 ୍ᕠఏ㐩㛵ᩘ: G₀(s) = C(s)G_P(s) 䛸䛚䛡䜀䚸 ༢⣧䝣䜱䞊䝗䝞䝑䜽 䛾ሙྜ䛸ྠ䛨

䝣䜱䞊䝗䝞䝑䜽⣔䛾ఏ㐩㛵ᩘ

₍₂₎

z 䝣䜱䞊䝗䝞䝑䜽䝹䞊䝥ෆ䛻⿵ൾჾ䜢2䛴ධ䜜䛯౛: z ୍ᕠఏ㐩㛵ᩘ…E(s) 䛛䜙ጞ䜎䛳䛶䚸䝣䜱䞊䝗䝞䝑䜽䛾ᯞ䛷ᡠ䛳䛶䛟䜛䜎䛷䛾୍ᕠ 䛾ఏ㐩㛵ᩘ䚹 z 䛹䛾ሙྜ䜒䚸䛂୍ᕠఏ㐩㛵ᩘ䛃G₀(s) 䛸䛂ධຊ䛛䜙㏣ᚑㄗᕪ䜎䛷䛾ఏ㐩㛵ᩘ䛃䛾 㛵ಀ䛿䚸E(s) / U(s) = 1 / (1 + G₀(s)) 䚹[㔜せ] G_P(s) – +

U(s) E(s) Y(s)

C₁(s) C₂(s) ) ( ) ( ) ( 1 1 ) ( ) ( ) ( ) ( ) ( ) ( 1 ) ( ) ( ) ( ) ( ) ( 2 1 2 1 1 s G s C s C s U s E s G s C s C s G s C s U s Y s G P P P   䛾ఏ㐩㛵ᩘ ධຊ䛛䜙㏣ᚑㄗᕪ䜎䛷

䝣䜱䞊䝗䝞䝑䜽⣔䛾ᴟ䛸䝊䝻Ⅼ

z ༢⣧䝣䜱䞊䝗䝞䝑䜽䚸䛒䜛䛔䛿ไᚚᑐ㇟䛾๓䛻⿵ൾჾ䜢⨨䛟ᵓᡂ䜢⪃䛘䜛䚹 z ୍ᕠఏ㐩㛵ᩘ䜢ḟ䛾䜘䛖䛻䛚䛟䚹 z 䛣䛾䛸䛝䚸 ) ( ) ( ) ( 0 s D s N s G ) ( ) ( ) ( ) ( / ) ( 1 1 ) ( ) ( ) ( ) ( ) ( ) ( / ) ( 1 ) ( / ) ( ) ( ) ( ) ( s D s N s D s D s N s U s E s D s N s N s D s N s D s N s U s Y s G     䝣䜱䞊䝗䝞䝑䜽䛻䜘䛳䛶 ศᏊ䛿ኚ䜟䜙䛺䛔 (ᴟ-䝊䝻┦ẅ䛾ሙྜ䜢㝖䛟) ศẕ䛿ኚ䛘䜛䛣䛸䛜䛷䛝䜛䚹 䛴䜎䜚䚸Ᏻᐃᛶ䜢ኚ䛘䜛䛣䛸䛜䛷䛝䜛䚹

ᐃᖖ೫ᕪ

z 䝥䝷䞁䝖䛾๓䛻⿵ൾჾ䜢⨨䛟ᵓᡂ䜢⪃䛘䜛䚹

z ධຊ u(t) = L–1_{[R(s)]䛜ฟຊ y(t) = L}–1_{[Y(s)] 䛾┠ᶆ್䛷䛒䜛ሙྜ䚸 e(t) =}

L–1[E(s)] 䛿䚸䇿ฟຊ䛸䛭䛾┠ᶆ್䛸䛾೫ᕪ䇿䛷䛒䜛䚹 ೫ᕪ e(t) 䛜䚸t o f 䛾䛸䛝䛒䜛್䛻཰᮰䛩䜛䛺䜙䚸䛭䛾್䜢ᐃᐃᖖ೫ᕪ䛸࿧䜆䚹 z ධຊ䛜 r(t) = 1 (༢఩䝇䝔䝑䝥ධຊ) 䛷䛒䜛䛸䛝䛾ᐃᖖ೫ᕪ … ᐃᖖ఩⨨೫ᕪ z ධຊ䛜 r(t) = t (༢఩䝷䞁䝥ධຊ) 䛷䛒䜛䛸䛝䛾ᐃᖖ೫ᕪ … ᐃᖖ㏿ᗘ೫ᕪ z ධຊ䛜 r(t) = t2_{/ 2 䛷䛒䜛䛸䛝䛾ᐃᖖ೫ᕪ … ᐃᖖຍ㏿ᗘ೫ᕪ} z 䛂ᐃᖖ఩⨨೫ᕪ䛃䛸䛔䛖⏝ㄒ䜘䜚䚸┤᥋ⓗ䛻䛂༢఩䝇䝔䝑䝥䛻ᑐ䛩䜛ᐃᖖ೫ᕪ䛃䛸 ゝ䛖䛣䛸䛜ከ䛔䚹 G_P(s) – + R(s) E(s) Y(s) C(s) _{୍ᕠఏ㐩㛵ᩘ:} G₀(s) = C(s)G_P(s)

᭱⤊್ᐃ⌮䛾᚟⩦

z ᫬㛫㛵ᩘ f(t) 䛾᭱⤊್ f(+f) 䜢䝷䝥䝷䝇ኚ᥮䛛䜙ồ䜑䜛᪉ἲ䚹 z [௬ᐃ1] ௵ព䛾 T > 0 䛻ᑐ䛧䛶䚸f(t) 䛿༊㛫 [0, T] 䛷✚ศྍ⬟䚹 z [௬ᐃ2] ᭱⤊್ f(+f) 䛜Ꮡᅾ䛩䜛 (ᴟ㝈䛜Ⓨᩓ䛧䛯䜚䚸᣺ື䛜ṧ䛳䛯䜚䛧䛺䛔)䚹 z 䛴䜎䜚䚸 䛾᭱⤊್䜢ồ䜑䜜䜀䚸ᐃᖖ೫ᕪ䛜ᚓ䜙䜜䜛䚹 䛯䛰䛧䚸䛂᭱⤊್䛜Ꮡᅾ䛩䜜䜀䛃䛸䛔䛖᮲௳䛜௜䛟䚹᭱⤊್䛜Ꮡᅾ䛧䛺䛔ሙྜ䛻 䛚䛔䛶䛿බᘧ䜢౑䛖䛸↓ព࿡䛺್䛜ฟ䛶䛧䜎䛖䚹 ᭱⤊್ᐃ⌮: ୖグ䛾௬ᐃ䜢‶䛯䛩䛺䜙䜀䚸 )] ( [ ) ( ), ( lim ) ( 0sF s F s f t f s L f o 䛯䛰䛧䚸 ) ( ) ( 1 1 ) ( 0 s R s G s E 

ᐃᖖ఩⨨೫ᕪ

₍

㔜せ

₎

z ᐃᖖ఩⨨೫ᕪ䛜Ꮡᅾ䛩䜛᮲௳: 㛢䝹䞊䝥⣔ G₀(s) / (1 + G₀(s)) 䛜Ᏻᐃ䛷䛒䜛䛣 䛸䚹 z 䛣䛾䛸䛝ᐃᖖ఩⨨೫ᕪ䛿ḟ䛾䜘䛖䛻ồ䜑䜙䜜䜛䚹 䛯䛰䛧䚸 䚹 䜢఩⨨೫ᕪᐃᩘ䛸䛔䛖䚹 z ᐃᖖ఩⨨೫ᕪ䛜 0 䛸䛺䜛᮲௳:㛢䝹䞊䝥⣔ G₀(s) / (1 + G₀(s)) 䛜Ᏻᐃ䛷䛒䜚䚸䛛 䛴 D(0) = 0 䛸䛺䜛䛣䛸䚹䛴䜎䜚䚸㛢䝹䞊䝥⣔䛜Ᏻᐃ䛷䚸୍ᕠఏ㐩㛵ᩘ䛾ᴟ䛜1䛴 ௨ୖ s = 0 䛻䛒䜛䛣䛸䚹 z ⿵ൾჾ䛾ศẕከ㡯ᘧ䛻ᅉᏊ䛸䛧䛶 s 䜢䜒䛱䚸㛢䝹䞊䝥⣔䛜Ᏻᐃ䛺䜙䜀ᐃᖖ఩ ⨨೫ᕪ䛜 0䚹 [౛] ) 0 ( ) 0 ( ) 0 ( ) ( 1 1 lim 1 ) ( 1 1 lim ) ( lim ) ( 0 0 0 0 0 N D D s G s s G s s sE e s s s  ˜   f o o o ) ( ) ( ) ( 0 s D s N s G ) 1 ( ) 3 )( 2 ( ) (    s s s s s C ศẕከ㡯ᘧ䛻ᅉᏊ䛸䛧䛶 s 䜢䜒䛴 ) ( lim ₀ 0G s so

ᐃᖖ㏿ᗘ೫ᕪ

₍

㔜せ

₎

z ᐃᖖ㏿ᗘ೫ᕪ䛜Ꮡᅾ䛩䜛᮲௳: ᐃᖖ఩⨨೫ᕪ䛜 0 䛷䛒䜛䛣䛸䚹 z 䛣䛾䛸䛝ᐃᖖ㏿ᗘ೫ᕪ䛿ḟ䛾䜘䛖䛻ồ䜑䜙䜜䜛䚹 䛯䛰䛧䚸 䚹 䜢㏿ᗘ೫ᕪᐃᩘ䛸䛔䛖䚹 z ᐃᖖ㏿ᗘ೫ᕪ䛜 0 䛸䛺䜛᮲௳: 㛢䝹䞊䝥⣔ G₀(s) / (1 + G₀(s)) 䛜Ᏻᐃ䛷䛒䜚䚸 䛛䛴 D(s) / so 0 (s o 0)䚹䛴䜎䜚䚸㛢䝹䞊䝥⣔䛜Ᏻᐃ䚸䛛䛴୍ᕠఏ㐩㛵ᩘ䛾ᴟ 䛜2䛴௨ୖ s = 0 䛻䛒䜛䛣䛸䚹 ) ( ) ( lim ) ( 1 lim )} ( 1 { 1 lim 1 ) ( 1 1 lim ) ( lim ) ( 0 0 0 0 0 2 0 0 0 s sN s D s sG s G s s s G s s sE e s s s s s o o o o o  ˜  f ) ( ) ( ) ( 0 s D s N s G lim ₀( ) 0 sG s so

ᐃᖖຍ㏿ᗘ೫ᕪ

z ᐃᖖຍ㏿ᗘ೫ᕪ䛜Ꮡᅾ䛩䜛᮲௳: ᐃᖖ㏿ᗘ೫ᕪ䛜 0 䛷䛒䜛䛣䛸䚹 z 䛣䛾䛸䛝ᐃᖖຍ㏿ᗘ೫ᕪ䛿ḟ䛾䜘䛖䛻ồ䜑䜙䜜䜛䚹 䛯䛰䛧䚸 䚹 䜢ຍ㏿ᗘ೫ᕪᐃᩘ䛸䛔䛖䚹 z ᐃᖖຍ㏿ᗘ೫ᕪ䛜 0 䛸䛺䜛᮲௳: 㛢䝹䞊䝥⣔ G₀(s) / (1 + G₀(s)) 䛜Ᏻᐃ䛷䛒䜚䚸 䛛䛴 D(s) / s2 _{o 0 (s o 0)䚹䛴䜎䜚䚸㛢䝹䞊䝥⣔䛜Ᏻᐃ䚸䛛䛴୍ᕠఏ㐩㛵ᩘ䛾} ᴟ䛜3䛴௨ୖ s = 0 䛻䛒䜛䛣䛸䚹 ) ( ) ( lim ) ( 1 lim )} ( 1 { 1 lim 1 ) ( 1 1 lim ) ( lim ) ( 2 0 0 2 0 0 2 0 3 0 0 0 s N s s D s G s s G s s s G s s sE e s s s s s o o o o o  ˜  f ) ( ) ( ) ( 0 s D s N s G lim 2 ₀( ) 0 s G s so

ᐃᖖ೫ᕪ䛾ィ⟬䛾౛

z [౛] z C(s) = K (ṇ䛾ᐃᩘ) 䛾ሙྜ: {G(s) = K / (Ts + K + 1) … Ᏻᐃ ĺᐃᖖ఩⨨೫ᕪ䛿Ꮡᅾ䛩䜛䚹 {ᐃᖖ఩⨨೫ᕪ䛿 z C(s) = K / s (䛯䛰䛧K > 0) 䛾ሙྜ: {G(s) = K / (Ts2_{+ s +K) … Ᏻᐃ ĺᐃᖖ఩⨨೫ᕪ䛿Ꮡᅾ䛩䜛䚹} {ᐃᖖ఩⨨೫ᕪ䛿 ĺᐃᖖ㏿ᗘ೫ᕪ䜒Ꮡᅾ {ᐃᖖ㏿ᗘ೫ᕪ䛿 G_P(s) – + R(s) E(s) Y(s) C(s) 0 1 1 ) ( !  T Ts s G_P 䛯䛰䛧䚸 1 1 1 ) ( ) ( 1 1 lim ) ( 0  ˜  f o s C s G s s K e P s 0 1 ) ( ) ( 1 1 lim ) ( 0  ˜ f o s _{C s G s s} e P s K s s G s C s e P s 1 1 ) ( ) ( 1 1 lim ) ( ₂ 0  ˜ f o

ṇᘻἼ┠ᶆಙྕ䜈䛾㏣ᚑ

z ྠᵝ䛻䚸ṇᘻἼ䜈䛾㏣ᚑ䜒⪃䛘䜛䛣䛸䛜䛷䛝䜛䚹 z ┠ᶆಙྕ: ݎ ݐ = cos ߱ݐ , ܴ ݏ = Τݏ ݏଶ + ߱ଶ z 㛢䝹䞊䝥⣔䛜Ᏻᐃ䛷䛒䜛䛣䛸䛜䚸ᐃᖖⓗ䛺೫ᕪ(䝊䝻䛻䛺䜙䛺䛡䜜䜀୍ᐃ್䛻 䛿䛺䜙䛺䛔)䛜᭷⏺䛷䛒䜛䛣䛸䛾ᚲせ᮲௳䚹эᏳᐃᛶ䜢௬ᐃ䚹 z 䛣䛾ሙྜ䚸᭱⤊್ᐃ⌮䛿౑䛘䛺䛔䛜䚸࿘Ἴᩘᛂ⟅䜘䜚䚸༑ศ᫬㛫䛜⤒㐣䛧䛯ᚋ 䛾݁(ݐ)䛿䚸 ݁ ݐ = 1 1 + ܩ(݆߱) cos ߱ݐ + ߶ , ߶ = arg ܩ(݆߱) z 䛴䜎䜚䚸ᐃᖖ೫ᕪ䛜䝊䝻䛻䛺䜛ᚲせ༑ศ᮲௳䛿䚸㛢䝹䞊䝥⣔䛜Ᏻᐃ䚸䛛䛴 ܩ ݆߱ = λ䚹ܩ ݆߱ = λ䛾᮲௳䛿䚸䛂ܩ(ݏ)䛾ศẕ䛻(ݏଶ+߱ଶ)䜢ྵ䜐䛣䛸䛃䛸ゝ䛔 ᥮䛘䛶䜒䜘䛔䚹

ෆ㒊䝰䝕䝹ཎ⌮

z ┠ᶆಙྕ䛾䝷䝥䝷䝇ኚ᥮䛜᭷⌮ᘧ݊_௥௘௙(ݏ)/݀_௥௘௙(ݏ)䛻䛺䜛ሙྜ䛻㝈ᐃ䚹 z ୍ᕠఏ㐩㛵ᩘ䜢ܩ_଴ ݏ = ݊_଴(ݏ)/݀_଴(ݏ)䛸䛚䛟䚹 z 㛢䝹䞊䝥⣔䛾ఏ㐩㛵ᩘܩ_଴(ݏ)/(1 + ܩ_଴ ݏ )䛾Ᏻᐃᛶ䜢௬ᐃ䚹 z 䜎䛪䚸㏣ᚑㄗᕪ ܧ ݏ = ݀଴(ݏ) ݀_଴ ݏ + ݊_଴(ݏ)ȉ ݊_௥௘௙ ݏ ݀_௥௘௙ ݏ 䜢㒊ศศᩘᒎ㛤 ܧ ݏ = ݍ(ݏ) ݀_଴ ݏ + ݊_଴(ݏ)+ ݌ ݏ ݀_௥௘௙(ݏ) z ݌ ݏ = 0䛻䛺䜛᮲௳䛿䚸ܧ(ݏ)䛾ศẕ䛛䜙݀_௥௘௙(ݏ)䛜ᾘ䛘䜛䛣䛸䚹 z 䛴䜎䜚䚸䛂ᐃᖖ೫ᕪ䝊䝻䛃䛻䛺䜛᮲௳䛿䚸䛂㛢䝹䞊䝥⣔䛜Ᏻᐃ䚸䛛䛴݀_௥௘௙(ݏ)䛾Ᏻ ᐃ䛷䛿䛺䛔ᅉᏊ䜢඲䛶݀_଴(ݏ)䛜ᣢ䛳䛶䛔䜛䛣䛸䛃 z 䛴䜎䜚䚸䛂┠ᶆಙྕ䛾Ⓨ⏕䝎䜲䝘䝭䜽䝇䜢୍ᕠఏ㐩㛵ᩘ䛭䛾䜒䛾䛜ಖᣢ䛧䛺䛟䛶 䛿䛺䜙䛺䛔䛃 эෆ㒊䝰䝕䝹ཎ⌮ 䛣䛣䛿䚸௬ᐃ䜘䜚 䝊䝻䛻₞㏆

PIDไᚚ

z ๓⨨⿵ൾჾ䛸䛧䛶䚸 䜢౑䛖ไᚚ䚹䛣䜜䛿䚸 {ẚ౛ไᚚ (Pไᚚ) K_P {✚ศไᚚ(Iไᚚ) K_I /s {ᚤศไᚚ (Dไᚚ) K_Ds 䜢⤌䜏ྜ䜟䛫䛯䜒䛾䛷䛒䜛䚹Iไᚚ䛾䛚䛛䛢䛷䚸ᐃᖖ఩⨨೫ᕪ䛿0䛷䛒䜛䚹 z K_D z 0 䛾䛸䛝䚸C(s) 䛿䝥䝻䝟䞊䛷䛿䛺䛟䛺䜛䚹䛭䛾䛯䜑䚸Dไᚚ䜢㝖䛔䛯䚸䛂PIไ ᚚ䛃䜒Ⰻ䛟⏝䛔䜙䜜䜛䚹 z 䛂PIDไᚚ䛃䛸䛔䛖ྡ๓䛠䜙䛔䛿ぬ䛘䛶䛚䛣䛖䚹 s s K K s K s C P I D 2 ) (   G_P(s) – + R(s) E(s) _Y(s) K_I /s K_P K_Ds + + + U(s)

PID䝀䜲䞁䛾Ỵᐃἲ(㝈⏺ឤᗘἲ䛺䛹)

z PID䛿⣔䜢Ᏻᐃ䛻䛩䜛䛸䛿㝈䜙䛺䛔䚹䝀䜲䞁䛾Ỵ䜑᪉䛿䜋䛸䜣䛹⤒㦂๎䚹 {㝈⏺ឤᗘἲ (Ziegler=Nichols 䛾㝈⏺ឤᗘἲ) {㒊ศⓗ䝰䝕䝹䝬䝑䝏䞁䜾䛻ᇶ䛵䛟᪉ἲ (໭᳃䛾᪉ἲ)…. z ୍⯡ㄽ䛰䛜䚸 z 㝈⏺ឤᗘἲ {ồ䜑䛯䛔ಖドჾ䜢 C(s) = K_P(1 + 1 /(T_Is) + T_D s) 䛾䜘䛖䛻䛚䛟䚹 {䛔䛳䛯䜣䚸C(s) = K_C (ᐃᩘ) 䛸䛧䚸Ᏻᐃ㝈⏺䛻䛺䜛䜎䛷 K_C 䜢኱䛝䛟䛩䜛䚹䛭 䛾䛸䛝䛾᣺ື࿘ᮇ䜢 T_C䛸䛚䛟䚹 {K_P, T_I, T_D 䜢ྑ䛾䜘䛖䛻Ỵ䜑䜛䚹 KP TI TD P 0.5K_C - -PI 0.45K_C T_C/ 1.2 -PID 0.6K_C T_C/ 2 T_C / 8 ❧䛱ୖ䛜䜚᫬㛫 ⾜䛝㐣䛞㔞 ᩚᐃ᫬㛫 ᐃᖖ೫ᕪ Ᏻᐃᛶ Kp኱ ῶᑡ ቑ኱ 䛒䜎䜚ኚ໬䛺䛧 ῶᑡ ᝏ໬ Ki኱ ῶᑡ ቑ኱ ቑ኱ ᏶඲㝖ཤ ᝏ໬ Kd኱ 䛒䜎䜚ኚ໬䛺䛧 ῶᑡ ῶᑡ ↓㛵ಀ 㐺ษ䛺䜙ᨵၿ

I-PDไᚚ

z PIDไᚚ⣔䛻䛚䛔䛶䚸┠ᶆ್ r(t) 䜢䝇䝔䝑䝥≧䛻ኚ໬䛥䛫䛯ሙྜ䚸ධຊ䜒ᛴᓧ 䛻ኚ໬䛩䜛䚹≉䛻Dືస䛜ධ䛳䛶䛔䜛ሙྜ䚸䜲䞁䝟䝹䝇≧䛾ධຊ䛻䛺䜛䚹 z 䛣䜜䜢㑊䛡䜛䛯䜑䛻䚸Pືస䛸Dືస䛻┠ᶆ್ r(t) 䛾ᙳ㡪䜢┤᥋ཷ䛡䛺䛔䜘䛖 䛻䛩䜛䛂I-PDไᚚ䛃䛜⪃᱌䛥䜜䛯䚹 z T_D z 0 䛾䛸䛝ᚤศჾ䛜ᚲせ䛻䛺䜛䛜䚸I-PDไᚚ䛾ሙྜ䚸≧ែ䛾୍㒊䜢ྲྀ䜚ฟ 䛩䛣䛸䛷ᚤศ䛾௦䜟䜚䛻䛩䜛䛣䛸䛜䛷䛝䜛䛣䛸䛜䛒䜛䚹䛯䛸䛘䜀䚸ᶵᲔ⣔䛷䛂఩ ⨨䛃䛜ฟຊ䛾䛸䛝䚸ᚤศჾ䜢⏝䛔䜛௦䜟䜚䛻䚸≧ែ䛾୍㒊䛷䛒䜛䛂㏿ᗘ䛃䜢⏝䛔 䜜䜀䜘䛔䚹 G_P(s) – + R(s) E(s) Y(s) K_P + + U(s) T_Ds 1 / T_Is 1 – –

2⮬⏤ᗘ㏣ᚑไᚚ⣔(1)

z R(s) 䛻 Y(s) 䜢㏣ᚑ䛥䛫䛯䛔䚹 z H(s) 䛸 C(s) 䜢タィ䚹 z H(s) 䛿Ᏻᐃ䛸௬ᐃ䚹 z ఏ㐩㛵ᩘ ܻ(ݏ) ܴ(ݏ) = ܥ(ݏ)ܲ(ݏ) 1 + ܥ ݏ ܲ(ݏ)+ ܪ(ݏ) ܲ(ݏ) 1 + ܥ ݏ ܲ(ݏ) H(s) 䛾Ᏻᐃᛶ䛾௬ᐃ䛾ୗ䛷䛿䚸㛢䝹䞊䝥⣔䛾Ᏻᐃᛶ䛿H(s) = 0 䛾䛸䛝䛸ྠ䛨䚹 z ୍⯡ⓗ䛻䚸ඛ䛻 C(s) 䜢タィ䛧䚸ᚋ䛛䜙 H(s) 䜢タィ䚹 z ⌮᝿ⓗ䛻䛿䚸 H(jZ) 䛜 1 / P(jZ) 䛻㏆䛟䛺䜜䜀䚸䛭䛾࿘Ἴᩘ䛷䛾㏣ᚑ≉ᛶ䛿Ⰻ 䛟䛺䜛䚹 P(s) – + R(s) E(s) Y(s) C(s) H(s) + +

2⮬⏤ᗘ㏣ᚑไᚚ⣔(2)

z ㏣ᚑㄗᕪ ܧ(ݏ) ܴ(ݏ)= 1 െ ܪ ݏ ܲ(ݏ) 1 + ܥ ݏ ܲ(ݏ) = ݀_஼ ݏ {݀_௉ ݏ െ ݊_௉ ݏ ܪ ݏ } ݀_௉ ݏ ݀_஼ ݏ + ݊_௉ ݏ ݊_஼(ݏ) z ݀_஼ 0 = 0 䛒䜛䛔䛿 ݀_௉ 0 െ ݊_௉ 0 ܪ 0 = 0 䛺䜙䜀䚸ᐃᖖ఩⨨೫ᕪ䛿䝊䝻䚹 {1⮬⏤ᗘ⣔䛸䛿␗䛺䜚䚸݀_௉ 0 = 0 䛿᮲௳䛷䛿䛺䛟䛺䛳䛯䚹 {݀_௉ 0 െ ݊_௉ 0 ܪ 0 = 0 䛿䚸ܪ(0) = 1/ܲ(0)䚸䛴䜎䜚ܲ(ݏ)䛾ప࿘Ἴ䝀䜲䞁 䛾㏫ᩘ䛸ܪ(ݏ)䛾ప࿘Ἴ䝀䜲䞁䛜୍⮴䛧䛶䛔䜛䛸䛔䛖᮲௳䚹 {䛧䛛䛧䚸݀_௉ 0 െ ݊_௉ 0 ܪ 0 = 0 䛾᮲௳䛿䚸䝅䝇䝔䝮ܲ(ݏ) 䛾ኚື䛻ᙳ㡪䜢 ཷ䛡䜛䚹(䝻䝞䝇䝖䛷䛿䛺䛔) z 䛴䜎䜚䚸݀_஼ 0 = 0 䛜(䝻䝞䝇䝖䛻)ᐃᖖ఩⨨೫ᕪ䛜䝊䝻䛻䛺䜛᮲௳䚹 z ᐃᖖ㏿ᗘ೫ᕪ䛺䛹䜒ྠᵝ䚹