D:/BOOK/MAIN/MAIN.DVI

Similar documents

2012 September 21, 2012, Rev.2.2

( ) 5. VSS (VIM ) 10. ( ) 11. (ANN ) ( )

[1.1] r 1 =10e j(ωt+π/4), r 2 =5e j(ωt+π/3), r 3 =3e j(ωt+π/6) ~r = ~r 1 + ~r 2 + ~r 3 = re j(ωt+φ) =(10e π 4 j +5e π 3 j +3e π 6 j )e jωt

S I. dy fx x fx y fx + C 3 C dy fx 4 x, y dy v C xt y C v e kt k > xt yt gt [ v dt dt v e kt xt v e kt + C k x v + C C k xt v k 3 r r + dr e kt S dt d

(3) (2),,. ( 20) ( s200103) 0.7 x C,, x 2 + y 2 + ax = 0 a.. D,. D, y C, C (x, y) (y 0) C m. (2) D y = y(x) (x ± y 0), (x, y) D, m, m = 1., D. (x 2 y

LCR e ix LC AM m k x m x x > 0 x < 0 F x > 0 x < 0 F = k x (k > 0) k x = x(t)

S I. dy fx x fx y fx + C 3 C vt dy fx 4 x, y dy yt gt + Ct + C dt v e kt xt v e kt + C k x v k + C C xt v k 3 r r + dr e kt S Sr πr dt d v } dt k e kt

C:/KENAR/0p1.dvi

,, 2. Matlab Simulink 2018 PC Matlab Scilab 2

Note.tex 2008/09/19( )

( ) 2.1. C. (1) x 4 dx = 1 5 x5 + C 1 (2) x dx = x 2 dx = x 1 + C = 1 2 x + C xdx (3) = x dx = 3 x C (4) (x + 1) 3 dx = (x 3 + 3x 2 + 3x +

曲面のパラメタ表示と接線ベクトル

24.15章.微分方程式

II K116 : January 14, ,. A = (a ij ) ij m n. ( ). B m n, C n l. A = max{ a ij }. ij A + B A + B, AC n A C (1) 1. m n (A k ) k=1,... m n A, A k k

1 No.1 5 C 1 I III F 1 F 2 F 1 F 2 2 Φ 2 (t) = Φ 1 (t) Φ 1 (t t). = Φ 1(t) t = ( 1.5e 0.5t 2.4e 4t 2e 10t ) τ < 0 t > τ Φ 2 (t) < 0 lim t Φ 2 (t) = 0

振動と波動

<4D F736F F D B B BB2D834A836F815B82D082C88C602E646F63>

<4D F736F F D B B83578B6594BB2D834A836F815B82D082C88C60202E646F63>

2 0.1 Introduction NMR 70% 1/2

閨75, 縺5 [ ｨﾁ573, 縺ｨｨ

A大扉・騒音振動.qxd

() (, y) E(, y) () E(, y) (3) q ( ) () E(, y) = k q q (, y) () E(, y) = k r r (3).3 [.7 ] f y = f y () f(, y) = y () f(, y) = tan y y ( ) () f y = f y

1 8, : 8.1 1, 2 z = ax + by + c ax by + z c = a b +1 x y z c = 0, (0, 0, c), n = ( a, b, 1). f = n i=1 a ii x 2 i + i<j 2a ij x i x j = ( x, A x), f =

入試の軌跡

( ) ( ) ( ) ( ) PID

さくらの個別指導 ( さくら教育研究所 ) A AB A B A B A AB AB AB B

36 th IChO : - 3 ( ) , G O O D L U C K final 1

1.1 ft t 2 ft = t 2 ft+ t = t+ t d t 2 t + t 2 t 2 = lim t 0 t = lim t 0 = lim t 0 t 2 + 2t t + t 2 t 2 t + t 2 t 2t t + t 2 t 2t + t = lim t 0

December 28, 2018

24 I ( ) 1. R 3 (i) C : x 2 + y 2 1 = 0 (ii) C : y = ± 1 x 2 ( 1 x 1) (iii) C : x = cos t, y = sin t (0 t 2π) 1.1. γ : [a, b] R n ; t γ(t) = (x

t θ, τ, α, β S(, 0 P sin(θ P θ S x cos(θ SP = θ P (cos(θ, sin(θ sin(θ P t tan(θ θ 0 cos(θ tan(θ = sin(θ cos(θ ( 0t tan(θ

Part () () Γ Part ,

II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2

構造と連続体の力学基礎

4.6: 3 sin 5 sin θ θ t θ 2t θ 4t : sin ωt ω sin θ θ ωt sin ωt 1 ω ω [rad/sec] 1 [sec] ω[rad] [rad/sec] 5.3 ω [rad/sec] 5.7: 2t 4t sin 2t sin 4t

2 1 κ c(t) = (x(t), y(t)) ( ) det(c (t), c x (t)) = det (t) x (t) y (t) y = x (t)y (t) x (t)y (t), (t) c (t) = (x (t)) 2 + (y (t)) 2. c (t) =

,. Black-Scholes u t t, x c u 0 t, x x u t t, x c u t, x x u t t, x + σ x u t, x + rx ut, x rux, t 0 x x,,.,. Step 3, 7,,, Step 6., Step 4,. Step 5,,.

<4D F736F F D B B83578B6594BB2D834A836F815B82D082C88C60202E646F63>

2.2 ( y = y(x ( (x 0, y 0 y (x 0 (y 0 = y(x 0 y = y(x ( y (x 0 = F (x 0, y(x 0 = F (x 0, y 0 (x 0, y 0 ( (x 0, y 0 F (x 0, y 0 xy (x, y (, F (x, y ( (

M3 x y f(x, y) (= x) (= y) x + y f(x, y) = x + y + *. f(x, y) π y f(x, y) x f(x + x, y) f(x, y) lim x x () f(x,y) x 3 -

< 1 > (1) f 0 (a) =6a ; g 0 (a) =6a 2 (2) y = f(x) x = 1 f( 1) = 3 ( 1) 2 =3 ; f 0 ( 1) = 6 ( 1) = 6 ; ( 1; 3) 6 x =1 f(1) = 3 ; f 0 (1) = 6 ; (1; 3)

名古屋工業大の数学 2000 年 ~2015 年大学入試数学動画解説サイト

2 Chapter 4 (f4a). 2. (f4cone) ( θ) () g M. 2. (f4b) T M L P a θ (f4eki) ρ H A a g. v ( ) 2. H(t) ( )

128 3 II S 1, S 2 Φ 1, Φ 2 Φ 1 = { B( r) n( r)}ds S 1 Φ 2 = { B( r) n( r)}ds (3.3) S 2 S S 1 +S 2 { B( r) n( r)}ds = 0 (3.4) S 1, S 2 { B( r) n( r)}ds

A (1) = 4 A( 1, 4) 1 A 4 () = tan A(0, 0) π A π

x i [, b], (i 0, 1, 2,, n),, [, b], [, b] [x 0, x 1 ] [x 1, x 2 ] [x n 1, x n ] ( 2 ). x 0 x 1 x 2 x 3 x n 1 x n b 2: [, b].,, (1) x 0, x 1, x 2,, x n

analog-control-mod : 2007/2/4(8:44) 2 E8 P M () r e K P ( ) T I u K M T M K D E8.: DC PID K D E8. (E8.) P M () E8.2 K P D () ( T ) (E8.2) K M T M K, T

[] x < T f(x), x < T f(x), < x < f(x) f(x) f(x) f(x + nt ) = f(x) x < T, n =, 1,, 1, (1.3) f(x) T x 2 f(x) T 2T x 3 f(x), f() = f(t ), f(x), f() f(t )

B. 41 II: 2 ;; 4 B [ ] S 1 S 2 S 1 S O S 1 S P 2 3 P P : 2.13:

But nothing s unconditional, The Bravery R R >0 = (0, ) ( ) R >0 = (0, ) f, g R >0 f (0, R), R >

II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R

1 1 H Li Be Na M g B A l C S i N P O S F He N Cl A e K Ca S c T i V C Mn Fe Co Ni Cu Zn Ga Ge As Se B K Rb S Y Z Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb T e

OABC OA OC 4, OB, AOB BOC COA 60 OA a OB b OC c () AB AC () ABC D OD ABC OD OA + p AB + q AC p q () OABC 4 f(x) + x ( ), () y f(x) P l 4 () y f(x) l P

F8302D_1目次_ doc

応力とひずみ.ppt

f(x) = x (1) f (1) (2) f (2) f(x) x = a y y = f(x) f (a) y = f(x) A(a, f(a)) f(a + h) f(x) = A f(a) A x (3, 3) O a a + h x 1 f(x) x = a

小川／小川

meiji_resume_1.PDF

I ( ) 1 de Broglie 1 (de Broglie) p λ k h Planck ( Js) p = h λ = k (1) h 2π : Dirac k B Boltzmann ( J/K) T U = 3 2 k BT

高等学校学習指導要領

高等学校学習指導要領

Transcription:

8 2 F (s) =L f(t) F (s) =L f(t) := Z 0 f()e ;s d (2.2) s s = + j! f(t) (f(0)=0 f(0) _ = 0 d n; f(0)=dt n; =0) L dn f(t) = s n F (s) (2.3) dt n Z t L 0 f()d = F (s) (2.4) s s =s f(t) L _ f(t) Z Z ;s L f(t) _ df() = 0 d ;s 0 e;s d = f()e ; f() de;s d 0 d 0 Z = f()e + s f()e ;s d = ;f(0) + sf (s) (2.5) 0 f(t) n L d n f(t) = ;s n; f(0) ; s n;2 f(0) _ dn; f(0) ;; dt n dt n; + s n F (s) (2.6) (f(0) = 0 0) (2.6) (2.3) f(t) g(t) = _g(t) Z t 0 _ f(0) = 0 d n; f(0)=dt n; = f()d G(s)

2.3 v R (t) =Ri R (t) (2.5) Z v C (t) = t i C ( )d (2.6) C 0 v L (t) =L d dt i L(t) (2.7) (a) (b) (c) 2.7 R []C [F]L [H]v R (t)v C (t) v L (t) [V]i R (t)i C (t)i L (t) [A] 2. RL 2.8 RL u(t) vin(t) y(t) i(t) (a) 2.8 u(t) = vin(t)y(t) = i(t) ( ) 2.8 RL L _y(t) +Ry(t) =u(t) (2.8) (b) (2.8) u(s) y(s) P (s)

2.4 () 5 () 2.3 f r (t) ( r (t)) () c f r (t) =;c _z(t) (2.34) r (t) =;c (t) _ (2.35) (a) (b) 2.3 () 2.3 (a) 2.3 (a) M z(t) =f (t) ; c _z(t) (2.36) u(t) =f (t) y(t) =z(t) M y(t) +c _y(t) =u(t) (2.37) (b) (2.37) P (s) P (s) = Ms 2 (2.38) + cs 2.4 2.3 (b) u(t) = (t)y(t) =

3. 37 (p i ) k i =(s ; p i )y(s) (3.30) s=p i bs + b0 y(s) = (s ; p)(s ; k p2) = s ; k2 p + s ; p2 (3.3) s ; p (s ; p)y(s) =k + k2(s ; p) s ; p2 (3.32) s = p k =(s ; p)y(s) s=p i k k2 (3.3) (3.32) (3.33) 3.0 3.8 3.8 (3.30) k = sy(s) s=0 = s + s=0 = k2 =(s +)y(s) s=; = s s=; = ; (b) p i (i = 2 n) p = p 2 = = p` (3.27) y(s) = k ` (s ; p )` + + k 2 (s ; p ) 2 + k s ; p + k`+ s ; p`+ + k`+2 s ; p`+2 + + k n s ; p n (3.34) y(s) y(t) =L ; y(s) = k `t` + + k 2 t + k e pt `! +k`+ e p`+t + k`+2 e p`+2t + + k n e pnt (3.35)

38 3 k i 8 >< >: (p i ) d`;i f(s ; p )`y(s)g k i = (` ; i)! ds`;i k j =(s ; p j )y(s) s=pj s=pi (i = 2 `) (j = ` + `+2 n) b2s2 + bs + b0 y(s) = (s ; p) 2 k2 (s ; p3) = (s ; p) 2 k k3 + s ; p + s ; p3 (3.37) (s ; p) 2 (s ; p) 2 k3(s ; p)2 y(s) =k2 + k(s ; p) + s ; p3 (3.38) s = p k2 =(s ; p) 2 y(s) s=p k2 (3.38) s df(s ; p) 2 y(s)g ds (3.36) (3.37) (3.38) (3.39) = k + k3f2(s ; p)(s ; p3) ; (s ; p)2 g (s ; p3) 2 (3.40) (3.40) s = p k = df(s ; p)2 y(s)g ds s=p (3.4) k k3 pi 3. 3.9 3.9 (3.36)

44 3 (a) T> 0 (b) T< 0 3.0 T T > 0 T < 0 T > 0 T T > 0 t = T y(t) y = K 63.2 % 3.6 y(t) = K T e;t=t (t 0) (3.52) 3.7 3. RL S ON () (2) (3) u(t) e(t) y(t) i(t) RL T S ON i(t) i R

3.3 2 47 (a) 0 < (b) ; <<0 (c) 3.4 y(t) =KL ; s ; 2 (d) ;! n (s +! n ) 2 ; s +! n = K ; e ;!nt (! n t +) (3.57) (3.57) = y = K ( 3.4 (c)) = ; ( 3.4 (d)) (iii) jj > P (s) (2 ) p = ;( + p 2 ; )! n p 2 = ;( ;p 2 ; )! n t 0

48 3 ; y(t) =KL s + p2 p ; p ; p 2 s ; p s ; p 2 ; + e! nt ; ; ; e ;! nt # = K " ; e;!nt 2 (3.58) =p 2 ; jj >>0 (3.58) > y = K ( 3.4 (c)) <; ( 3.4 (d)) 2 (a) Tp (3.54)(3.57)(3.58) 0 << 0 << (3.54) y(t) =K ( ; e ;!nt p ; 2 sin! dt + cos! d t!) y(t) _y(t) = K! n p ; 2 e;!nt sin! d t (3.59) T p! d t = (sin! d t =0 t>0) T p T p = = (3.60)! d! np ; 2 (b) Amax y max y max = y(t p )=K ; +e ;!ntp (3.6) y = K A max

3.3 2 49 A max = y max ; y = Ke ;!ntp = Kexp ; p ; 2! (3.62) (c) (3.59) i y i! d t i =(2i ; ) (i = 2 ) t i y(t) i A i = A i+ =A i = A i+ A i y i = y(t i )=K ; +e ;!nti (3.63) A i = y i ; y = Ke ;!nti (3.64) = e;!nti+ e ;!nti = exp ; 2 p ; 2 0 =log e 2! (3.65) 0 = ; (3.66) p ; 2 2 2 () () <0 () =0 () 0 << A max 0 <<!! A max = Kexp ; 2 = exp ; p ; p 2 ; 2 y = K

6. 09 u(t) =Asin!t (A >0!>0) y(t) u(t) =Asin!t u(s) =A!=(s 2 +! 2 ) y(t) y(s) =P (s)u(s) = k = A! +! s + A! s 2 +! 2 = A(j ;!) k2 = 2 2( +! 2 ) k s + + k2 s + j! + k3 = ; A(j +!) 2( +! 2 ) k3 s ; j! y(t) y(t) =L ; [y(s)] = k e ;t + k 2e ;j!t + k 3e j!t (6.2) = A! +! 2 e;t + A (sin!t ;! cos!t) (t 0) (6.3) +! 2 (6.3) e ;t = 0 y(t) u(t) = A sin!t y(t) = A (sin!t ;! cos!t) +! 2 = B(!) sin(!t + G p(!)) (= y app(t)) (6.4) A B(!) = p +! 2 Gp(!) =tan; (;!) =;tan ;! (a) u(t) = sin0:t 6.2 (b) P (s) ==(s +) u(t) = sin0t 6.2 A =! =0: 0 u(t)y(t) y(t) y app(t) 6.2 u(t) y(t)

6. 3 P (j!)= N (j!)n2(j!) N m (j!) D(j!)D2(j!) D n (j!) = jn (j!)je j\n(j!) jn2(j!)je j\n2(j!) jn m (j!)je j\nm(j!) jd(j!)je j\d(j!) jd2(j!)je j\d2(j!) jd n (j!)je j\dn(j!) jn (j!)jjn2(j!)jjn m (j!)j = jd(j!)jjd2(j!)jjd n (j!)j exp ( j mx nx \N i (j!) ; \D i (j!) i= i=!) (6.20) (6.9) jp (j!)j \P (j!) jp jn (j!)jjn2(j!)jjn m (j!)j (j!)j = jd(j!)jjd2(j!)jjd n (j!)j mx (6.2) \P (j!)= \N i (j!) ; \D i (j!) (6.22) i= i= 6.4 6.3 P (s) ==(s +)(s +2) P (s) = D(s) =s + D2(s) =s +2 D (s)d 2(s) p jd (j!)j = +! 2 \D (j!) = tan ;! jd 2(j!)j = p +4! 2 \D 2(j!) = tan ; 2! P (s) jp (j!)j = jd = ; (j!)jjd 2(j!)j p( (6.23) +! 2 )( + 4! 2 ) \P (j!) =; \D (j!)+\d 2(j!) = ; tan ;! + tan ; 2! (6.24) (6.23) (6.5) = tan ;! 2 = tan ; 2! nx

8 6 M p jp (0)j =! p u(t) y(t) u(t) () 6.3 6.3. 5 P (s) = +Ts jp (j!)j \P (j!) (6.27) jp (j!)j = p +(!T ) 2 \P (j!)=;tan;!t (6.28) (6.28) ( 20log!T << 0 jp (j!)j = 20log 0 = 0 [db] \P (j!) = ;tan ; 0=0[deg] 8 <!T = : 20log 0jP (j!)j =20log 0 p = ;3:0 [db] 2 \P (j!)=;tan ; =;45 [deg] 8 <!T >> : 20log 0jP (j!)j = 20log 0!T = ;20log 0!T [db] \P (j!) = ;tan ; = ;90 [deg] 6.76.8 6.9! ==T 0[dB] ;20 [db/dec] 0 <! =5T 0 [deg]! 5=T ;90 [deg] 5 2.6.2 (20 )

20 6! b jp (j!)j () T (!<< =T 0 [db] 0 [rad]!>> =T ) () ()! c ==T () 6.0 6.0 6.5 (6.27) (=2 0) =2 6.6 P (s) ==( + 0s) 6.3.2 2 2 6 6 2 2.6.3 (2 )

7. 37 (P (s)c(s) ) P (s)c(s) P (s)c(s) (; 0) (a) (b) 7.5 P (s)c(s) 7.2 P P (s) = +Ts T >0 C(s) =kp kp > 0 7. L(s) :=P (s)c(s) =kp =( + Ts) jl(j!)j \L(j!) jl(j!)j = kp p +(!T) 2 \L(j!) =;tan;!t! =0 jl(j!)j = kp \L(j!) = 0 [deg]! = jl(j!)j =0 \L(j!) =;90 [deg] L(j!) kp L(j!) = +j!t = kp ( ; j!t) +(!T) 2 L(j!) Im L(j!) =0! =0 P (j!)c(j!) 7.6 kp > 0 P (j!)c(j!) (; 0) kp > 0

38 7 7.6 7.2 P (s)c(s) 7.7 7.3 P (s)c(s) 7.3 2 P P (s) = (s +) 3 (7.) C(s) =k P k P > 0 (7.2) 7. k P k P > 0 L(s) :=P (s)c(s) jl(j!)j \L(j!) jl(j!)j = k P j +j!j 3 = k P ( +! 2 ) 3=2 \L(j!) =;3tan;! (7.3)! =0 jl(j!)j = k P \L(j!) = 0 [deg]! = jl(j!)j =0 \L(j!) =;270 [deg] L(j!) L(j!) = kp D(j!) D(j!) =(; 3!2 )+j!(3 ;! 2 ) D(j!) Im D(j!) =0 0 <!<! = p 3 \L(j!) =;80 [deg] p! =! pc! pc = 3 7.! =! pc jl(j! pc)j = k P ( +! 2 pc) 3=2 = kp 8 < (7.4) 0 <k P < 8 7. k P =8

60 8 8. D =0 2 Ann Bn Cn D u(t) y(t) ( ) 3 (2.) n>m() D =0 8. 8. 2.4 (2.39) (t) =0 J (t) =;c _ (t) ; M`g(t) + (t) (8.3) x(t) u(t) y(t) " # " # x (t) (t) x(t) = = x 2(t) _(t) u(t) = (t) y(t) =(t) _x (t) = (t) _ =x 2(t) _x 2(t) = (t) = ;;c (t) _ ; M`g(t) + (t) J = ; M`g J x(t) ; c J x2(t) + J u(t) y(t) =(t) =x (t) (8.3) 2 3 2 3 0 0 A = 4 ; M`g ; c 5 B = 4 5 C = 0 D =0 (8.4) J J J 2 MATLAB 8.5. (73 ) 3

8.3 67 8.3 D =0 8.3 8.5 P{D 5.3.2 P{D u(t) =k P e(t) ; k D _y(t) e(t) =r ; y(t) (8.28) u(t) = (t)y(t) =(t) x (t) =(t) x 2(t) = _ (t) (8.28) P{D u(t) =k P ; r ; x (t) ; k Dx 2(t) = ;k P " # x (t) ;k D + k P r x 2(t) = Kx(t) +Hr K = ;k P ;k D H = kp (8.29) (8.27) r =0(8.27) H =0 u(t) =Kx(t) (8.30) (8.30) x(t) (8.30) (8.) ; _x(t) = A + BK x(t) (8.3) A + BK K t! x(t)! 0 (8.30) K

72 8 8.8 2.4 y(t) =x (t) =(t) r (8.45)(8.46) K 8.8 8.6 y(t) r = 8.6 Q = diag q q > 0 0 R = (r = x(0) = 0) 8.4.2 8.7 Z t u(t) =Kx(t) +k I w(t) w(t) := e( )d e(t) =r ; y(t) (8.47) 0 x(t) = y(t) (5.0) (8.47) _y(t)t I{PD x e (t) = x(t) T w(t)t 8.7

202 2 2. () P (s) = s ;2 +2 2s + (2) P (s) = ;p 2j ; 3s 2 +2s + 3 2 C 2.2 P (s) = CLs 2 + RCs + Cs 2.3 () P (s) = RCs + (2) P (s) = RCs + 2.4 P (s) = Js 2 + cs 2.5 P (s) = Ms + c 2.6 P (s) = Ms 2 +(c + c 2 )s + k 2.7 2.8 T (t) = 2 M _z(t)2 U (t) =0D(t) = 2 c _z(t)2 q(t) =z(t)(t) =f (t) (2.46) (2.36) r T = M c K = 2.9! n = p = R C K = c CL 2 L 2.0 ;:043 0:5935j0:4793 0:752j;:0000 :442j 0 7 2. P (s) = s 2 ;450 280:2j + 2900s +07 3 3. 3 3.2 () ; s s +2 + 2 s ; (2) s 2 + 2 s 3 + 6 6 s 4 (3) s 2 +9 + s s 2 +4 (4) ; s +3 s s 2 +6s +0 (5) 6 s +5 (s +2) 3 (6) s 2 +4s +3 3.3 () f (t) =2+3e;2t (2) f (t) = t2 2 e ;t (3) f (t) =cos5t + 5 sin5t (4) f (t) =e ;t 2cos2t + 32 sin2t 3.4 () y(t) = 3 2 ( ; e ;2t ) (2) y(t) =2; 3e;t + e;2t cos2t + 2 sin2t (3) y(t) = 2( ; te;t ; e;t ) (4) y(t) =; e;t 3.5 () y = 2 (2) y =2

203 K 3.6 y(t) =L; y(t) = K +Ts T e ;t=t y(0) = K T 3.7 () P (s) = Ls + R T = L R (2) y(t) =K( ; e;t=t )= R ( ; e ;Rt=L )(t 0)y = R (3) R T L T 3.8 3.7 R = =50[]L = RT =0:2 [H] y 3.9 R 2r L r C k 3.0 ()! n = M = c K = 2p km k (2) K = y =0:04! d = A max = 6:28 = ; log e = 2:77 T p T p K (3)! n = q! d 2 + 2 = 6:87 = = 0:404 k = = 25! n K M = k =! n 2 0:530c =2! nm = 2:94 3. () (2) (3) (4) 3.2 3.5 4 4. 4.2 () s = ; p 3j 2 (2) s = ; p 5 2 4.3, 4.4 () k P > ; 2 5 (2) k P > ; 2 5 0 <k I < 2 5 (2 + 5k P ) 4.5 4.5 4.6 () C(s) =2e = 2 C(s) =5e = 6 27 4.7 () C(s) =2y = 5 5 C(s) =5y = 2 27 4.8 G yr(s) = 0s +6:25 s 3 +2s 2 +2s +6:25, G yd(s) = (2) e =0 (2) y =0 5s s 3 +2s 2 +2s +6:25, s 3 +2s 2 +2s G er(s) = s 3 +2s 2 +2s +6:25, G ;5s ed(s) = s 3 +2s 2 +2s +6:25 G yr(s)gyd (s) 4.8 4.9 4.8 4.0 4.5

205 6 6. () y(t) = 2 et ; 2 (cost +sint) t! et! y(t) y(t) (6.7) 6.2 () jp (j!)j = p 25 +! 2, \P! (j!)=;tan; 5 (2) jp (j!)j = p 25 +! 2, \P (j!) =! tan; 5 (3) 2 jp (j!)j = p 4+! 4, \P 2! (j!)=;tan; 2 ;! 2 (4) jp (j!)j =! 2s +! 2 (9 +! 2 )(6 +! 2 )(25 +! 2 ), \P (j!) = 90 + tan ;! ; tan ;! ;! 3 tan; ;! 4 tan; 5 (5) jp (j!)j = ( +! 2 ) 5, \P (j!)=;0tan;! 6.3 y(t) = sin(t + ), = tan ; 2 ; tan; 2 6.4 B(! ) A = 0, B(! 2) A =, B(! 3) A = 0, B(! 4) A = 6.5 P (j!) ==( + j!t) =x + jy jp (j!)j ==p +(!T ) 2 = px 2 + y 2 \P (j!)=;tan ;!T =tan ; y=x y=x = ;!T p +(!T ) 2 = p px +(;y=x) 2 = 2 + y 2 00 (x ; =2) 2 + y 2 =(=2) 2 6.6 6.6 6.7 6.7 6.8 () P (j!) = e ;j!l = cos!l ; jsin!l jp (j!)j =\P (j!) = ;!L 6.8 (a) (2) jp (j!)j ==p +(!T ) 2 \P (j!) =;(!L +tan ;!T ) 6.8 (b) 6.9 6.0 7 7. =0) =0) 7.2 () 0 <k P < 8 (! =! pc = p 5 Im P (j! pc)c(j! pc) (2) 0 <k P < 6(! =! pc = p 2 Im P (j! pc)c(j! pc)

7.3 () 8>< >: 8>< >:!gc =!pc = 0 [rad/s] k G M =80; P 20log 0 4 qk [db] =2 ; P 02 [rad/s] (k P > 0 4 ) P M = 80 ; 4tan ; q (2) k P = 6 9 04 k =2 ; P 02 0 207 [deg] (k P > 0 4 ) 7.4 7.5 P k P =8:5 P M =49:98 [deg]pi k P =5:8T I =0:85 P M =50:23 [deg]pid k P =8:5T I =0:85T D =0:04 P M =50:30 [deg] S(s)T (s) 8 8. () (2.36) x(t) = T z(t) _z(t) Z t _x(t) =" 0 0 ;c=m y(t) = 0 x(t) # x(t) +" 0 =M # u(t) P (s) ==(Ms 2 + cs) (2) RCL (2.20)(2.2) T x(t) = i( )d i(t) 0 _x(t) =" 0 ;=CL ;R=L y(t) = =C 0 x(t) 8.2 e At = e ;2t" # ;3t" 3 ;2 # ; + e # x(t) +" 0 =L # u(t) P (s) ==(CLs 2 + RCs +) ;6 ;2 6 3