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

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1 analog-control-mod : 2007/2/4(8:44) E8 E8. PID DC. PID 2. DC PID 3. E8.2 DC PID C8 E8. DC PID E6 DC P M () K M ( T M ) (E8.) DC PID C8 E8. r e u E8.2 PID E8. PID

2 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 K M K D K M K D (E8.3) P D () E8. PI K P ( T I ) DC P M () /T K D /T K K P u K M T M K D E8.2: PI K D K P K P P D () E8.3 r H P () K K P /T 2 /T K K P /T 2 (E8.4) K KP ω n, ζ T 2 K K P T. (E8.5)

3 analog-control-mod : 2007/2/4(8:44) E8.2. DC PID C8 3 K P ω n ζ ω n T K P ζ P D () r e K P K T E8.3: PD K P T I E8. E8.4 e(t) L P ID () K K P T I 2 ( T ) (E8.6) P D () r e K P ( ) T I K T E8.4: PID E8.5 L P ID () /T I [rad/] K D K P T I /T I /T K D K P PI (E8.3) (E8.4) E8. E8.5 20dB/dec /T > ω c > /T I /T I ω c ω c /T I /T ω c /T I K D K P T I

4 analog-control-mod : 2007/2/4(8:44) 4 E8 L PID 40dB/dec 0 20dB/dec 20 log K K P T 40dB/dec! c T I T! E8.5: PID E8.3 PID 0 u K M T M! T M K D n E8.6: K D K D E8.6 n K D α/t M K P = α K D /T M α α 0 E8.6 n K M K D (E8.7) K M K D T K D K D /T n K D

5 analog-control-mod : 2007/2/4(8:44) E8.3. DC PID 5 K P K D E8.7 r K P E8.5 ω c < /T K P < /K r e K P K T E8.7: K P K I K D K P E8.8 d K I /T I /T d r e K P T I T I K T E8.8: K I E8.3 DC PID E8. PID E8. PID E6 E8. E8.9 T D T E8.0 ab v d v n R R 2

6 analog-control-mod : 2007/2/4(8:44) 6 E8 E8.9 PID K D = C D R D, T D = C D R 3, K P = R 2 R R D R P, T I = C I R I. (E8.8) P M () v r e T I T I K P v u K M T M v K D T D E8.9: PID E8.0: PID E8. PID PID. K D = 0T I = K P (a) K D = 0 (E8.3) K = K M T = T M E6 (b) T I = L P ID ω c = 0./T M K P E8.5 Bode (c) ζω n (E8.5)

7 analog-control-mod : 2007/2/4(8:44) E8.3. DC PID 7 2. K P (E8.8) K D T I T D (a) K P ±0% R P E2 ˆ C D = 0.047µF T D T M /300 R 3 E2 (E8.3) T T M T D T T T M T D T M /300 C D K D ˆ R = 00kWR 2 = 22kW V cc = 5V 2 ±5V A V cc /5 R 2 /R 0.2 R 00 IC E2 R = 00kWR 2 = 22kW ˆ R P R D R I C I R D = 0kWR I = MWC I = 2.2µF (b) K P K D T ω c T I ζω n E8. PID E8.0. ˆ IC LM358N 2

8 analog-control-mod : 2007/2/4(8:44) 8 E8 ˆ v d A 3 R D 2. ˆ ˆ V cc = 5V 2 ˆ ab ˆ ˆ PID E8. DC ˆ ±5V ˆ PWM 2.5V PWM 5V v u kw E8 % E8.: PID 5. v r = 0 v r

9 analog-control-mod : 2007/2/4(8:44) E8.3. DC PID 9 6. FG ±0.5V v r E8.2 PID PID PID. K D R D (a) R P A 3 0 ab v d A 3 v r = 0V (b) R D 0kW v n ±0.5V (c) R D R P C I 2 2. K P R P (a) R D ab v n (b) R P v r ±0.5V (c) R P 3. K I C I (a) R D R P ab E8.0 v d R D v r v n (b) C I v d ±0.5V

10 analog-control-mod : 2007/2/4(8:44) 0 E8 (c) R I C I R I 4. DC PID (a) v r v 90 (b) v d (c) T ω c T I E8. PID. v r v v d 3. T ω c T I E8.4 G() b n n b n n b b 0 n a n n a a 0 { ( ) n ( ) } n d d d a n a dt dt dt a 0 (t) { ( n ( ) } n d d d = b n b n b dt) dt dt b 0 u(t) (E8.9) (E8.0)

11 analog-control-mod : 2007/2/4(8:44) E8.4. E8.2 2 G() b 2 2 b b 0 2 a a 0 ÿ(t) a ẏ(t) a 0 (t) = b 2 ü(t) b u(t) b 0 u(t) (E8.) (E8.2) E8.2 (E8.9) E8.2 d x c u x 0 c 0 a a 0 E8.2: 2 E8.2 (t) = c x (t) c 0 x 0 (t) d u(t), ẋ 0 (t) = x (t), ẋ (t) = a x (t) a 0 x 0 (t) u(t). (E8.3) (E8.4) (E8.5) ÿ(t) a ẏ(t) a 0 (t) = b 2 ü(t) b u(t) b 0 u(t), (E8.6) b 2 = d, b = c a d, b 0 = c 0 a 0 d (E8.7) E8.3 2

12 analog-control-mod : 2007/2/4(8:44) 2 E8 E8.2 E8.2 E8.3 d a 0 T T 0 v u - T v - T 0 v 0 c 0 T T 0 v a T c T E8.3: 2 E8.4 E8.2 E8.3 a = R R T, a 0 = R, c = R, c 0 = R 2 T 0 T R 7 T R R 6 T 0 T, d = R R 5, T = C R 3, T 0 = C R 4. (E8.8) E8. 2 b 0 G() 2 a a 0 (E8.9) E8.5 v i (t) v a (t)v b (t) v c (t) G a () b a 2 2 a a 0, b c G c () 2, a a 0 a b a R R 5, R C R R 3, b b b b G b () 2, a a 0 R a 0 C 2, R 2 R 3 R 4 R R, b c C R 3 R 5 C 2 R 3 R 4 R 5 (E8.20) (E8.2) (E8.22) (E8.23)

13 analog-control-mod : 2007/2/4(8:44) E E8.4: 2 E8.6 v i (t) E ±0% 2 E8.5: 2

14 analog-control-mod : 2007/2/4(8:44) 4 E8 E8.6: 2 E2 kw MW (a) G b f n = khz (b) G c ζ = 2/2 (c) G c 0dB (d) G a 0dB 2. G a G b G c E8.5 ˆ DC PID PID ˆ IC PID ˆ PID ˆ 2

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<4D F736F F D B B83578B6594BB2D834A836F815B82D082C88C60202E646F63> MATLAB/Simulink による現代制御入門 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/9241 このサンプルページの内容は, 初版 1 刷発行当時のものです. i MATLAB/Simulink MATLAB/Simulink 1. 1 2. 3. MATLAB/Simulink

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