1.控制系统模型 ............................................................................................................................................. 3
例8_1 ...................................................................................................................................................... 3 例8_2 ...................................................................................................................................................... 4 例8_3 ...................................................................................................................................................... 6 例8_4 ...................................................................................................................................................... 8 例8_5 ...................................................................................................................................................... 9 例8_6 .....................................................................................................................................................10 例8_7 .....................................................................................................................................................11 2．控制系统的时域分析 .............................................................................................................................13
例8_8 .....................................................................................................................................................13 例8_9 .....................................................................................................................................................14 例8_10 ...................................................................................................................................................15 例8_11 ...................................................................................................................................................16 例8_12 ...................................................................................................................................................17 例8_13 ...................................................................................................................................................19 例8_14 ...................................................................................................................................................20 例8_15 ...................................................................................................................................................22 3．控制系统的根轨迹 .................................................................................................................................23
例8_16 ...................................................................................................................................................23 例8_17 ...................................................................................................................................................24 例8_18 ...................................................................................................................................................25 例8_19 ...................................................................................................................................................26 4．控制系统的频域分析 .....................................................................................................................28 例8_20 ...................................................................................................................................................28 例8_21 ...................................................................................................................................................30 例8_22 ...................................................................................................................................................31 例8_23 ...................................................................................................................................................32 例8_24 ...................................................................................................................................................33 例8_25 ...................................................................................................................................................34 例8_26 ...................................................................................................................................................35 例8_27 ...................................................................................................................................................37 例8_28 ...................................................................................................................................................38 例8_29 ...................................................................................................................................................40 例8_30 ...................................................................................................................................................42 例8_31 ...................................................................................................................................................43 例8_32 ...................................................................................................................................................45 例8_33 ...................................................................................................................................................47 例8_34 ...................................................................................................................................................49 例8_35 ...................................................................................................................................................50 例8_36 ...................................................................................................................................................51 例8_37 ...................................................................................................................................................52 例8_38 ...................................................................................................................................................53 例8_39 ...................................................................................................................................................54 例8_40 ...................................................................................................................................................56 例8_41 ...................................................................................................................................................57 例8_42 ...................................................................................................................................................58 6．最优控制器设计 .....................................................................................................................................59
例8_43 ...................................................................................................................................................59 例8_44 ...................................................................................................................................................60
例8_45 ...................................................................................................................................................61 例8_46 ...................................................................................................................................................62 例8_47 ...................................................................................................................................................64 例8_48 ...................................................................................................................................................66 例8_49 ...................................................................................................................................................68 例8_50 ...................................................................................................................................................70 例8_51 ...................................................................................................................................................71 例8_52 ...................................................................................................................................................73
1.控制系统模型 例8_1
设系统的零极点增益模型为：
H(s)?6(s?3)(s?1)(s?2)(s?5)
求系统的传递函数及状态空间模型。 解： k=6; z=[-3];
p=[-1,-2,-5];
[num,den]=zp2tf(z,p,k); [a,b,c,d]=zp2ss(z,p,k); printsys(num,den); printsys(a,b,c,d);
num/den =
6 s + 18
----------------------- s^3 + 8 s^2 + 17 s + 10 a =
x1 x2 x3 x1 -1.00000 0 0 x2 2.00000 -7.00000 -3.16228 x3 0 3.16228 0 b =
u1 x1 1.00000 x2 1.00000 x3 0 c =
x1 x2 x3 y1 0 0 1.89737 d =
u1 y1 0
例8_2
给定离散系统的状态空间方程，
?00???2.8?1.4?1???1.4??0?000??x(k)???u(k)?x(k?1)?? ???1.8?0.3?1.4?0.6??1??????000.60???0???y(k)??0001?x(k)?求传递函数模型和零极点模型，并判断其稳定性。 解：
a=[-2.8 -1.4 0 0; 1.4 0 0 0; -1.8 -0.3 -1.4 -0.6; 0 0 0.6 0;]; b=[1;0; 1; 0]; c=[0 0 0 1]; d=[0];
[num,den]=ss2tf(a,b,c,d); [z,p,k]=ss2zp(a,b,c,d) pzmap(p,z);
title('Pole-Zero Map');
z =
-0.5000 + 1.1358i -0.5000 - 1.1358i p =
-1.4000 + 0.0000i -1.4000 - 0.0000i -1.0606 -0.3394 k =
0. 6000
回目录
Pole-Zero Map1.510.5Imag Axis0-0.5-1-1.5-1.4-1.2-1-0.8-0.6Real Axis-0.4-0.20 回目录