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17.2.2016, 1:57
17.2.2016, 1:57
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2016

[4]. . 6.1, ; .

. 6.1.

. : (), (), - (), - () -- ().

.. . . , . , . . , , - , , .

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:

, c :

- . , :

c :

clear

close all

clc

num=[3];

den=[1 4 2 ];

W=tf(num,den)

m=0.5%

tz=5%

sigz=20;%

[y,t]=step(W);

figure(1)

plot(t,y,"g","LineWidth",1)

grid on

w=[0:0.1:10];%

Wreg=-polyval(den,(j-m)*w)./polyval(num,(j-m)*w);%

R=real(Wreg);%

I=imag(Wreg);%

K2=[0 0.5 1.5 2 3]

dif=length(K2)% 2

for i=1:dif

K1=R-m*I+K2(i)*m*w;%

K0=-(m^2+1)*I.*w+K2(i)*(m^2+1)*w.*w;%

kp=0; K1_plus=[]; K0_plus=[]; %

figure(2+i)

sig=[]; tp=[]; J=[];

for j=1:length(K1)

if (K1(j)>0) && (K0(j)>0) && (K0(j)*K2(i)/K1(j)^2<=0.5)

kp=kp+1;

K1_plus(kp)=K1(j);

K0_plus(kp)=K0(j);

Wr=tf([K2(i) K1_plus(kp) K0_plus(kp)],[1 0]);%

F=feedback(W*Wr,1,-1);

%r=pole(F)

[y1,t1]=step(F);

plot(t1,y1,"b")

grid on

hold on

tp(kp)=t1(end);

sig(kp)=(max(y1)/y1(end)-1)*100;

K1_plus;

K0_plus;

end;

end;

tp

sig

ws=1

wt=1

J=ws*abs(sig-sigz)/sigz+abs(tp-tz)/tz

[Jmin(i),kmin(i)]=min(J)

K1_opt(i)=K1_plus(kmin(i))

K0_opt(i)=K0_plus(kmin(i))

Wopt=tf([K2(i) K1_opt(i) K0_opt(i)],[1 0]);

Fopt=feedback(W*Wopt,1,-1);

%r=pole(F)

[y2,t2]=step(Fopt);

plot(t2,y2,"r")

figure(3+dif)

plot(t2,y2,"r")

grid on

hold on

figure(2)

plot(K1_plus,K0_plus,"m")

hold on

plot(K1_plus,K0_plus,"*r")

grid on

hold on

plot(K1_opt(i),K0_opt(i),"^k")

xlabel("K1");ylabel("K0");title(" K0=f(K1)")

end

Jmin

[Jbest,kbest]=min(Jmin)

Wr=tf([K2(kbest) K1_opt(kbest) K0_opt(kbest)],[1 0]);

F=feedback(W*Wr,1,-1);

[y1,t1]=step(F);

figure(3 +dif)

plot(t1,y1,"b")

grid on

hold on

Transfer function:

3

-------------

s^2 + 4 s + 2

m = 0.5000

tz = 5

K2 = 0 0.5000 1.5000 2.0000 3.0000

dif =5

tp =

Columns 1 through 13

19.3048 16.0873 13.7891 11.7056 15.4557 13.7645 12.1880 7.7298 10.2640 6.5500 8.6673 8.0326 7.5811

Columns 14 through 26

7.2361 7.0568 6.9403 6.2950 6.0089 6.2950 6.0327 5.7914 5.5687 5.3624 5.1709 4.9926 4.8262

Columns 27 through 35

4.6705 4.5246 4.3874 2.8389 2.7578 6.6739 6.4935 16.8144 23.4853

sig =

Columns 1 through 13

19.4573 19.8246 20.6441 21.5902 23.9968 25.2339 26.4786 26.0183 28.6746 27.8497 30.5213 31.2778 31.8398

Columns 14 through 26

32.2752 32.4955 32.5597 32.7651 32.6429 32.1792 31.8401 31.3428 30.6877 29.9152 29.0296 27.9857 26.7892

Columns 27 through 35

25.4514 24.0398 22.5441 19.9157 18.7816 17.6681 16.2702 13.5190 11.9446

ws =1

wt =1

J =

Columns 1 through 13

2.8881 2.2262 1.7900 1.4206 2.2910 2.0146 1.7615 0.8469 1.4865 0.7025 1.2595 1.1704 1.1082

Columns 14 through 26

1.0610 1.0361 1.0160 0.8973 0.8339 0.8680 0.7986 0.7254 0.6481 0.5682 0.4857 0.4008 0.3742

Columns 27 through 35

0.3385 0.2971 0.2497 0.4364 0.5094 0.4514 0.4852 2.6869 4.0998

Jmin = 0.2497

kmin = 29

K1_opt = 4.6408

K0_opt = 3.1762

tp =

Columns 1 through 13

7.5675 7.1488 7.3603 7.1940 6.4128 7.0764 5.7299 6.7877 5.8665 5.6140 5.3736 5.1438 4.9236

Columns 14 through 26

4.7122 4.5092 4.3144 4.1278 4.3714 4.1837 4.0059 4.2424 4.0688 3.9069 3.7565 3.9619 3.8210

Columns 27 through 39

3.6910 3.5710 3.7359 3.6249 3.5219 4.7367 2.0602 2.0085 2.4286 2.3720 11.6946 6.1675 11.6461

sig =

Columns 1 through 13

27.7549 28.5462 28.8696 29.3274 30.4857 30.0252 31.6294 30.8764 31.8468 32.2751 32.6268 32.8814 33.0882

Columns 14 through 26

33.2670 33.2914 33.2443 33.1177 32.5991 32.4481 32.1220 31.4837 31.0530 30.6130 30.0306 29.2473 28.5155

Columns 27 through 39

27.7806 26.9111 25.9454 24.9600 23.8782 22.9228 20.3859 19.4522 19.3914 18.5899 16.6980 16.2998 15.2306

ws = 1

wt = 1

J =

Columns 1 through 13

0.9012 0.8571 0.9155 0.9052 0.8069 0.9165 0.7275 0.9014 0.7656 0.7366 0.7061 0.6728 0.6697

Columns 14 through 26

0.7209 0.7627 0.7993 0.8303 0.7557 0.7857 0.8049 0.7257 0.7389 0.7493 0.7502 0.6700 0.6616

Columns 27 through 39

0.6508 0.6314 0.5501 0.5230 0.4895 0.1988 0.6073 0.6257 0.5447 0.5961 1.5040 0.4185 1.5677

Jmin = 0.2497 0.1988

kmin = 29 32

K1_opt =

4.6408 8.6158

K0_opt =

3.1762 7.3633

tp =

Columns 1 through 13

4.0487 3.9775 4.0117 3.9250 3.9586 3.9971 3.0164 2.7823 3.1048 2.8132 2.6624 2.8042 2.7492

Columns 14 through 26

2.6501 2.5539 2.4609 2.6246 2.5298 2.4395 2.6016 2.5125 1.7735 1.7165 1.6634 1.6141 1.5684

Columns 27 through 39

1.5260 1.4867 1.4501 1.4161 1.3844 1.3547 1.3269 1.6118 1.5812 1.5524 1.5251 1.3545 1.3322

Columns 40 through 41

1.3110 1.2907

sig =

Columns 1 through 13

31.6155 31.7560 32.0263 32.0709 32.2669 32.4025 33.0393 33.5399 32.3557 32.9887 33.0524 32.4162 32.2867

Columns 14 through 26

32.2232 31.9828 31.7709 31.1931 30.9978 30.6619 30.1145 29.7624 28.1139 27.6470 27.2053 26.7056 26.2235

Columns 27 through 39

25.6535 25.0991 24.4868 23.8181 23.1845 22.5208 21.8469 21.7952 21.1200 20.4850 19.9162 19.1025 18.7857

Columns 40 through 41

18.6182 18.6332

ws = 1

wt = 1

J =

Columns 1 through 13

0.7710 0.7923 0.7990 0.8185 0.8216 0.8207 1.0487 1.1205 0.9968 1.0868 1.1201 1.0600 1.0645

Columns 14 through 26

1.0811 1.0884 1.0964 1.0347 1.0439 1.0452 0.9854 0.9856 1.0510 1.0391 1.0276 1.0124 0.9975

Columns 27 through 39

0.9775 0.9576 0.9343 0.9077 0.8823 0.8551 0.8270 0.7674 0.7398 0.7138 0.6992 0.7740 0.7943

Columns 40 through 41

0.8069 0.8102

Jmin = 0.2497 0.1988 0.6992

kmin = 29 32 37

K1_opt = 4.6408 8.6158 21.3333

K0_opt = 3.1762 7.3633 13.3333

tp =

Columns 1 through 13

3.2236 3.1827 3.2310 3.2318 3.2541 2.3739 2.4456 2.4019 2.5022 2.4516 2.2086 2.5113 2.1627

Columns 14 through 26

2.1912 2.1178 2.2654 2.1896 2.1169 2.2630 2.1901 2.3232 1.5014 1.4569 1.4153 1.3765 1.3404

Columns 27 through 39

1.3067 1.2753 1.2461 1.2188 1.1933 1.4490 1.4211 1.3949 1.3702 1.3468 1.3246 1.3036 1.2836

Columns 40 through 43

1.1425 1.1260 1.1103 1.0952

sig =

Columns 1 through 13

31.9391 31.9997 32.1940 32.2754 32.3518 33.5678 33.0589 33.0022 32.3741 32.3487 32.7519 31.7431 32.3022

Columns 14 through 26

31.9478 31.7682 31.1862 31.0434 30.7702 30.2749 29.9803 29.5534 28.0865 27.7576 27.3553 27.0124 26.6037

Columns 27 through 39

26.1847 25.7455 25.2404 24.7475 24.2224 24.3071 23.6851 23.0840 22.4755 21.8738 21.2943 20.7658 20.3110

Columns 40 through 43

19.6258 19.3587 19.1980 19.1647

ws =1

wt =1

J =

Columns 1 through 13

0.9522 0.9635 0.9635 0.9674 0.9668 1.2036 1.1638 1.1697 1.1183 1.1271 1.1959 1.0849 1.1826

Columns 14 through 26

1.1591 1.1648 1.1062 1.1142 1.1151 1.0611 1.0610 1.0130 1.1040 1.0965 1.0847 1.0753 1.0621

Columns 27 through 39

1.0479 1.0322 1.0128 0.9936 0.9725 0.9256 0.9000 0.8752 0.8497 0.8243 0.7998 0.7776 0.7588

Columns 40 through 43

0.7902 0.8069 0.8180 0.8227

Jmin = 0.2497 0.1988 0.6992 0.7588

kmin = 29 32 37 39

K1_opt = 4.6408 8.6158 21.3333 29.0208

K0_opt = 3.1762 7.3633 13.3333 18.8021

tp =

Columns 1 through 13

2.3954 1.7703 2.3975 1.7485 1.7793 1.7415 1.7905 1.6548 1.8005 1.6473 1.7032 1.6271 1.6724

Columns 14 through 18

1.7224 1.7268 1.6772 1.6293 1.7499

sig =

Columns 1 through 13

32.3495 34.0259 32.3532 33.7043 33.3803 33.3239 32.8907 33.0568 32.4250 32.6352 32.2937 32.1801 31.8807

Columns 14 through 18

31.5271 31.2556 31.1137 30.9057 30.4700

ws =1

wt =1

J =

Columns 1 through 13

1.1384 1.3472 1.1382 1.3355 1.3132 1.3179 1.2864 1.3219 1.2612 1.3023 1.2740 1.2836 1.2596

Columns 14 through 18

1.2319 1.2174 1.2202 1.2194 1.1735

Jmin = 0.2497 0.1988 0.6992 0.7588 1.1382

kmin = 29 32 37 39 3

K1_opt = 4.6408 8.6158 21.3333 29.0208 29.4375

K0_opt = 3.1762 7.3633 13.3333 18.8021 135.4688

Jmin = 0.2497 0.1988 0.6992 0.7588 1.1382

Jbest =0.1988

kbest = 2

:

. 1 , m=0.4, sig 15 % tz=5 c .

- . 2.

. 3 - 7 J , .

. 7 J , .

(1)

Y(t)

t

(3) 2=1

Y(t)

t

(5) 2=2

Y(t)

t

(4)

(6)

(7) 2=3

(2) -

(8)

y(t)

t



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