Vaishnav_37_b2.docx

TUTORIAL 10 DONE BY VAISHNAV SHANKAR ROLL NO – 37 REG NO – 150906260

1] CODE A=[-2 -1 -3; 0 -2 1; -7 -8 -9] B=[2;1;2]; C=[ 4 6 8]; Q=obsv(A,C) d=det(Q) r=rank(Q) if(size(Q)==r) disp('Observable s/m') else disp('not observable') end t=ctrb(A,B) D=det(t) R=rank(t) if(size(t)==R) disp('CONTROLABLE s/m') else disp('not CONTROLLABLE') end

OUTPUTA= -2 -1 -3 0 -2

1

-7 -8 -9

Q= 4

6

8

-64 -80 -78 674 848 814 d= -1.5760e+03 r=

3

Observable s/m t= 2 -11 142 1

0 -40

2 -40 437

D= -3.1930e+03 R= 3 CONTROLABLE s/m

2] CODE num=20*[1 5] den=poly([0 -1 -4]) sys=tf(num,den) [a b c d] = tf2ss(num,den) ap=fliplr(flipud(a)) bp=flipud(b); cp=fliplr(c) dp=d pos=9.5;

ts=0.74; z=(-log(pos/100))/(sqrt(pi^2+log(pos/100)^2)) wn =4/(z*ts) [num,den]=ord2(wn,z) r=roots(den) p1=[r(1) r(2) -5] k=acker(ap,bp,p1) anew=ap-bp*k; tss=ss(anew,bp,cp,dp) figure,step(feedback(sys,1)) figure,step(tss)

OUTPUTnum = 20 100 den = 1

5

4

0

sys = 20 s + 100 ----------------s^3 + 5 s^2 + 4 s

Continuous-time transfer function. a= -5 -4

0

1

0

0

0

1

0

b= 1 0 0

c= 0 20 100

d=

0

ap = 0

1

0

0

0

1

0 -4 -5 cp = 100 20

dp =

0

0

z= 0.5996

wn = 9.0147

num = 1

den = 1.0000 10.8108 81.2645 r= -5.4054 + 7.2143i -5.4054 - 7.2143i

p1 =

-5.4054 + 7.2143i -5.4054 - 7.2143i -5.0000 + 0.0000i

k= 406.3226 131.3186 10.8108

tss = A= x1

x2

x3

x1

0

1

0

x2

0

0

1

x3 -406.3 -135.3 -15.81

B= u1 x1 0 x2 0 x3 1

C= x1 x2 x3 y1 100 20 0

D= u1 y1 0

Continuous-time state-space model.

3] CODE clc;clear; num = 407*[1 .916]; den= poly([-1.27 -2.69]); sys= tf(num,den); [a b c d]=tf2ss(num,den); ap= fliplr(flipud(a)); bp= flipud(b); cp= fliplr(c); dp=d; z= 0.7; wn= 100; [num,den]= ord2(wn,z); r= roots(den); p1= [r(1) r(2)]; l= acker(ap',cp',p1)'

OUTPUTl= -38.6236 35.7135

4] CODE A=[0 -83.33; 500 -10]; B=[166.67;0]; C=[0 1]; D=0; [n d]=ss2tf(A,B,C,D) %state feedback controller AP=fliplr(flipud(A)); BP=flipud(B) CP=fliplr(C); DP=D; pos=20; Ts=0.5;

z=(-log(pos/100))/(sqrt(pi^2+log(pos/100)^2)) wn=4/(z*Ts); [num,den]=ord2(wn,z); r=roots(den); P1=[r(1) r(2)]; K=acker(AP,BP,P1) Anew=AP-BP*K; Tss=ss(Anew,BP,CP,DP) [num den]=ss2tf(Anew,BP,CP,DP); figure(1) step(num,den) title('With Controller') figure(2) step(n,d) title('Given System') %observer L=acker(AP',CP',P1)' Z=[0 0;0 0]; BPP=[BP;0;0]; CPP=[CP 0 0]; Anew1=[AP-BP*K BP*K;Z AP-L*CP] Oss=ss(Anew1,BPP,CPP,DP) [num1 den1]=ss2tf(Anew1,BPP,CPP,DP); figure(3) step(num1,den1) title('With Controller and Observed’)

OUTPUTn=

0

0

83335

d= 1.0e+04 * 0.0001 0.0010 4.1665

BP =

0 166.6700 z= 0.4559 K= -0.4970 0.0360

Tss = A= x1 x1

x2

-10

x2 -0.4957

B= u1 x1

0

x2 166.7

C= x1 x2 y1 1 0

D= u1 y1 0

500 -6

Continuous-time state-space model. L= 6.0000 -82.7143 Anew1 = -10.0000 500.0000

0

0

-0.4957 -6.0000 -82.8343 6.0000 0

0 -16.0000 500.0000

0

0 -0.6157

0

Oss = A= x1 x1

-10

x2

x3

500

x2 -0.4957

x4 0

-6 -82.83

x3

0

0

x4

0

0 -0.6157

B= u1 x1

0

x2 166.7 x3

0

x4

0

0

C= x1 x2 x3 x4 y1 1 0 0 0

-16

6

500 0

D= u1 y1 0

Continuous-time state-space model.