Advance Control Lab

EXP-2

clc

close all

clear all

a=[0 1 0 0;0 -1.818 2.6727 0;0 0 0 1;0 -0.4545 31.1818 0];

b=[0;1.8182;0;4.545];

c=[1 0 0 0;0 0 1 0];

d=[0;0];

sys=ss(a,b,c,d);

if(rank(ctrb(sys))==length(a))

    disp('controllable')

else

    disp('uncontrollable')

end

if((rank(obsv(sys)))==length(a))

    disp('observable')

else

    disp('unobservable')

end

e=eig(a)

if(e<0)

    disp('stable')

else

    disp('unstable')

end

Exp -5 

clc

close all

clear all

a=[0 1 0 0;4.4537 0 0 0;0 0 0 1;-0.5809 0 0 0];

b=[0 ;-0.3947; 0; 0.9211];

c=[0 0 1 0];

d=[0];

s=tf('s');

x0=[1;1;1;1];

sys=ss(a,b,c,d);

if(eig(a)<0)

    disp('stable')

else

    disp('unstable')

end

eigen=eig(a)

if(rank(ctrb(sys))==length(a))

    disp('controllable')

else

    disp('uncontrollable')

end

if((rank(obsv(sys)))==length(a))

    disp('observable')

else

    disp('unobservable')

end

g=tf(sys)

step(sys)

figure

impulse(sys)

figure

step(sys/s)

figure

initial(sys,x0)

figure

[num,den]=ss2tf(a,b,c,d);

ce=den

r=roots(den)

f=feedback(g,1)

step(f)

if(eig(f)<0)

    disp('stable')

else

    disp('unstable')

end

p=[-2+i*5 -2-i*5 -3 -10];

k=acker(a,b,p)

sys2=canon(sys,'companion')

sys3=canon(sys,'modal')

J=jordan(a)

EXP-6

clc

clear all

close all

syms s

s=tf('s');

g=[1/(s+1) 0 (s+1)/((s+1)*(s+2)) ;-1/(s-1) 1/(s+2) 1/(s+2)]

sys=ss(g);

[A,B,C,D]=ssdata(sys)

step(g)

figure

step(g/s)

co=ctrb(A,B);

if(rank(co)==length(A))

    disp('controllable')

else

    disp('uncontrollable')

end

ob=obsv(A,C);

if(rank(ob)==length(A))

    disp('observable')

else

    disp('unobservable')

end

if(eig(g)<0)

EXP-7

clc

clear all

close all

A=[0 1 0 0;4.4537 0 0 0;0 0 0 1;-0.5805 0 0 0];

B=[0;-0.3947;0;0.5211];

C=[0 0 1 0];

D=[0];

p1=[-2 -1 -3+i*4 -3-i*4];

p2=[-3+i*3 ;-3-i*3; -10; -10];

sys=ss(A,B,C,D);

if(rank(ctrb(sys))==length(A))

    k=acker(A,B,p1)

    A1=A-B*k;

  sys1=ss(A1,B,C,D)

else

    disp('since system is uncontrollable state feedback cant be formed')

end

if(rank(obsv(sys))==length(A))

    k1=acker(A',C',p2)

    A2=A'-k1*C';

  sys2=ss(A2,B,C,D)

else

    disp('since system is unobservable state feedback cant be formed')

end

EXP-8

clc

clear all

close all

A=[0 1 0 0 0 0 ;-4.7059 -0.0887 0 0 1.3588 0;0 0 0 1 0 0;0 0 0 -5 1.617 4.5;0 0 0 0 -0.9091 0;0 0 0 0 0 1];

B=[0 0;0 0;0 0;0 0;1 0;0 0.8];

C=[1 0 0 0 0 0;0 0 1 0 0 0];

D=[0 0; 0 0];

sys=ss(A,B,C,D);

syms s S

s=tf('s');

if(rank(ctrb(sys))==length(A))

    disp('controllable')

else

    disp('uncontrollable')

end

if(rank(obsv(sys))==length(A))

    disp('observable')

else

    disp('unobservable')

end

step(sys)

figure

impulse(sys)

figure

 EXP-9

clc

clear all

close all

z=tf('z');

num=[0.3679 0.2642];

den=[1 -1.3679 0.3679];

sys=filt(num,den,0.1)

step(sys)

figure

impulse(sys)

figure

step(sys/z)

if(eig(sys)<1)

    disp('stable')

else

    disp('unstable')

end

EXP-10

clc

clear all

close all

Kp1=5;Kp2=5;

Ki1=0;

Ki2=10;

t1=1;

t2=5;

s=tf('s');

G=1/s*(s+1);

z1=c2d(G,1);

d1z=5;

num1=d1z*z1;

sys1=feedback(num1,1)

subplot(2,2,1);

step(sys1)

z2=c2d(G,5);

num2=d1z*z2;

sys2=feedback(num2,1);

subplot(2,2,2);

step(sys2)

d2z=Kp2*Ki2/s;

num3=[5,10];

den3=[1,10];

[d2z1,d2z2]=bilinear(num3,den3,1);

sys3=tf(d2z1,d2z2,1);

z3=c2d(G,1);

num4=sys3*z3;

sys4=feedback(num4,1);

subplot(2,2,3);

step(sys4)

[d3z1,d3z2]=bilinear(num3,den3,02);

sys5=tf(d3z1,d3z2,5);

z4=c2d(G,5);

num5=sys5*z4;

EXP-11

clc

clear all

close all

s=tf('s');

Kp=1.65*10^6;

Kg=3.71*10^5;

Jv=41822;

t1=0.2;

t2=0.5;

t3=0.8;

G=Kp/(s*(Kg+(Jv*s)))

tf1=c2d(G,t1);

tf2=c2d(G,t2);

tf3=c2d(G,t3);

rlocus(tf1)

figure

rlocus(tf2)

figure

rlocus(tf3)

EXP-12

clc

clear all

close all

s=tf('s');

Kp=1.65*10^6;

Kg=3.71*10^5;

Jv=41822;

t1=0.2;

t2=0.5;

t3=0.8;

G=Kp/(s*(Kg+(Jv*s)))

tf1=c2d(G*0.048,t1);

tf2=c2d(G*0.03,t1);

tf3=c2d(G*3.2,t1);

tf4=c2d(G*0.269,t2);

tf5=c2d(G*0.2,t2);

tf6=c2d(G*2,t2);

tf7=c2d(G*0.269,t3);

tf8=c2d(G*0.2,t3);

tf9=c2d(G*1,t3);

bode(tf1)

figure

nyquist(tf1)

figure

EXP-13

clc

clear all

close all

A=[0 1 0 0 0 0;-4.7059 -0.0852 0 0 1.3585 0;0 0 0 1 0 0;0 0 0 -5 1.617 4.5;0 0 0 0 -0.9091 0;0 0 0 0 0 -1];

B=[0 0;0 0;0 0;0 0;1 0;0 0.8];

C=[1 0 0 0 0 0;0 0 1 0 0 0];

D=[0 0;0 0];

t=0.5;

sys=ss(A,B,C,D);

g=tf(sys);

z=tf('z');

sysd=c2d(g,t)

[f,g,c,d]=ssdata(sysd)

p=[-0.5+i*0.25 -0.5-i*0.25 0.5+i*0.25 0.5-i*0.25 0.5 -0.5];

k=place(A,B,p)

m=A-B*k

e=eig(A)

EXP-14

clc

close all

clear all

m=0.1;

M=1;

k=0.091;

b=0.0036;

A=[0 1 0 0;-k/m -b/m k/m b/m;0 0 0 1;k/M b/M k/M b/M];

B=[0;0;0;1/M];

C=[1 0 0 0;0 0 1 0];

%X=[d;d';x;x'];

D=[0];

sys=ss(A,B,C,D);

z=tf('z')

tfd=c2d(sys,0.5);

[f,g,c,d]=ssdata(tfd)

p=[-0.00001 -0.05 -0.04 -0.03];

k=place(f,g,p)

Ad=f-g*k

Bd=zeros(4,1);

dbc=ss(Ad,Bd,C,D,0.5)

step(dbc)