1. ROOT LOCUS (SAMPLE ASSIGNMENT)
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Routh Hurwitz Criterion
RouthHurwitzCriterion.m
% PROGRAM BY ASUTOSH MISHRA %
clc;
close all;
clear all;
y1 = input('Press "y" and "Enter" to Start The Program:: ','s');
disp(' ');
if (y1~='y')
errordlg('**Please Type "y" to continue Else The Program Will Terminate**','Caution');
y1 = input('Press "y" and Enter to Continue:: ','s');
end
if (y1~='y')
disp(' ');
disp('Program Terminates');
end
y2 = y1;
y3 = y1;
clc;
while (y1=='y') && (y2=='y')
if (y3~='y')
clc;
end
disp('~:~:~:~:~:~:~:~:~:~ROUTH HURWITZ CRITERION~:~:~:~:~:~:~:~:~:~');
disp(' ');
disp(' Stability Analysis Using Characteristic Equation ');
disp(' ');
if (y1=='y');
clear a b c D1 D2 G G1 G2 H i I k K L1 L2 m n P P1 P2 Q r R R1 R2 R3 Z Z1;
disp('~:~:Analysis Using Characteristic Equation:~:~');
disp(' ');
helpdlg(sprintf('--> The Charateristic Equation Is " a(0) * x^n + a(1) * x^(n-1) + ... + a(n)"
n--> a(0) , a(1) , a(2) ... are coefficients n--> If n is odd then Even Power Coefficients are
:: a(1) , a(2) , a(3) ... a(n-1) n--> If n is even then the Even Power Coefficients are :: a(0) ,
info@assignmentpedia.com

2. a(2) , ... a(n) n--> Give The values of all the Coefficients(Even if they are "0") n'),'Note On
Entering Input');
a = input('Even Power Coefficients in decreasing order of power of "x"(Ex. Within []) :: ');
b = input('Odd Power Coefficients in decreasing order of power of "x"(Ex. Within []) :: ');
disp(' ');
digits(5)
L1 = length(a);
L2 = length(b);
disp(['No. Of The Roots:: ',num2str(L1+L2-1)]);
disp(' ');
disp('~:~:~:~:~:~:~:~:~:~:~:~Routh Array~:~:~:~:~:~:~:~:~:~:~:~');
if (L2>L1)
P = 0;
P1 = 0;
P2 = 0;
Z = zeros(1,(L2-L1));
R = horzcat(a,Z);
Z1 = horzcat(a,Z);
R1 = b;
disp(vpa(b));
disp(vpa(Z1));
H = 1;
for n = 1:(L2+L1-2)
R2 = R;
for m = 1:(L2-1)
if (R2(1,1)~=0)
if (abs(R2(1,1))~=inf)
R(1,m) = (((R2(1,1).*R1(1,m+1))-(R1(1,1).*R2(1,m+1)))./(R2(1,1)));
else
R2(1,1) = 1;
R(1,m) = (((R2(1,1).*R1(1,m+1))-(R1(1,1).*R2(1,m+1)))./(R2(1,1)));
end
else
if (R2(1,1)==0)
R(1,m) = R1(1,m+1);
if ((R1(1,1)*R2(1,2))>R1(1,2))
R(1,1) = -(1./0);
P1 = P1+1;
else
R(1,1) = (1./0);
end
end
end
end
if (R(1,1)==0)&&(R(1,m)==0)

3. H = R(1,1);
for i = 1:L1+L2-n
if (rem(i,2)~=0)
G(1,i) = R2(1,(i+1)./2);
else
if (rem(i,2)==0)
G(1,i) = 0;
end
end
end
r = roots(G);
R3 = r';
for j = 1:length(R3)
if (real(R3(1,j))<0.0001)
P2 = P2+1;
end
end
k = polyder(G);
i = 2:4:(length(k)*2);
k(:,(i+2)./2) = [];
G1 = zeros(1,length(R2)-length(k));
R = horzcat(k,G1);
end
if (R(1,1)<0)
P = P+1;
end
if (R2(1,1)*R(1,1)<0)
P1 = P1+1;
end
disp(vpa(R));
R1 = R2;
R2 = R;
end
if (P>0)
disp(' ');
disp('~:~:~:~:~:~:~The System is Unstable~:~:~:~:~:~:~');
else
if (P==0) && (H==0)
disp(' ');
disp('~:~:~:~:~:~:~The System is Marginally Stable~:~:~:~:~:~:~');
else
if (P==0)
disp(' ');
disp('~:~:~:~:~:~:~The System is Stable~:~:~:~:~:~:~')
end

4. end
end
disp(' ');
disp(['Roots to the right of imaginary axis in Z-plane:: ',num2str(P1)]);
disp(['Roots to the left of imaginary axis in Z-plane:: ',num2str(L1+L2-P1-1-P2)]);
disp(['Roots on the imaginary axis in Z-plane:: ',num2str(P2)]);
else
if (L1>L2)
P = 0;
P1 = 0;
P2 = 0;
Z = zeros(1,(L1-L2));
R = horzcat(b,Z);
Z1 = horzcat(b,Z);
R1 = a;
disp(vpa(a));
disp(vpa(Z1));
H = 1;
for n = 1:(L1+L2-2)
R2 = R;
for m = 1:(L1-1)
if (R2(1,1)~=0)
if (abs(R2(1,1))~=inf)
R(1,m) = (((R2(1,1).*R1(1,m+1))-(R1(1,1).*R2(1,m+1)))./(R2(1,1)));
else
R2(1,1) = 1;
R(1,m) = (((R2(1,1).*R1(1,m+1))-(R1(1,1).*R2(1,m+1)))./(R2(1,1)));
end
else
if (R2(1,1)==0)
R(1,m) = R1(1,m+1);
if ((R1(1,1)*R2(1,2))>R1(1,2))
R(1,1) = -(1./0);
P1 = P1+1;
else
R(1,1) = (1./0);
end
end
end
end
if (R(1,1)==0)&&(R(1,m)==0)
H = R(1,1);
for i = 1:L1+L2-n
if (rem(i,2)~=0)
G(1,i) = R2(1,(i+1)./2);

5. else
if (rem(i,2)==0)
G(1,i) = 0;
end
end
end
r = roots(G);
R3 = (r');
for j = 1:length(R3)
if (real((R3(1,j)))<0.0001)
P2 = P2+1;
end
end
k = polyder(G);
i = 2:4:(length(k)*2);
k(:,(i+2)./2) = [];
G1 = zeros(1,length(R2)-length(k));
R = horzcat(k,G1);
end
if (R(1,1)<0)
P = P+1;
end
if (R2(1,1)*R(1,1)<0)
P1 = P1+1;
end
disp(vpa(R));
R1 = R2;
R2 = R;
end
if (P>0)
disp(' ');
disp('~:~:~:~:~:~:~The System is Unstable~:~:~:~:~:~:~');
else
if (P==0) && (H==0)
disp(' ');
disp('~:~:~:~:~:~:~The System is Marginally Stable~:~:~:~:~:~:~');
disp(' ');
disp(['The Roots Of The Auxiliary Eqn. are:: ',num2str(R3)]);
else
if (P==0)
disp(' ');
disp('~:~:~:~:~:~:~The System is Stable~:~:~:~:~:~:~')
end
end
end

6. disp(' ');
disp(['Roots to the right of imaginary axis in Z-plane:: ',num2str(P1)]);
disp(['Roots to the left of imaginary axis in Z-plane:: ',num2str(L1+L2-1-P1-P2)]);
disp(['Roots on the imaginary axis in Z-plane:: ',num2str(P2)]);
end
end
if (L1 == L2)
P = 0;
P1 = 0;
P2 = 0;
H = 1;
for h = 1:(L1-1)
Q(1,h) = (((a(1,1).*b(1,h+1))-(b(1,1).*a(1,h+1)))./(a(1,1)));
end
L3 = length(Q);
T = a;
if (Q(1,1)==0)&&(Q(1,h)==0)
for j = 1:(length(a)+length(b)-1)
if (rem(j,2)~=0)
Q(1,j) = T(1,(j+1)./2);
else
Q(1,j) = 0;
end
end
r = roots(Q);
R3 = r';
for j = 1:length(R3)
if (real(R3(1,j))<0.0001)
P2 = P2+1;
end
end
K = polyder(Q);
I = 2:4:(length(K)*2);
K(:,(I+2)./2) = [];
G2 = zeros(1,length(b)-length(K));
Q = horzcat(K,G2);
end
if (Q(1,1)<0)
P = P+1;
P1 = P1+1;
end
P3 = 0;
Z = zeros(1,(L2-L3));
R = horzcat(Q,Z);
Z1 = horzcat(Q,Z);

7. R1 = a;
Z0 = zeros(1,(length(Z1)-L1));
D1 = horzcat(a,Z0);
D2 = horzcat(b,Z0);
disp(vpa(D2));
disp(vpa(D1));
disp(vpa(Z1));
for n = 1:(L1+L2-3)
R2 = R;
for m = 1:(L1-1)
if (R2(1,1)~=0)
if (abs(R2(1,1))~=inf)
R(1,m) = (((R2(1,1).*R1(1,m+1))-(R1(1,1).*R2(1,m+1)))./(R2(1,1)));
else
R2(1,1) = 1;
R(1,m) = (((R2(1,1).*R1(1,m+1))-(R1(1,1).*R2(1,m+1)))./(R2(1,1)));
end
else
if (R2(1,1)==0)
R(1,m) = R1(1,m+1);
if ((R1(1,1)*R2(1,2))>R1(1,2))
R(1,1) = -(1./0);
P1 = P1+1;
else
R(1,1) = (1./0);
end
end
end
end
if (R(1,1)==0)&&(R(1,m)==0)
H = R(1,1);
for i = 1:L1+L2-n
if (rem(i,2)~=0)
G(1,i) = R2(1,(i+1)./2);
else
if (rem(i,2)==0)
G(1,i) = 0;
end
end
end
r = roots(G);
R3 = r';
for j = 1:length(R3)
if (real(R3(1,j))<0.0001)
P2 = P2+1;

8. end
end
k = polyder(G);
i = 2:4:(length(k)*2);
k(:,(i+2)./2) = [];
G1 = zeros(1,length(R2)-length(k));
R = horzcat(k,G1);
end
if (R(1,1)<0)
P = P+1;
end
if (R2(1,1)*R(1,1)<0)
P1 = P1+1;
end
disp(vpa(R))
R1 = R2;
R2 = R;
end
if (P>0)
disp(' ');
disp('~:~:~:~:~:~:~The System is Unstable~:~:~:~:~:~:~');
else
if (P==0) && (H==0)
disp(' ');
disp('~:~:~:~:~:~:~The System is Marginally Stable~:~:~:~:~:~:~');
disp(' ');
disp(['The Roots Of The Auxiliary Equations Are:: ',num2str(R3)])
else
if (P==0)
disp(' ');
disp('~:~:~:~:~:~:~The System is Stable~:~:~:~:~:~:~')
end
end
end
disp(' ');
disp(['Effective no. of Roots to the right of imaginary axis in Z-plane:: ',num2str(P1)]);
disp(['Effective no. of Roots to the left of imaginary axis in Z-plane:: ',num2str(L1+L2-
P1-1-P2)]);
disp(['Effective no. of Roots on the imaginary axis in Z-plane:: ',num2str(P2)]);
end
else
.....
end
disp(' ');
y2 = input('Do you want to Rerun Program again?(y/n):: ','s');

9. if (y2~='y')&&(y2~='n')
disp(' ');
disp('Please Type "y" or "n"');
disp(' ');
y2 = input('Do you want to Rerun Program again?(y/n):: ','s');
end
if (y2=='y')
y3 = input('Do you want to keep the previous analysis?(y/n):: ','s');
if (y3~='y')&&(y3~='n')
disp(' ');
disp('Please Type "y" or "n"');
disp(' ');
y3 = input('Do you want to keep the previous analysis?(y/n):: ','s');
end
end
end
if (y2=='n')
disp(' ');
disp('Program Terminated');
disp(' ');
disp('*****You can "Press Any Key" to clear screen and "End Program"*****');
pause
pause on;
clc;
end
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