function stability 96 tau T1 25 T2 lambda T1 T0 4916 floor tau T0 kp 4

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function stability
k = 1.96;
tau = 7.2;
T1 = 4.25;
T2 = 2.2;
%lambda = 1/T1;
%
T0 = 3.4916;
d = floor(tau/T0)
%�� �� kp = 0.4564
Ti = 25.3066
%
%zet = @(w) cos(w) + i*sin(w);
a = 1 - (tau - d*T0)/T0;
C1 = 1 - exp(-a*T0/T1);
C2 = exp(-a*T0/T1) - exp(-T0/T1);
%%%%%%%%%%%%%
R1 = C1;
R2 = C2;
A = exp(-T0/T1);
B = exp(-T0/T2);
f = @(z) k*kp*(Ti*T0*z*(z-1)+(T0*z)^2)*(z*R1+R2) + Ti*T0*z^(d+1)*(z-1)*(z-A)*(z-B);
syms z
g = k*kp*(Ti*z*(z-1)+T0*z^2)*(z*R1+R2) + Ti*z^(d+1)*(z-1)*(z-A)*(z-B);
simplify(g)
c = [7123174645625887/281474976710656 -421983958235669778884261308610467/10141204801825835211973625643008 +1697190256267010684454471021875822147435259807907/91343852333181432387730302044767688728495783936 10315350112694100632721416999589450954526273551132562293/892029807941224925661428730905934460239216640000000000 -1145741365101122648329632007938844028199/99035203142830421991929937920000000000 -82555056186637299581348541013924377/158456325028528675187087900672000000]
r = roots(c)
p = 1:5;
absr = abs(r(p))
%re = @(w) real(f(zet(w)));
%im = @(w) imag(f(zet(w)));
%del = 1000;
%steps = pi*del;
%for t = 0:steps
% x(t+1) = re(t/del);
% y(t+1) = im(t/del);
%end
%t = 0:steps;
%plot(x, y)
%xlabel('Re')
%ylabel('Im')
%title('Godograf. First function. T_0 = 1.1954')
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T0 = 3.7624
kp = 0.4397
Ti = 26.6257
d = floor(tau/T0)
%
%zet = @(w) cos(w) + i*sin(w);
C3 = 1 + (T2*exp(-T0/T2) - T1*exp(-T0/T1))/(T1 - T2);
C4 = exp(-T0/T1-T0/T2) + (T2*exp(-T0/T1) - T1*exp(-T0/T2))/(T1 - T2);
%%%%%%%%%%%%%
R1 = C3;
R2 = C4;
A = exp(-T0/T1);
B = exp(-T0/T2);
f = @(z) k*kp*(Ti*z*(z-1)+T0*z^2)*(z*R1+R2) + Ti*z^(d+1)*(z-1)*(z-A)*(z-B);
syms z
g = k*kp*(Ti*z*(z-1)+T0*z^2)*(z*R1+R2) + Ti*z^(d+1)*(z-1)*(z-A)*(z-B);
simplify(g)
c = [7494468287404913/281474976710656 -215127068815884112719223494271367/5070602400912917605986812821504 760910886759091522720229305860175764107366785633343/28544953854119197621165719388989902727654932480000 -86001855943957559074524021928721024718013247204411/14272476927059598810582859694494951363827466240000 -149348474356404748080198897502968436296000930521/45671926166590716193865151022383844364247891968]
r = roots(c)
p = 1:4;
absr = abs(r(p))
%re = @(w) real(f(zet(w)));
%im = @(w) imag(f(zet(w)));
%del = 1000;
%steps = pi*del;
%for t = 0:steps
% x(t+1) = re(t/del);
% y(t+1) = im(t/del);
%end
%t = 0:steps;
%plot(x, y)
%xlabel('Re')
%ylabel('Im')
%title('Godograf. Second function. T_0 = 1.8005')
%grid on