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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89``` ```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') %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%% 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 ```