Ziegler-Nichols

Function de transferencia seleccionadaG=((55.88*(4600000000*s^5 + 417544600000*s^4 + 9191438684000*s^3 + 69416671160220*s^2 + 979880254296824*s + 2193289421218597)))/((5000000000000*s^7 + 902830000000000*s^6 + 44327682270000000*s^5+ 787679602626800000*s^4 + 6113001903819759500*s^3+ 60099060080282675600*s^2 + 149630469847316466365*s + 10618145563144266472));

%%Matlab codigo.

s=tf('s');G=((55.88*(4600000000*s^5 + 417544600000*s^4 + 9191438684000*s^3 + 69416671160220*s^2 + 979880254296824*s + 2193289421218597)))/((5000000000000*s^7 + 902830000000000*s^6 + 44327682270000000*s^5+ 787679602626800000*s^4 + 6113001903819759500*s^3+ 60099060080282675600*s^2 + 149630469847316466365*s + 10618145563144266472));nyquist(G); axis([-0.2,0.5,-0.4,0.4]);[Gm,Pm,wcg,wcp]=margin(G) Kc=Gm; wc=wcg; Tc=2*pi/wc;Gcp=0.5*Kc; Gcl1=feedback(G*Gcp,1);Gcpi=0.4*Kc*(1+1/0.8/Tc/s); Gcl2=feedback(G*Gcpi,1);Gcpid=0.6*Kc*(1+1/0.5/Tc/s+0.12*Tc*s);Gcl3=feedback(G*Gcpid,1);step(Gcl1,Gcl2,Gcl3);

resuestaGM= the gain margin, factor by which the total loop gain can be increased which will make the system just unstablePM= the phase margin, the difference between -180 degrees and the phase angle at the frequency for which the amplitude ratio is one. PM represents the additional amount of phase lag required to make the system unstable. wc = the critical frequency, the frequency where the GM=1

Gm = 4.1658e+03Pm = Infwcg = 9.3369

Fig 1: controller based on Ziegler-Nichols

Sintonizacion IMC

A continuacin se muestran las posibles sintonizaciones con controles P, PI Y PID.

Fig 2. Sintonizacin IMC para un control P

Fig 3. Sintonizacin IMC para un control PI

Fig 3. Sintonizacin IMC para un control PID

6) compensador polinomio en adelanto y atraso

fig. Respuesta en frecuencia de un compensador

fig. Respuesta en el tiempo de un compensador