Bachiller

C(s)R(S)=Kp+Kds2.25S21.02+2.25 KdS+(2.25)Kp
2ϑW=(2.5018+5.8564 Kd)
2(0.5169)(2.42)-1.02=2.25Kd1.4818=2.25Kd
Kd=1.48182.25
Kd=0.66

(Wn)2=Wn2 KP
(2.42)2=2.25Kp
Kp= (2.42)22.25= 2.6

ϑ(s)c= R4R3.R2R1.(R1.C1.S+1)ϑ(s)c=Ra2.ϑs+Ra2Rb2=Kds+Kp
Ra2.CsRb + Ra2Rb2=066s+2.6
Sustituyendo
Ra2Rb2=2.6----≫ Ra2=2.6Rb2
Ra=1.61Rb
ASUMIENDO Rb=10k y Ra 16.1KRa2.CsRb=0.66s
(16.1k)2(10K).C1=0.66=≫C1=25.46 μf

Controlador PI

ϑ(s)c= Kp+KiS= Kp(1+1Tis)

Estableciendo que TI=ᴔ y ϑ(s)c=Kp
Y(s)R(s)= 2.25 KpS2+1.025+2.25Kp
(2.42)2=2.25 Kp5.85642.25=Kp---------- Kp=2.60 s=jw

S2+1.02S+2.252.60=0
W2+1.02S+5.8564=0
w=-1.02±(1.02)2-4(-1)(2.25)-2
w=-1.02±-1.04+9-2
w=-1.02±2.82-2
w=(0.51)2+(1.41)2w=0.2601+1.9881
w=2.2482=1.50
Pur=2π1.5=34π=4.19
Kp=0.6Kcr ===> KcrKp0.6 ======Kcr=2.60.6=4.03 Ti=1/1.2*(4.19)=3.49 Ti=3.49
ϑ(s)c=2.6(1+13.49s) =ϑ(s)c=(2.6+0.74S)

ϑ(s)c=R4 R2R3R1*(R2C2S+1R2C2S) R4=R2=RA y R3=R1=Rb

ϑ(s)c= (Ra)2(Rb)2*(1+1RaC2s) = ϑ(s)c (Ra)2(Rb)2+(Ra(Rb)2C2S)= ϑ(s)c=Kp+KiS

(Ra)2(Rb)2+(Ra(Rb)2C2S)=2.6+0.74s(Ra)2(Rb)2=2.6

Ra=2.6 Rb= 1.61Rb Ra=16.1K Rb 10K
C2=Ra(Rb)2(0.74)= 16.1K(10k)2(0.74)=2.1756x10-4
C2=220μf

CONTROLADOR PID
ϑ(s)c=Kp(1+1TiS+TdS)
ϑ(s)c=(Wn)2SS+2ϑWn
Usandozeingler-nichols
Ti=∞, Td=0, Kp=2.6
Y(s)R(s)=2.25KpS2+2ϑWnS+W(n)2Kp
YsRs=2.25KpS2+1.02S+2.25Kp

Kp=0.6Kcr
Kcr=Kp0.6=2.60.6= 4.33 entonces S2+1.02S+2.25(4.33)=0
S2+1.02S+9.25=0w2+1.02jw+9.75=0
w=-(0.5)±(1.04)2-4(1)(9.75)-2
w=0.512+(3.08)2
w=9.75=3.12


Pcr=2πw=2π3.12=2.01 Kp=0.6Kcr=2.6 ϑ(s)c=2.6(1+1S+0.255)...