Second order system

CODE zeta=input('input the value of zeta ='); t=input('input the vlaue of time constant chosen='); wn=1/(zeta*t) num=[wn*wn] den=[1 2*zeta*wn wn*wn] sys=tf(num,den); figure(2); pzmap(sys) f=input('press any key for the step response'); step(sys)  

Procedure

Open matlab, open the editor and type the above code.

Save the code and run it. Go to the command window and and

enter the value of zeta and t. The pole zero plot is shown. Enter any key to get the step response

input the value of zeta =2 input the vlaue of time constant chosen=5

wn =

0.1000

num =

0.0100

den =

1.0000 0.4000 0.0100

Transfer function = .001 s^2+0.4s+.001

Pole zero plot

Step response

secondor input the value of zeta =0.1 input the vlaue of time constant chosen=5

wn =

2

num =

4

den =

1.0000 0.4000 4.0000

Pole zero

Step response

input the value of zeta =1 input the vlaue of time constant chosen=5

wn =

0.2000

num =

0.0400

den =

1.0000 0.4000 0.0400

Pole zero

Step response

Lead network Code phi_deg=input('input the given value of phi in degrees=') phi_rad=pi*phi_deg/180 wm=input('input the given value of frequency in radians per second=') alpha=(1-sin(phi_rad))/(1+sin(phi_rad)) T=1/(sqrt(alpha)*wm) f1=1/(2*pi*T) fm=wm/(2*pi); f2i=(pi*T*alpha)/2 C=0.11e-06 R1=T/C R2=alpha*R1/(1-alpha) numg=[1 1/T] deng=[1 1/(alpha*T)] sys=tf(numg,deng) figure(2); pzmap(sys) f=input('Press any key to observe the plot') bode(sys)

Procedure

input the given value of phi in degrees=54.9

phi_deg =

54.9000

phi_rad =

0.9582

input the given value of frequency in radians per second=2010

wm =

2010

alpha =

0.1000

T =

0.0016

f1 =

101.1715

f2i =

2.4715e-04

C =

1.1000e-07

R1 =

1.4301e+04

R2 =

1.5894e+03

numg =

1.0000 635.6795

deng =

1.0e+03 *

0.0010 6.3556

sys = s + 635.7 --------- s + 6356 Continuous-time transfer function.

Press any key to observe the plot

Pole zero

Bode plot

Lag network

phi_deg=input('input the given value of phi in degrees=')

phi_rad=pi*phi_deg/180 wm=input('input the given value of

frequency in radians per second =') beta=(1-sin(phi_rad))/(1+sin(phi_rad)) T=1/(sqrt(beta)*wm) f1=1/(2*pi*beta*T) fm=wm/(2*pi); f2=1/(2*pi*T)

C=1.0e-06 R2=T/C R1=(beta-1)/R2 numg=[1 1/T] deng=[beta*T 1] sys=tf(numg,deng) figure(2); pzmap(sys) f=input('Press any key to observe the plot') figure(3); bode(sys)

Procedure

input the given value of phi in degrees=-54.8

phi_deg =

-54.8000

phi_rad =

-0.9564

input the given value of frequency in radians per second =198.8

wm =

198.8000

beta =

9.9376

T =

0.0016

f1 =

10.0368

f2 =

99.7419

C =

1.0000e-06

R2 =

1.5957e+03

R1 =

0.0056

numg =

1.0000 626.6970

deng =

0.0159 1.0000

sys = s + 626.7

------------- 0.01586 s + 1 Continuous-time transfer function.

Press any key to observe the plot

f =

[]

>>

Bode plot

Pole zero

num=[1] den=conv(conv([1 0],[.2 1]),[.05 1]) sys=tf(num,den) figure(1); bode(sys) [mag,phase,w]=bode(sys) margin(sys) f=input('press any key to uose the rltool') figure(2); rltool(sys)

num =

1

den =

0.0100 0.2500 1.0000 0

sys = 1 ----------------------- 0.01 s^3 + 0.25 s^2 + s Continuous-time transfer function.

procedure

The transfer function is shown. Press any key to get the bode plot The magnitude and phase value of w is

shown. Press any key to get the root locus of the

transfer function.