how can i find Open loop Transfer Function from Closed loop Transfer Function

Asked by chiranjib biswal

chiranjib biswal (view profile)

on 28 Oct 2018
Latest activity Edited by Aquatris

Aquatris (view profile)

on 29 Oct 2018
A unity feedback system is having Closed loop transfer function T(s)=361/s^2 16s 361. how can i find Open loop Transfer Function and dc gain of the system using matlab

Aquatris (view profile)

on 29 Oct 2018
Edited by Aquatris

Aquatris (view profile)

on 29 Oct 2018

From the basics of control theory you should know that for a given system G(s), the closed loop transfer function with unity feedback P(s) is;
P(s) = G(s)/(1+G(s));
From there you can do some algebra. Since it is a SISO case, I will not care about the order of multiplication;
1.P(s) = G(s)/(1+G(s))
2.P(s)*(1+G(s)) = G(s)
3.P(s)+P(s)G(s) = G(s)
4.P(s) = G(s)-P(s)G(s)
5.P(s) = G(s)*(1-P(s))
6.G(s) = P(s)/(1-P(s))
If you followed it so far, it should be easy to see that if
P(s) = 361/(s^2+16*s+361)
then;
G(s) = 361/(s^2+16*s)
To get the gain you can simply plug s=0*1i into the transfer function. Since G(s) has a pole at zero, DC gain of G(s) is infinity. Alternatively you can use bode() command to draw bode diagram of the G(s) and see the DC gain, or there is a dcgain() command in Matlab.