Feedback characteristics of Control Systems:

In control system ,the feedback reduces the error, also reduces the sensitivity of the system to parameter variations .The parameter may vary due to some change in conditions .The variation in parameter affects the performance  of the system. So it is necessary to make the system in sensitive to such parameter variations.

Effect of feedback on sensitivity :

The parameters of any control system changes with the change environment conditions. Also these parameters cannot be constant throughout the life. These parameter variations affect the performance of the system. For example, the resistance of winding of a motor changes due to change in temperature during its operation.

• Sensitivity to model uncertainties 

S^T_G  = Ratio of % change in sys T.F./Ratio of % change in process T.F.

\(\frac{ΔT}{\frac{T}{\frac{ΔG}{G}}}\) = \(\frac{θ\,in\,T}{θ\,in\,G}=\frac{θ\,T\,G}{θ\,G\,T}\) 

Open loop:

Δγ(s) = ΔG(s)R(s)  ΔT(s) = \(\frac{Δγ(s)}{R(s)}\) = ΔG(s)

Closed‐loop:

T(s) = \(\frac{G}{1+GH}\) ,\(\frac{θT}{θG}=\frac{(1+GH)-GH}{(1+GH)^2}\) = \(\frac{1}{(1+GH)^2}\) 

S^T_G = \(\frac{θTG}{θGT}\) = \(\frac{1}{(1+GH)^2}\) \(\frac{G}{\frac{G}{1+GH}}\) =   \(\frac{1}{(1+GH)}\) 

→ Reduced SK below that of the open‐loop sys by increasing G*H (>>1.0).

S_H^T =  \(\frac{θTH}{θHT}\)  = \(\frac{-GH}{1+GH}\)

* if GH >>1.0 →SK =  -1 

Feedback components should not be varied with environmental changes →change in H(s) directly affects output response