Close loop transfer function depends on all type of controller
e(s) ∝ sTd ∝ \(\dfrac{de}{dt}\) (Derivative controller)
e(s) ∝ K (Proportional controller)
e(s) ∝ KI/s ∝ \(\int {e\left( t \right)\,dt}\)(Integral controller)
Where, \(s = \frac{d}{dt}\) and \( \frac{1}{s}=\int dt\)
Important Points
Proportional controller 
Integral Controller 
Derivative controller 
a(t) ∝ e(t) \(\frac{{A\left( s \right)}}{{E\left( s \right)}} = {K_p}\) 
\(\frac{{da\left( t \right)}}{{dt}} \propto e\left( t \right)\) \(\frac{{A\left( s \right)}}{{E\left( s \right)}} = \frac{{{K_I}}}{s}\) 
\(a\left( t \right) \propto \frac{{de\left( t \right)}}{{dt}}\) \(\frac{{A\left( s \right)}}{{E\left( s \right)}} = {K_D}.s\) 
Speed of response is good i.e. ζ↑ 
Speed of response not good i.e ζ ↓ 
Sped is very high i.e ζ ↑↑ but ωn remains constant 
Stability ↓ ↓ 
Stability ↓ 
Stability ↑↑ 
Accuracy ↑ 
Accuracy ↑↑ i.e. Ess ↓↓ 
Accuracy ↓↓ i.e Ess ↑↑ 
It does affect the type or order & system 
It increases the type of system 
Not connected in series because it converts the IInd order system in 1st order. 


Feedback cascading topology used 
ζ is the damping factor
ωn is the natural frequency
Ess is the steadystate error.
↓ = Decrement
↑ = Increment