Which of the following is a correct statement

Concept:

Proportional + Derivate(PD):

The additive combination of proportional & Derivative control is known as P-D control.

The overall transfer function for a PD controller is given by:

\({G_C}\left( s \right) = \dfrac{{U\left( s \right)}}{{E\left( s \right)}} = {K_P} + s{K_D}\)

PD controller is nothing but a differentiator (or) a High Pass Filter.

The frequency of noise is very high. 

So this high pass filter will allow noise into the system which results in noise amplification. 

PD Controllers reduce the response time and thus improve transient response

Effects of Proportional Derivative (PD) controllers:

• Decreases the type of the system by one
• Reduces the rise time and settling time
• It has high sensitivity.
• Rise time and settling time decreases and Bandwidth increases
• The speed of response is increased i.e. the transient response is improved
• Improves gain margin, phase margin, and resonant peak
• Increases the input noise
• Improves the stability

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Proportional Integral Controller:

This controller resembles the combination of the proportional and integral controller.

The structure of this controller is shown below:

This is used to decrease the steady-state error without affecting the stability of the system.

The transfer function is defined as:

\(TF = \dfrac{{{K_P}s\; + \;{K_I}}}{s}\)

Analysis:

The transfer function of the system is calculated as:

\(\dfrac{{{V_0}\left( s \right)}}{{{V_i}\left( s \right)}} = \dfrac{{{R_2} + \dfrac{1}{{s{C_2}}}}}{{{R_1}}}\)

\(\dfrac{{{V_0}\left( s \right)}}{{{V_i}\left( s \right)}} = \dfrac{{{R_2}s{C_2} + 1}}{{s{C_2}}}\)

Disadvantages: Slow reaction to the disturbances.

Advantages:

•  It provides the zero control error
• It is insensitive to the interference of the measurement channel.
• PI Controllers increase the type of the system and thus reduce steady state error and improve steady state
  response