Which one of the following is the transfer function of the PI-controller?

Question

Question

This question was previously asked in

ESE Electronics 2014 Paper 2: Official Paper

Attempt Online

\(G\left( s \right) = \frac{{\left( {{k_1}s + {k_2}} \right)}}{{{k_3}}}\)
\(G\left( s \right) = \frac{{\left( {{k_1}s + {K_2}s + {k_3}} \right)}}{{{k_{{4^3}}}}}\)
\(G\left( s \right) = .\frac{{\left( {{k_1}s + {k_2}} \right)}}{{{k_3}s}}\)
\(G\left( s \right) = \frac{{{k_1}s}}{{{k_2}s}}\)

Answer 1

Proportional Integral Controller:

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

The structure of this controller is shown below:

F12 Shubham 7-11-2020 Swati D1

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

The transfer function is defined as:

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

Analysis:

The transfer function of the system is calculated as:

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

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

Disadvantages: Slow reaction to the disturbances.

Advantages:

1) It provides the zero control error

2) It is insensitive to the interference of the measurement channel.