A ______ is suitable for systems with unsatisfactory transient response but it provides only a limited improvement in steady-state response.

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BDL MT Electrical 17 April 2022 Official Paper
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  1. Lead-lag compensator
  2. Lag-lead compensator
  3. Lead compensator
  4. Lag compensator

Answer (Detailed Solution Below)

Option 3 : Lead compensator
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ST 1: BDL MT Thermodynamics
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Detailed Solution

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Concept:

Lead compensator:

Transfer function:

If it is in the form of \(\frac{{1 + aTs}}{{1 + Ts}}\), then a > 1

If it is in the form of \(\frac{{s + a}}{{s + b}}\), then a < b

Maximum phase lead frequency: \({\omega _m} = \frac{1}{{T\sqrt a }}\)

Maximum phase lead: \({\phi _m} = {\sin ^{ - 1}}\left( {\frac{{a - 1}}{{a + 1}}} \right)\)

ϕis positive

Pole zero plot:

F1 U.B Madhu 2.12.19 D16

The zero is nearer to the origin.

Filter: It is a high pass filter (HPF)

Effect on the system:

  • Rise time and settling time decreases and Bandwidth increases.
  • The transient response becomes faster
  • The steady-state response is not affected
  • Improves the stability
  • The velocity constant is usually increased
  • Helps to increase the system error constant though to a limited extent
  • The slope of the magnitude curve is reduced at the gain crossover frequency, as a result, relative stability improves
  • The margin of stability of a system (phase margin) increased

 

Additional Information

 Lag compensator:

Transfer function:

If it is in the form of \(\frac{{1 + aTs}}{{1 + Ts}}\), then a < 1

If it is in the form of \(\frac{{s + a}}{{s + b}}\), then a > b

Maximum phase lag frequency: \({\omega _m} = \frac{1}{{T\sqrt a }}\)

Maximum phase lag: \({\phi _m} = {\sin ^{ - 1}}\left( {\frac{{a - 1}}{{a + 1}}} \right)\)

ϕis negative

Pole zero plot:

F1 U.B Madhu 2.12.19 D1

The pole is nearer to the origin.

Filter: It is a low pass filter (LPF)

Effect on the system:

  • Rise time and settling time increases and Bandwidth decreases
  • The transient response becomes slower
  • The steady-state response is improved
  • Stability decreases
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