# ______ increases the steady-state accuracy.

#### SOLUTION

Lag compensation increases the steady-state accuracy.

Detailed Explanation

Lead compensation and lag compensation are the most commonly used methods of compensation in the conventional frequency domain design of control systems.

### Lag compensator

The transfer function of a lag compensator is given by

$G\left( s \right) = \frac{{\tau s + 1}}{{\beta \tau s + 1}}$

Where

$\beta = \frac{{{Z_c}}}{{{P_c}}} > 1$

• Both pole and zero lie in LHS of the real plane but PC < ZC i.e. zero is farther away from the origin.
• Lag Compensation adds a pole at origin (or for low frequencies).
• It helps to reduce the steady-state error of the system.
• An unstable system is a system that has at least one pole at the right side of the s-plane.
• Even if we add a lag compensator to an unstable system, it will remain unstable.

### Effects of phase-lag compensator:

1. Since the lag compensator allows high gain at low frequencies, it is basically a low pass filter. Therefore, it improves the steady-state performance.
2. In lag compensation, the attenuation characteristics are used for the compensation, whereas the phase lag characteristics are of no use in compensation.
3. Since the attenuation due to a lag compensator shifts the gain crossover frequency to a lower frequency point, the bandwidth of the system is reduced. Hence a slower response occurs. Therefore, rise time and settling time are usually longer and hence the transient response lasts for a longer time.
4. The system is very sensitive to parameter variation.
5. Since a lag compensator approximately acts as a proportional plus integral controller, it thus tends to make a system less stable.

The integrator produces an output proportional to the time integral of error, any finite error will cause the integrator output to keep on increasing and forcing the error to zero. Once the error has reached zero, the integrator output stops increasing but holds the value necessary to remove the error. Phase lag compensation is an integrator, as it reduces the steady-state error and increases steady-state accuracy.

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