## Frequency Response

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The Frequency Response of the system is the steady-state response of the system obtained as the output when a sinusoidal input signal is given to the system. For determining the frequency response of a control system sinusoidal signal is given as input to the system with different frequencies and response of the output was determined at different frequencies.

In a linear Time-Invariant control system when the input is given as sinusoidal signal output will also be having a sinusoidal signal with same frequency however with ‘**change in magnitude and phase**‘ of the input sinusoidal signal. Therefore in determining the frequency response of the control system at the different band of frequencies the change in the magnitude and phase difference of the system is determined.

## Frequency Domain Analysis

Thus frequency domain analysis helps to determine the absolute and relative stability of the closed-loop system, frequency domain analysis can also be extended for analyzing and designing nonlinear control systems.

Bode plots, M and N charts, Nicholas charts, and polar plots (Nyquist plots) are the different graphical techniques available for determining the frequency response of the system. From these plots frequency domain specifications such as Bandwidth, Gain Margin, Phase Margin and other frequency domain specifications are determined. These details help in determining the stability of the system, adjust the gain of the control system and helps in designing the control system.

In * frequency response analysis,* the input to the control system is fed with a sinusoidal signal with different frequencies. The output from the (LTI) Linear Time Invariant system will be the same sinusoidal signal with same input frequency but variation in the magnitude and phase. Hence the change in the magnitude of the input signal and phase for a wide band of input frequencies are determined in Frequency Domain Analysis.

## Advantages of Frequency Domain Analysis

Some of the advantages of frequency domain analysis are:

- Transfer functions which are complicated to determine the behavior of the experimentally can be determined using the frequency response analysis.
- Design of the system and adjusting the parameters of the system can be easily carried out.
- Corrective measurement for noise disturbance generated in the system and parameters variation can be easily determined using frequency analysis.
- Absolute and Relative stability of the closed-loop system can be estimated from the knowledge of the open loop frequency system.
- Frequency domain analysis can also be carried out for the nonlinear control systems.