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 for 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 sinusoidal signal with same frequency however with 'change in magnitude and phase' of the input sinusoidal signal. Therefore in determining frequency response of the control system at 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 non linear 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 helps in determining the stability of the system, adjust the gain of the control system and helps in designing the control system.