Frequency Response Analysis

We have already discussed time response analysis of the control systems and the time domain specifications of the second order control systems. In this chapter, let us discuss the frequency response analysis of the control systems and the frequency domain specifications of the second order control systems.

What is Frequency Response?

The response of a system can be partitioned into both the transient response and the steady state response. We can find the transient response by using Fourier integrals. The steady state response of a system for an input sinusoidal signal is known as the frequency response. In this chapter, we will focus only on the steady state response.

If a sinusoidal signal is applied as an input to a Linear Time-Invariant (LTI) system, then it produces the steady state output, which is also a sinusoidal signal. The input and output sinusoidal signals have the same frequency, but different amplitudes and phase angles.

Let the input signal be −