Frequency response plots depicts the complex values of a transfer function as a function of frequency. for linear dynamic systems, the transfer function G is essentially an operator that takes the input u of a linear system to the output y:
Frequency response of a model can be plotted in MATLAB to gain insight into the specifications of linear model dynamics, including the frequency of the peak response and stability margins. Frequency-response plots are available for all linear models. The frequency response of a linear dynamic model describes how the model behaves to sinusoidal inputs. If the input u(t) is a sinusoid of a certain frequency, then the output y(t) is also a sinusoid for the same frequency. However, the response magnitude is different from the magnitude of the input signal, and the phase of the response is shifted relative to the input signal.
Frequency response plots shows insight into linear systems dynamics, such as frequency-dependent gains, resonances, and phase shifts. Frequency response plots also contain information about controller requirements and achievable bandwidths. Finally, frequency response plots can help user validate how well a linear parametric model, such as a linear ARX model or a state-space model, captures the dynamics. One example of how frequency-response plots help validate other models is that someone can estimate a frequency response from the data using spectral analysis (nonparametric model), and then plot the spectral analysis result over the frequency response of the parametric models. Because nonparametric and parametric models are formed using different algorithms, agreement between these models increases confidence in the parametric model results.