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What Is a Frequency Response Model?

Frequency response describes the steady-state response of a system to sinusoidal inputs.

For a linear system, a sinusoidal input of frequency ω:

`$u\left(t\right)={A}_{u}\mathrm{sin}\omega t$`

results in an output that is also a sinusoid with the same frequency, but with a different amplitude and phase θ:

`$y\left(t\right)={A}_{y}\mathrm{sin}\left(\omega t+\theta \right)$`

Frequency response G(s) for a stable system describes the amplitude change and phase shift as a function of frequency:

where Y(s) and U(s) are the Laplace transforms of y(t) and u(t), respectively.

Frequency Response Model Applications

You can estimate the frequency response of a Simulink® model as a frequency response model (`frd` object), without modifying your Simulink model.

Applications of frequency response models include:

• Validating exact linearization results.

Frequency response estimation uses a different algorithm to compute a linear model approximation and serves as an independent test of exact linearization. See Validate Linearization In Frequency Domain.

• Analyzing linear model dynamics.

Designing controller for the plant represented by the estimated frequency response using Control System Toolbox™ software.

• Estimating parametric models.