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Process Control: Modeling, Design, and Simulation by B. Wayne Bequette

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7.2. Bode and Nyquist Plots

In the previous section the basic concept of frequency response was presented. For linear systems, an input forcing with a certain frequency results in an output with the same frequency, shifted by the phase angle. There are two ways to perform frequency response analysis: (i) conversion of the input signal to the Laplace domain, partial fraction expansion of the output, and inversion to the time domain, or (ii) substitution of s = jω in the transfer function.

Method 2, substitution of s = jω in the transfer function, is the easiest approach. There are also two ways to display the frequency response information: Bode plots and Nyquist plots. The following first-order example is used to illustrate these concepts.

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