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Modern Control System Theory and Design, 2nd Edition by Stanley M. Shinners

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7.7.  APPROXIMATE METHODS FOR PRELIMINARY COMPENSATION AND DESIGN USING THE BODE DIAGRAM

Having presented detailed compensation methods, let us next focus our attention on approximate methods for obtaining a first cut at compensation utilizing the Bode diagram [810]. Although the procedures presented in this section are approximate, they are generally adequate for the preliminary stage of design. Before the system design is completed, however, the exact magnitude and phase curves should be drawn as indicated previously. The practice of utilizing approximate methods for preliminary design is generally employed as a convenience in obtaining significant time constants, gains, and phase characteristics required for a design.

A.  Approximate Closed-Loop Response from the Bode Diagram

In order to develop the concept of this approach, let us consider the feedback system illustrated in Figure 7.31. The closed-loop transfer of this system is given by

Image

Let us modify this equation into the following more convenient form:

Image

As shown previously, the magnitude (in decibels) of G(s)H(s) can be approximated by straight lines of constant slope when plotted against frequency on a log scale. Therefore, it appears reasonable that the term 1 + G(s)H(s) in Eq. (7.87) may also be dealt with in a similar ...

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