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Chapter 10 - Digital Control Systems - Section 3.2: Design Example

By Harold Rothbart and Thomas H. Brown
From Mechanical Design Handbook 2nd Edition
For a 1/s2 plant, we wish to design a digital controller to have a closed-loop natural

frequency ωn, of ~0.3 rad/s and ζ = 0.7. The first step is to find the proper D(s) defined in Fig. 10.8. The specifications can be met with

as can be verified by the root locus in Fig. 10.9. To digitize this D(s), we first need to select a sample rate. For a system with ωn = 0.3 rad/s a very “safe” sample rate would be a factor of 20 faster than ωn, yielding

Thus, let us pick T = 1 s. The matched
pole-zero digitization of Eq. (10.22) is
given by Eq. (10.19) and yields

FIG. 10.9 s-Plane locus versus k.

This completes the digital algorithm design. The complete digital system is shown in
Fig. 10.10.

FIG. 10.10 Digital control system.

 

© 2009 McGraw-Hill Companies, Inc. (The)
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