By J. William Helton
One of many major accomplishments of keep watch over within the Nineteen Eighties used to be the improvement of H8 innovations. This publication teaches keep an eye on process layout utilizing H8 tools. scholars will locate this booklet effortless to exploit since it is conceptually uncomplicated. they'll locate it important as a result of common charm of classical frequency area equipment. Classical keep watch over has regularly been offered as trial and blunder utilized to precise circumstances; Helton and Merino offer a way more designated strategy. This has the super benefit of changing an engineering challenge to 1 that may be placed at once right into a mathematical optimization package deal. After finishing this direction, scholars should be conversant in how engineering specifications are coded as exact mathematical constraints.
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Additional resources for Classical Control Using H-infinity Methods: An Introduction to Design
Define the gain-phase margin of the system S to be 20 CHAPTER 3. FREQUENCY DOMAIN PERFORMANCE Graphically m is just the distance of the Nyquist plot of PC to the point -1 in the complex plane. 3) to We can easily compare the gain-phase margin m with the gain margin g and the phase margin 0 by looking at the Nyquist plot in Fig. 3. Typically m is more conservative than either > or g. Fig. 3. The gain margin g, phase margin (f>, and gain-phase margin m. If a given stable system has m near 0, then it is close to the unstable case, which is undesirable.
A 3-D plot of the requirements envelope (see Fig. 2) is produced with EnvelopePlotSD[Radius->rO,Center->kO] Fig. 2. 3-D plot of the requirements envelope. A plot of the discrete profile of the requirements envelope can be used to judge if there are enough frequency gridpoints in the band of interest (see Fig. 50 CHAPTER 5. 3). 0, which is where the center and radius functions have their distinctive features. This is desirable. },Discrete -> True]; If we do not like either of the plots in Figs. 3, then several input parameters can be modified to rerun the problem and to obtain more satisfactory plots.
We first construct the center and radius functions for our problem. Recall that the gain-phase margin constant m is the closest acceptable distance from the function L •= PC to the point — 1; in other words. The requirement on the roll-off can be written as Thus the frequency domain performance requirements are described by (see Fig. 12) can be cast as a single disk inequality where CHAPTER 4. OPTIMIZATION 40 Fig. 3. The performance envelope defined by center and radius functions in the example is outlined by the thick curves.
Classical Control Using H-infinity Methods: An Introduction to Design by J. William Helton