By Uwe Mackenroth
"Robust keep an eye on Systems" provides a self-contained advent to fashionable keep an eye on concept. It hence provides a textbook to the prevailing research-oriented literature on strong keep watch over. the writer lays emphasis at the glossy features of the layout of controllers with prescribed functionality and robustness houses. diversified to the classical engineering strategy, a rigorous mathematical therapy is key for the whole knowing and applicability of the trendy tools similar to H2 or H8 keep an eye on or equipment in line with the based singular price µ. however, no earlier wisdom of keep an eye on conception is needed because the classical basics are brought in the first few chapters. hence a wide a part of the textual content offers straight forward examples and business case reports, that are constructed in complete aspect to teach how sleek tools may be utilized to complicated difficulties. They make extensive use of MATLAB, in particular the keep watch over platforms Toolbox and the µ-Analysis and Synthesis Toolbox.
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Extra resources for Robust Control Systems: Theory and Case Studies
Example text
Since G(s) is stable, the limit for t ~ 00 exists. Thus, from the final-value theorem we get (using that s =0 is not a pole of G(s) ) ~~~ Ye(t) =~~ [s Je (s)] =~~[s G(S)~] =limG(s) =G(O) . 8. Step responses for p1ants of type 0 (a), 1 (b), 2 (c), -1 (d) We conclude this section by studying examples for the different types of transfer functions which were introduced in Sect. 1. 12) and Z I N is assumed to be stable. Plants with oftype 0: Prom the preceding result we get lim Ye (t) =k . I--+~ This means that for large times the step response approximately coincides with the gain k .
4) we get diA . s d 2 2 2 CA T s + 2 dTs + 1 and the constants 1 k __ - , We now consider the position control for the machine too1. From Fig. 3 it is seen that the screw converts the rotation al motion into a translational motion. Let n be the number of revolutions of the shaft and let the position x of the tool be changed by the value hG for one rotation. Then we have W =2nn and x =hGn . Thus the transfer function which transforms u A into x is given by (with k1 =khG /2n) Hovering ball. We consider now the position control for a ball containing iron, as shown in Fig.
16, where the step responses are plotted. A second-order all-pass transfer function has the form (for d G(s) = T 2 / -2dTs+l T 2 / +2dTs+l . 24) Minimum-phase transfer functioDS. A proper rational transfer function G(s) is said to be minimum-phase if it has no zeros in the open RHP. The reason for this name can be explained as follows. Let F be an all-pass transfer function. Then GF has the same magnitude as G, but a greater phase. Thus, of all the transfer functions having the magnitude of G , the one with minimum-phase is G.
