By William S. Levine
At ebook, The regulate guide instantly turned the definitive source that engineers operating with smooth regulate structures required. between its many accolades, that first version was once mentioned by way of the AAP because the most sensible Engineering guide of 1996. Now, 15 years later, William Levine has once more compiled the main accomplished and authoritative source on keep watch over engineering. He has totally reorganized the textual content to mirror the technical advances accomplished because the final variation and has extended its contents to incorporate the multidisciplinary point of view that's making keep watch over engineering a serious part in such a lot of fields. Now improved from one to 3 volumes, The regulate guide, moment variation brilliantly organizes state of the art contributions from greater than two hundred top specialists representing each nook of the globe. the 1st quantity, regulate process basics, bargains an outline for these new to the sphere yet is additionally of serious price to these throughout any variety of fields whose paintings is reliant on yet no longer solely devoted to keep watch over platforms. masking mathematical basics, defining ideas, and uncomplicated process methods, this quantity — info crucial history, together with transforms and intricate variables contains mathematical and graphical types used for dynamical structures Covers research and layout tools and balance checking out for continuous-time structures Delves into electronic keep an eye on and discrete-time platforms, together with real-time software program for imposing suggestions keep watch over and programmable controllers Analyzes layout equipment for nonlinear structures As with the 1st version, the hot variation not just stands as a checklist of feat up to the mark engineering yet offers researchers with the capacity to make additional advances. gradually prepared, the opposite volumes within the set contain: keep an eye on method functions keep an eye on procedure complicated tools
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Extra resources for The Control Handbook, Second Edition: Control System Fundamentals, Second Edition (Electrical Engineering Handbook)
28, the residues cr+1 , cr+2 , . . , cn are calculated as in the distinct-pole case; that is, ci = [(s − pi )F(s)]s=pi , i = r + 1, r + 2, . . 29) and the residues c1 , c2 , . . , cr are given by ci = 1 (r − i)! 28 yields f (t) = c1 ep1 t + c2 tep1 t + · · · + cr t r−1 ep1 t + cr+1 epr+1 t + · · · + cn epn t (r − 1)! 31) The above results reveal that the analytical form of the function f (t) depends directly on the poles of F(s). In particular, if F(s) has a nonrepeated real pole p, then f (t) contains a real exponential term of the form cept for some real constant c.
These can be determined iteratively by observing that h[k] is the solution of (E 2 − 3E + 2)h[k] = (E + 2)δ[k], that is, h[k + 2] − 3h[k + 1] + 2h[k] = δ[k + 1] + 2δ[k] (1 59) subject to initial conditions h[−1] = h[−2] = 0. 59. 58 and substituting h = 0, h = 1 yields 0 = 1 + A1 + A2 1 = A1 + 2A2 and Solution of these two equations yields A1 = −3 and A2 = 2. 5 − 8 + 7 5 Solution of these equations yields c1 = 4 and c2 = −2. 5(3)k which confirms the result obtained by the classical method.
The function f (t) can be viewed as a signal that is a function of the continuous-time variable t (in units of seconds) and where t takes values from −∞ to ∞. 3, it is seen that in general the FT F(ω) is a complex-valued function of the frequency variable ω. 4. The function |F(ω)| represents the magnitude of the frequency components comprising f (t), and thus the plot of |F(ω)| versus ✐ ✐ ✐ ✐ ✐ ✐ 2-3 The Fourier, Laplace, and z-Transforms ω is called the magnitude spectrum of f (t). The function ∠F(ω) represents the phase of the frequency components comprising f (t), and thus the plot of ∠F(ω) versus ω is called the phase spectrum of f (t).
The Control Handbook, Second Edition: Control System Fundamentals, Second Edition (Electrical Engineering Handbook) by William S. Levine