By Ya. Z. Tsypkin, R. C. Hutchinson, I. Cochrane
Sampling platforms thought and its software, quantity 2 is a two-chapter textual content that specializes in closed pulse systems.
The first bankruptcy highlights the basics of closed pulse structures. This bankruptcy fairly tackles the equations, move features, balance, frequency, features, techniques, and synthesis of those structures. the second one bankruptcy discusses the automated temperature, ranging, and frequency keep an eye on method and non-contact servo-system of closed pulse structures. This bankruptcy additionally appears to be like into the smoothing and prediction of discrete info in electronic computers.
This ebook will turn out beneficial to mathematicians, engineers, and physicists.
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Additional resources for Sampling Systems Theory and its Application, Volumes 1-2
Sample text
E-ß e? - e-ß k e* - 1 kerß e? — e-ß 10 e^-e-ß If the difference in the degrees of the denominator and numerator of K(q) exceeds unity, then # % , - 0 ) = Z*(g,0). If, in the transfer function of an open pulse system with arbitrary shape of pulses, we let y tend to zero and p u t Jcpy = 1 we shall always obtain K*(q, —0). With 1c(0) φ 0 or h(0) = 0, the use of K*(q, 0) and K*(q, —0) for the investigation of stability leads, quite naturally, to different results. EXAMPLE. For the elementary pulse system (Fig.
41&. Here part of the frequency characteristic, in the case of increasing ώ, passes through quadrants r 7Γ (a) J, J, K* (jâ7, K*(jâ7, π J 0 It (b) Γ Γ 0 (c) K* (jâ ' (d) FIG. 42. Qualitative shape of frequency characteristics of open pulse systems with astatism of the first order: (a) and (b) for ö>iim = π (c) and (d) for ω1ΐηι < π. I and IV and consequently for these frequencies the real part of the frequency characteristic Β(ω) is positive. Selecting T so t h a t point ώ = π is near ω', and utilising the build-up described above, it is possible to get K*(j ω, 0) to intersect the real axis to the right of K(j ω).
0) = ΕΖ*(;ω,0). This factor h is usually the gain coefficient of an open system. I t is non-dimensional for static systems and has dimensionality see - " where v = 1, 2, 3, . . for astatic systems. e. the part played by point (—1, jO) will be performed by point (—llk,j0). In this case all criteria formulations will differ only inasmuch as point (—1/Jfc, jO) should be taken instead of point (1—, jO) and segment (—co, —l/Jc) instead of segment (—oo, —1). STABILITY AND STABILIZATION 413 When proving the stability criterion, it was assumed t h a t on the boundaries of band L2 L± there are no zeros or poles of the function A*(q).