Computer Controlled Systems - download pdf or read online

By Astrem, Wittenmark

ISBN-10: 0133148998

ISBN-13: 9780133148992

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16) is independent of the state-space represen ta tion. Prool Given the pulse-transfer operator and a transformation matrix T. In the new coordinates fJ(q) ~ C(qI- ~)-lf + b = G-T- 1{qTT- 1 - Tqlr-1t1Tr + D == CT- 1 (T (q/ -r1T-1Tr + D ::: C(qI - «t»-lr + D = H(q) • Sec. 26). 1, which gives H(q) for some standard systems. . Programs for computer algebra such as Maple® and Mathematica® are very convenient for performing sampling because the result is obtained in algebraic form and it can easily be converted to computer code.

The period ofthis signal is thus 11 s. This is the low-frequency component that is clearly visihle in Fig. 11. 4 illustrated that lowerfrequencies can be created hy sampling. 6) that sampling also can givefrequencies that are higher than the excitation frequency. This is illustrated in the following example. 1, which has a sampling period of 10 Hz. 1 Hz is created by sampling. 1 Hz shown in the figure, _ Computer Control 20 (u) Chap. , :l 0. ~ 0 H -1 (b ) .... ;:I 0 -e 0 Q. ~ u: (c) -1 0 1 +-' ::l 0.

19) o with k I + k'2 + .. ' + k; = n. i are the eigenvalues of (J), not necessarily distinct. 19) is called the Jordan form. See Appendix B. In this form the transformed matrix, cil, has the eigenvalues in the diagonal and some I's in the superdiagonal. Output Models A dynamic system can be described using either internal models or external models. Internal models-for instance, the state-space models discussed in Sec. 3-describe all internal couplings among the system variables. The external models give onlythe relationship between the input and the output of the system.

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Computer Controlled Systems by Astrem, Wittenmark


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