For the system of Fig. P4.4-3, the filter solves the difference equation m(k) = 0.9m(k 1)+ 0.2e(k)
Question:
For the system of Fig. P4.4-3, the filter solves the difference equation m(k) = 0.9m(k −1)+ 0.2e(k)
The sampling rate is 1 Hz and the plant transfer function is given by
Transcribed Image Text:
E(s) e(t) T using E*(s) e(KT) D(z) 2-z-1 Fig. P4.4-3 (a) Find the system transfer function G (s) = = M(z) m(kT) 1 s+ 0.2 1-g-Ts G(s) s+1 C(z)/E (2)* (b) Find the system de gain from the results of part (a). (c) Verify the results of part (b) by finding the de gain of the filter using C(s) D(z) and that of the plant G (s) (d) Use the results of part (b) to find the steady-state value of the unit-step response. (e) Verify the results of part (d) by calculating c(kT) for a unit-step input. (f) Note that in part (e), the coefficients in the partial-fraction expansion add to zero. Why does this occur?
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a Mz 09zMz 02Ez Mz Ez Dz G2 Cz Ez Z 1 c D1 N 200 b D1G1 02z Z09 09063 Z08187 1 ss02 1 DzGz 0181...View the full answer
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Related Book For
Digital Control System Analysis And Design
ISBN: 9780132938310
4th Edition
Authors: Charles Phillips, H. Nagle, Aranya Chakrabortty
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