Consider the general bilinear transformation where a is real and nonzero. (a) Show that this function transforms

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Consider the general bilinear transformation || z = 1 + 1 - aw aw

where a is real and nonzero.

(a) Show that this function transforms the stability boundary of the z-plane into the imaginary axis in the w-plane.

(b) Find the relationship of frequency in the s-plane to frequency in the w-plane.

(c) Find the stable region of the w-plane for a 6 0 and for a > 0.

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Digital Control System Analysis And Design

ISBN: 9780132938310

4th Edition

Authors: Charles Phillips, H. Nagle, Aranya Chakrabortty

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Question Posted: Jan 22, 2024 03:00 AM

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Consider the general bilinear transformation where a is real and nonzero. (a) Show that this function transforms

Question:

|| z = 1 + 1 - aw aw

Step by Step Answer:

a z 1 aw 1aw b 00 W 1 z1 a z1 tan a W W1 Re w 1 21 a 21 2 COT Fo...View the full answer

Digital Control System Analysis And Design

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