Lec_13

# Lec_13 - Lecture 13 Direct Design Method Direct Design...

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1 Lecture 13: Direct Design Method Direct Design Method of Ragazzini Reading: Chap. 7.5, Digital Control Dynamic Systems , G. F. Franklin, J. D. Powell, and M. Workman, 3 rd Edition Idea of Direct Design Method Given a plant with The desired closed-loop transfer function H ( z ) is chosen with good (time characteristics, tracking error) performance Idea : Find the compensator D ( z ) directly by solving D ( z ) is chosen to “cancel” the plant and achieve the desired H ( z ) Question : for what H ( z ) will the above procedure work? C ( s ) G ( s ) R ( s ) T + ¡ D ( z ) G ( z ) = Z [ G ( s )] C ( z ) R ( z ) = H ( z ) D ( z ) G ( z ) 1+ D ( z ) G ( z ) = H ( z ) ) D ( z ) = 1 G ( z ) H ( z ) 1 ¡ H ( z )

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2 Zeros and Poles at Infinity Given a rational transfer function H ( z ) has n - m zeros at infinity if n > m m - n poles at infinity if n < m No zero or pole at infinity if n = m For H ( z ) to be causal (hence physically feasible): H ( z ) cannot have poles at infinity: Or equivalently, . Thus, H ( z ) has a delay of n - m time steps H ( z ) = a m z m + a m ¡ 1 z m ¡ 1 + ¢¢¢ + a 0 b n z n + b n ¡ 1 z n ¡ 1 + ¢¢¢ + b 0 ( a m 6 = 0 ; b n 6 = 0) lim z !1 H ( z ) = 0
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Lec_13 - Lecture 13 Direct Design Method Direct Design...

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