332-3Solutions

# 332-3Solutions - H a i s − 1 s 1 ii s 2 − √ 2 s 1 s 2...

This preview shows pages 1–15. Sign up to view the full content.

ECE 332 Homework #3 1) Design a second-order transfer function H d ( s ) to meet all of the following speci cations. Choose ω n as small as possible. a) e ss 0 =0 b) M r 1 . 3 c) M p 1 . 3 d) e ss 1 . 8 s e) ω b 1 . 5 rad/s f) ω r . 7 rad/s g) T r 2 . 3 s h) T p 3 . 5 s Find the poles of the system. 2) Let H R ( s )= H d ( s ) R ( s + R ) s 2 + . 05 Rs + R 2 , where H d was found in 1). a) Find the poles and zeros of H R for R =5 . What is the damping factor ξ for the high-frequency poles? b) Use MATLAB to nd the smallest value of R so that i) 20 log | H R ( ) | < 40 dB and 20 log | H d ( ) | < 40 dB for all ω such that | 20 log | H R ( ) | 20 log | H d ( ) || > 1 dB ii) | y d ( t ) y R ( t ) | . 01 , where y d and y R are the step responses corresponding to H d and H R . To do this, enter xi = ξ ; wn = ω n ; R =5 ; hw 32” , where ξ and ω n are the values of damping ratio and natural frequency chosen in part 1). MATLAB will display the frequency and step responses for H d and H 5 . Increase R until i) and ii) are met. Print the nal plots and identify which curves correspond to each transfer function. c) Find the poles and zeros of H R for the value of R selected in b).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: H a . i) s − 1 s +1 ii) s 2 − √ 2 s +1 s 2 + √ 2 s +1 iii) ( s − 1) ( s 2 − √ 2 s +1 ) ( s +1) ( s 2 + √ 2 s +1 ) For each case, let H = H d H a , where H d was obtained in problem 1). a) Find the poles and zeros of H . b) Using MATLAB, draw Bode plots for H d and H. Also plot y d ( t ) and ( − 1) n y ( t ) , where y d and y are the step responses corresponding to H d and H, and n is the order of H a . For case i), this is done by entering “ xi = ξ ; wn = ω n ; hw 33 i ” . Compare the responses of the minimum-phase and the non-minimum-phase systems. Print the graphs and identify which correspond to H d and H. Repeat a) and b) for cases ii) and iii) using the commands “ xi = ξ ; wn = ω n ; hw 33 ii ” and “ xi = ξ ; wn = ω n ; hw 33 iii ” ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 15

332-3Solutions - H a i s − 1 s 1 ii s 2 − √ 2 s 1 s 2...

This preview shows document pages 1 - 15. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online