332-3Solutions

332-3Solutions - H a . i) s 1 s +1 ii) s 2 2 s +1 s 2 + 2 s...

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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).
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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 = ; wn = 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 = ; wn = n ; hw 33 ii and xi = ; wn = n ; hw 33 iii ....
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332-3Solutions - H a . i) s 1 s +1 ii) s 2 2 s +1 s 2 + 2 s...

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