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HW4_08S-1

# HW4_08S-1 - 2 2 2 2 1 1 n n n s s Ts s G ξϖ = Compare...

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University of California at Berkeley Department of Mechanical Engineering ME132 Dynamic Systems and Feedback Spring 2008 Homework Set #4 Assigned: February 28 (Th) Due: March 18 (Tu) [1] 10.3.1 Note: follow the instructions in Problem 1 on page 96 instead of page 82. [2] 11.8-1 [3] 11.8-2 [4] 11.8-5 [5] 12.3-4 [6] Note that the frequency response of a dynamic system described by the transfer function G ( s ) is ) ( ϖ j G . Assume that G ( s ) represents the cascade connection of G 1 ( s ) and G 2 ( s ) (see Fig. on pages 106/107). Show that the frequency response of G ( s ) satisfies the following rules. 1. | ) ( | | ) ( | | ) ( | 2 1 ϖ ϖ ϖ j G j G j G × = or ) ( log( 20 ) ( log( 20 ) ( log( 20 2 1 ϖ ϖ ϖ j G j G j G + = 2. ) ( ) ( ) ( 2 1 ϖ ϖ ϖ j G j G j G + = By making use of these properties, hand sketch the frequency response Bode plot of
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Unformatted text preview: 2 2 2 2 1 1 ) ( n n n s s Ts s G ξϖ + + + = Compare your hand sketches with matlab generated plots. You can assume any numbers for the parameters, ) 10 , 2 . , 1 ( ) , , ( = n T ξ and ) 1 , 2 . , 10 ( ) , , ( = n T . Rules 1 and 2 may be extended to cases where more than two transfer function blocks are multiplied. Hand sketch the frequency response Bode plot of ) 1 5 )( 1 2 ( 1 ) ( + + + = s s s s G Note that this transfer function is the product of s+ 1, 1/(2 s +1) and 1/(5 s +1). [7] 15.1-1...
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