Exam 3 (Version 1) - Solution , Sp'12

Alternate method we compare this to the standard form

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Unformatted text preview: r system (we know this is a second order system since there are only 2 poles). () () where ( )( ) are the poles of the system. 6 Thus, () () ( ( ) )( ( )) ( √ Therefore, and ) √ . This gives us the transfer function () () with √ which implies this is an underdamped system. (b) Using the values of √ and √ obtained above, we compute the following parameters for a second order system with unit step response. a. Maximum Overshoot ( ): ( where √ and ( ) . Therefore, ) b. Peak time ( ): c. Settling time ( ): For the 2% criterion, 7 For the 5% criterion, (c) Steady state error is defined as ( ) as where () () () Where ( ), ( ) is the input and output signals in the time domain. In this problem, the input is a unit step response, and thus ( ) () () . The output ( ) is defi...
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This note was uploaded on 08/03/2012 for the course IE 474 taught by Professor Srinivasan,c during the Spring '08 term at Purdue University-West Lafayette.

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