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

# Alternate method we compare this to the standard form

This preview shows page 1. Sign up to view the full content.

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

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...
View Full Document

## 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.

Ask a homework question - tutors are online