Second Order System PDF

Introduction A general second-order system is characterized by the following transfer function. C( s )  n2  2 R( s ) s  2 n s   n2  Introduction C( s )  n2...

Introduction A general second-order system is characterized by the following transfer function. C( s )  n2  2 R( s ) s  2 n s   n2  Introduction C( s )  n2  2 R( s ) s  2 n s   n2 n un-damped natural frequency of the second order system, which is the frequency of oscillation of the system without damping.  damping ratio of the second order system, which is a measure of the degree of resistance to change in the system output.  Example#1 Determine the un-damped natural frequency and damping ratio of the following second order system. C( s ) 4  2 R( s ) s  2s  4 Compare the numerator and denominator of the given transfer function with the general 2nd order transfer function. C( s )  n2  2 R( s ) s  2 n s   n2 n2  4  n  2 rad / sec  2 n s  2s   n  1 s 2  2 n s  n2  s 2  2s  4    0.5  Introduction C( s )  n2  2 R( s ) s  2 n s   n2 Two poles of the system are   n   n  2  1   n   n  2  1  Introduction   n   n  2  1   n   n  2  1 According the value of  , a second-order system can be set into one of the four categories: 1. Overdamped - when the system has two real distinct poles (  >1). jω δ -c -b -a  Introduction   n   n  2  1   n   n  2  1 According the value of  , a second-order system can be set into one of the four categories: 2. Underdamped - when the system has two complex conjugate poles (0