الملزمه الثامنه.pdf
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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