Chapter 4 - EEL4657 - Dr. Haniph Latchman Chapter 4...

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Unformatted text preview: EEL4657 - Dr. Haniph Latchman Chapter 4 Solutions 1. The second order system is given by: G ( s ) = 2 n s 2 + 2 s + 2 n The impulse response is determined by: G ( s ) = 2 n s 2 + s n s + 2 n = n p 1- 2 n p 1- 2 ( s + n ) 2 + 2 n (1- 2 ) g ( t ) = n p 1- 2 e- n t sin( n p 1- 2 t ) = n e- n t sin( n t ) and set = p 1- 2 = tan- 1 1 The step response is the integral of the impulse response y ( t ) = Z t n e- n sin( n ) d =- 1 Z t sin( n ) de- n =- 1 e- n sin( n ) t + n Z t e- n cos( n ) d =- 1 e- n t sin( n t )- 1 2 Z t cos( n ) de- n =- 1 e- n t sin( n t )- 1 2 e- n cos( n ) t- 2 2 Z t n e- n sin( n ) d =- 1 e- n t sin( n t )- 1 2 e- n t cos( n t ) + 1 2- 2 2 y ( t ) = 1- 1 e- n t [ sin( n t ) + cos( n t )] Y STEP ( t ) = 1- 1 e- n t sin( n t + ) 2. The impulse response of G ( s ) = 2 n s 2 + 2 s + 2 n 2 is given by G ( s ) = 2 n s 2 + s n s + 2 n = n p 1- 2 n p 1- 2 ( s + n ) 2 +...
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Chapter 4 - EEL4657 - Dr. Haniph Latchman Chapter 4...

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