HW_5_sol[1]

# HW_5_sol[1] - HW 5 ECE 2704 Due A system is given by its...

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DKL:10/18/06 HW 5 solutiions 1/3 HW 5 ECE 2704 Due 10-16-06 A system is given by its pole-zero diagram 1. (5) What is the transfer function of this system? (gain = 1) Solution Y ( s ) X ( s ) = H ( s ) = 1 s + 1 ( ) 2 + 6 2 = 1 s 2 + 2 s + 37 2. (5) Find ! , " n ( ) for these poles. Solution ! n 2 = 37 " ! n = 6.08 rad/sec , 2 !" n s = 2 s # ! = 1 " n # ! = 0.164 Other approach to obtain this solution is to use damp command in Matlab. h = tf ([1], [1 2 37]) Transfer function: 1 ----------------- s^2 + 2 s + 37 >> damp (h) Eigenvalue Damping Freq. (rad/s) -1.00e+000 + 6.00e+000i 1.64e-001 6.08e+000 -1.00e+000 - 6.00e+000i 1.64e-001 6.08e+000

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DKL:10/18/06 HW 5 solutiions 2/3 3. (10) Find y ( t ) by Laplace transforms. Solution Y ( s ) = H ( s ) X ( s ) = 1 s 2 + 2 s + 37 1 s y ( t ) = 1 ! n 2 1 " 1 1 " # 2 e "#! n t sin ! c t + \$ ( ) % & ( ) * * = 1 37 1 " 1 1 " 0.164 2 e " t sin 6 t + cos " 1 (0.164) ( ) % & ( ) * 4. (20) Plot the step response of this system using Matlab. First, define the system using tf . Then generate a unit step function for the input signal. (What time interval did you chose?) Then simulate the system using the
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• Spring '08
• DJStilwell
• \$1, #, Heaviside step function

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