MEM355W07-08.HW1.soln_stud

MEM355W07-08.HW1.soln_stud - .10 For G6(s k = 0 for i...

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MEM355: PERFORMANCE ENHANCEMENT OF DYNAMIC SYSTEMS Home work #1 solution A: A (aliter – using signals): B:
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B (using signals): C,i: Step(tf(65*[1 60],[1 90])) Time (sec.) error step response (65 mph) 0 0.014 0.028 0.042 0.056 0.07 40 45 50 55 60 65 From: U(1) To: Y(1) C,ii . Step(tf(65*[1 60 0],[1 60 800]))
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Time (sec.) error step response (65mph) w/ integral 0 0.05 0.1 0.15 0.2 0.25 0.3 0 10 20 30 40 50 60 70 From: U(1) To: Y(1) Step(tf(65*[1 60 0],[1 60 1800])) Time (sec.) step response (65mph) w/ integrator 0 0.05 0.1 0.15 0.2 -10 0 10 20 30 40 50 60 70 From: U(1) D .
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With K=1 , he loop transfer functions in slides 6 and 7 respectively are 6 600 ( ) 60 G s s = + and 7 600 ( ) ( 60) G s s s = + respectively. With , s j ϖ = we get 6 2 2 2 600 600(60 ) 36000 600 ( ) 60 60 60 60 j G j j j - = = = - + + + + , and 2 7 2 4 2 2 3 600 600 600( 60 ) 600 36000 ( ) ( 60) 60 ( 3600 ) ( 3600) ( 3600 ) j G j j j j j - + = = = = - - + - + + + . With these expressions available, one needs to use the identity 2 2 | | j σ + = + to generate the plots. Thisis achieved using Matlab as follows for 3 3 [10 .
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Unformatted text preview: ..10 ].-: For G6(s): k = 0; for i = -3:.01:3; k = k + 1; ome = 10^i; sigma = 36000/(60+ome^2); omega = -600/(60+ome^2); mag = sqrt(sigma^2+omega^2); log_mag(k) = log10(mag); log_ome(k) = log10(ome); end plot(log_ome,log_mag)-3-2-1 1 2 3-2-1 1 2 3 mag .vs. freq for G6 log(freq) log(mag) For G7(s): k = 0; for i = -3:.01:3; k = k + 1; ome = 10^i; sigma = -600/(3600+ome^2); omega = -36000/((3600+ome^2)*ome); mag = sqrt(sigma^2+omega^2); log_mag(k) = log10(mag); log_ome(k) = log10(ome); end plot(log_ome,log_mag) title( 'mag .vs. freq for G7' ) xlabel( 'log(freq)' ) ylabel( 'log(mag)' ) grid on-3-2-1 1 2 3-4-2 2 4 mag .vs. freq for G7 log(freq) log(mag)...
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This note was uploaded on 07/07/2008 for the course MEM 355 taught by Professor Kwatny during the Spring '07 term at Drexel.

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MEM355W07-08.HW1.soln_stud - .10 For G6(s k = 0 for i...

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