ps8_soln

# ps8_soln - EE 428 Problem Set 8 Solutions-3 Problem 34 EE...

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EE 428 Problem Set 8 Solutions -3- Problem 34: % EE 428 Fall 2007 % Problem Set 8, Problem 34 % plant transfer function num_Gp = 100; den_Gp = conv([1,1], [1, 10, 100]); % generate Bode plot figure(1) bode(num_Gp, den_Gp) title( 'Probelm 31: Bode Plot of Plant Transfer Function' ) % determine the phase crossover frequency and gain margin [mag, phase, omega] = bode(num_Gp, den_Gp); wpc = interp1(phase, omega, -180); gain_wpc = interp1(omega, mag, wpc); GM = 1 / gain_wpc; [wpc, gain_wpc, GM, 20*log10(GM)] % use the MATLAB command margin [Gm,Pm,Wcg,Wcp] = margin(num_Gp, den_Gp)

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EE 428 Problem Set 8 Solutions -6- Problem 35: 10 -1 10 0 10 1 -20 -10 0 mag [dB] Problem 32: Bode Plot of Plant with Time-Delay GM = 4.3dB 10 -1 10 0 10 1 -200 -100 0 phase [deg] freq [rad/sec] G p = -180 ω pc =1.3 rad/sec
EE 428 Problem Set 8 Solutions -7- Problem 32: % EE 428 Fall 2007 % Problem Set 8, Problem 35 % plant transfer function with out delay num_Gp = 100; den_Gp = conv([1,1], [1, 10, 100]); % determine the gain and phase for no time delay omega = logspace(-2, 3, 10000); [mag, phase, omega] = bode(num_Gp, den_Gp, omega); % modify the phase to include the delay phase_with_delay = phase - (pi/2)*omega*(180/pi); % determine the gain margin wpc = interp1(phase_wd, omega, -180); gain_wpc = interp1(omega, mag, wpc); GM = 1 / gain_wpc; GM_dB = 20*log10(GM);

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## This note was uploaded on 07/23/2008 for the course EE 428 taught by Professor Schiano during the Fall '07 term at Penn State.

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ps8_soln - EE 428 Problem Set 8 Solutions-3 Problem 34 EE...

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