M6.3. Bode Analysis

Here, we enter the first-order + time-delay model in the MATLAB command window.

» fodt = tf([1],[10 1],'InputDelay',5)

Transfer function:
10 s + 1

Input delay: 5

Now, let us perform a Bode analysis assuming a proportional controller gain of 1.

» kc = 1;
» [mag,phase,w] = bode(kc*fodt);
» subplot(2,1,1), loglog(w,squeeze(mag))
» subplot(2,1,2), semilogx(w,squeeze(phase),[0.01 1],
  [-180 -180],'--')

The resulting Bode plot, with the –180° line drawn for convenience, is shown in Figure M6-3. Notice that the crossover frequency is around 0.36 rad/min, where the amplitude ratio is approximately 0.26. The gain margin is then 1/0.26 = 3.8. This means that the controller gain could be increased to roughly 3.8 before ...

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