HW8 - ME360 Winter 2011 HW#8 1 Consider the second order...

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Unformatted text preview: ME360 Winter 2011 HW #8 1. Consider the second order system represented in standard form ? ( ¡ ) = ¢ £ 2 ¡ 2 +2 ¤¢ £ ¡ + ¥ £ 2 . a) From the time domain analysis, the condition for the existence of overshoot (for the step input) is ¤ < 1 . Similarly, in the frequency domain analysis, we may have the resonance peak ¦ ? ( ¢ ) ≔ max ¢ | ? ( §¢ )| > | ? (0)| in the frequency response. Find the range of ¤ that we do not have this resonance peak, i.e. the range of ¤ that | ? ( §¢ )| < | ? (0)|, ∀¢ > 0 . In the pole-zero map, indicate the region for the poles that you do not have the resonance peak. Explain why people typically design the controller such that the desired damping ratio of the closed loop system (2 nd order) is 1 √ 2 ≅ 0.707 , i.e. ¨ = 45 © . b) Find the bandwidth ¢ ª« required for 20% overshoot and 2 second settling time. c) Find ? ¬ ( ¡ ) that would have given you ? ( ¡ ) as your closed-loop transfer function when you have a unity feedback. Draw a block diagram using ­ ( ¡ ) as a reference input and ® ( ¡ ) as the output. d) Instead of the unity feedback (P-control with gain 1), implement a PD controller ?...
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HW8 - ME360 Winter 2011 HW#8 1 Consider the second order...

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