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The transfer function from applied force to arm
Chapter 11, Problem 26(choose chapter or problem)
The transfer function from applied force to arm displacement for the arm of a hard disk drive has been identified as
G(s) = \(\frac{X(s)}{F(s)}=\frac{3.3333 \times 10^4}{s^2}\)
The position of the arm will be controlled using the feedback loop shown in Figure P11.1 (Yan, 2003).
a. Design a lead compensator to achieve closed-loop stability with a transient response of 16% overshoot and a settling time of 2 msec for a step input.
b. Verify your design through MATLAB simulations.
Questions & Answers
QUESTION:
The transfer function from applied force to arm displacement for the arm of a hard disk drive has been identified as
G(s) = \(\frac{X(s)}{F(s)}=\frac{3.3333 \times 10^4}{s^2}\)
The position of the arm will be controlled using the feedback loop shown in Figure P11.1 (Yan, 2003).
a. Design a lead compensator to achieve closed-loop stability with a transient response of 16% overshoot and a settling time of 2 msec for a step input.
b. Verify your design through MATLAB simulations.
ANSWER:Step 1 of 4
a) The %OS spec required a damping factor of \(\xi=\frac{-\ln (\% O S / 100)}{\sqrt{\pi^{2}+\ln ^{2}(\% O S / 100)}}=0.5\), which in turn requires a phase margin of \(\Phi_{M}=\tan ^{-1} \frac{2 \xi}{\sqrt{-2 \xi^{2}+\sqrt{1+4 \xi^{4}}}}=52^{\circ}\). The bandwidth requirement is obtained from \(\omega_{B W}=\frac{4}{T_{s} \xi} \sqrt{1-2 \xi^{2}+\sqrt{4 \xi^{4}-4 \xi^{2}+2}}=5088.1 \frac{\mathrm{rad}}{\mathrm{sec}}\).