A hard disk drive (HDD) arm has an open-loop unstable

Chapter 8, Problem 58

(choose chapter or problem)

A hard disk drive (HDD) arm has an open-loop unstable transfer function,

P(s) = \(\frac{X(s)}{F(s)}=\frac{1}{I_b s^2}\)

where X(s) is arm displacement and F(s) is the applied force (Yan, 2003). Assume the arm has an inertia of \(I_b\) = \(3 \times 10^{-5} \mathrm{~kg}-\mathrm{m}^2\) and that a lead controller, \(G_c(s)\) (used to improve transient response and discussed in Chapter 9), is placed in cascade to yield

\(P(s) G_c(s)\) = G(s) = \(\frac{K}{I_b} \frac{(s+1)}{s^2(s+10)}\)

as in Figure P8.3.

a. Plot the root locus of the system as a function of K.

b. Find the value of K that will result in dominant complex conjugate poles with a \(\zeta\) = 0.7 damping factor.