A hard disk drive (HDD) arm has an open-loop unstable transfer function,
where X(s) is arm displacement and F(s) is the applied force (Yan, 2003). Assume the arm has an inertia of Ib = 3 × 10-5 kg-m2 and that a lead controller, Gc(s), is placed in cascade to yield
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 ζ = 0.7 damping factor.
