Double integrator processes damped by transient velocity feedback are designed by minimising quadratic performance integrals involving error, error rate and error acceleration using step, ramp and step-plus-ramp testing functions. The approach is unified via the Liapunov matrix equation. Comparisons are drawn with earlier frequency-response and analytical-root-locus studies in instrument servomechanisms with inertial damping, which are characterised by the same overall transfer function. An adaptive control strategy is outlined.
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