Double integrator processes with transient rate feedback: tutorial redesign using integral performance measures

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.