  Nonlinear extension of the integral part of PID feedback control is proposed
for the perturbed second-order systems. For the matched constant perturbations,
the global asymptotic stability is shown, and for Lipschitz perturbations an
ultimately bounded output error is guaranteed. The second-order system plants
can also be expanded by an additional (parasitic) actuator dynamics with
low-pass characteristics. The proposed nonlinear control is proven to
outperform its linear (PID) benchmarking counterpart during the settling phase,
i.e. at convergence of the residual output error. An experimental case study of
the second-order system with an additional actuator dynamics and considerable
perturbation is demonstrated to confirm and benchmark the control performance.
