Nonlinear integral extension of PID control with improved convergence of perturbed second-order dynamic systems (2404.02502v2)
Abstract: Nonlinear extension of the integral part of a standard proportional-integral-derivative (PID) feedback control is proposed for the perturbed second-order systems. For the matched constant perturbations, the global asymptotic stability is shown, while for Lipschitz perturbations an ultimately bounded output error is guaranteed. It is shown that the proposed control is also applicable to second-order systems extended by additional (parasitic) actuator dynamics with low-pass characteristics, thus representing a frequently encountered application case. The proposed nonlinear control is proven to outperform its linear PID 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 perturbations is demonstrated to confirm and benchmark the control performance.
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