Sampled-Data Control using Hermite-Obreschkoff Methods with an IDA-PBC Example

TL;DR

This paper develops a unifying framework for sampled-data control using Hermite-Obreschkoff methods, extending previous collocation schemes, and demonstrates its application with an IDA-PBC controller for magnetic levitation, including experimental validation.

Contribution

It introduces a unifying derivation for high-order Hermite-Obreschkoff schemes in sampled-data control and applies it to design an IDA-PBC controller with experimental results.

Findings

Higher order schemes improve sampling times before instability.

The derived IDA-PBC controller effectively stabilizes magnetic levitation.

Experimental results confirm the practical viability of the approach.

Abstract

The motivation for this paper is the implementation of nonlinear state feedback control, designed based on the continuous-time plant model, in a sampled control loop under relatively slow sampling. In previous work we have shown that using one-step predictions of the target dynamics with higher order integration schemes, together with possibly higher order input shaping, is a simple and effective way to increase the feasible sampling times until performance degradation and instability occur. In this contribution we present a unifying derivation for arbitrary orders of the previously used Lobatto IIIA collocation and Hermite interpolation schemes through the Hermite-Obreschkoff formula. We derive, moreover, an IDA-PBC controller for a magnetic levitation system, which requires a non-constant target interconnection matrix, and show experimental results.