Efficient Relay Autotuner of Industrial Controllers via Rank-Constrained Identification of Low-Order Time-Delay Models

Relay feedback tuning has been a state-of-the-art autotuning technique in process control, where frequency-domain analysis is generically carried out using limit cycle data for model identification and controller tuning. However, due to noise and disturbance, nonnegligible approximation errors exist in frequency information distilled from data, resulting in model mismatch and a huge obstacle for automating the tuning procedure. In this article, we propose an efficient time-domain identification approach toward relay feedback autotuning. A new rank-constrained nonparametric formulation of model identification is proposed, which is in correspondence to low-order parametric transfer functions. Based on this, an efficient initialization strategy for nonparametric models is put forward using kernel-based regularization, which helps to circumvent local optima and eventually deliver better model estimates than conventional gradient-based approaches. Moreover, nonzero initial conditions can be tackled by means of regularization heuristics. Numerical examples and experiments on a real-world system showcase that the proposed identification approach not only improves accuracy but also effectively circumvents unfaithful models contradicting prior knowledge, thereby substantially benefiting the automated tuning of industrial controllers.