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Modern automation systems rely on closed loop control, wherein a controllerinteracts with a controlled process, based on observations. These systems areincreasingly complex, yet most controllers are linearProportional-Integral-Derivative (PID) controllers. PID controllers performwell on linear and near-linear systems but their simplicity is at odds with therobustness required to reliably control complex processes. Modern machinelearning offers a way to extend PID controllers beyond their linearcapabilities by using neural networks. However, such an extension comes at thecost of losing stability guarantees and controller interpretability. In thispaper, we examine the utility of extending PID controllers with recurrentneural networks-namely, General Dynamic Neural Networks (GDNN); we show thatGDNN (neural) PID controllers perform well on a range of control systems andhighlight how they can be a scalable and interpretable option for controlsystems. To do so, we provide an extensive study using four benchmark systemsthat represent the most common control engineering benchmarks. All controlbenchmarks are evaluated with and without noise as well as with and withoutdisturbances. The neural PID controller performs better than standard PIDcontrol in 15 of 16 tasks and better than model-based control in 13 of 16tasks. As a second contribution, we address the lack of interpretability thatprevents neural networks from being used in real-world control processes. Weuse bounded-input bounded-output stability analysis to evaluate the parameterssuggested by the neural network, thus making them understandable. Thiscombination of rigorous evaluation paired with better interpretability is animportant step towards the acceptance of neural-network-based controlapproaches. It is furthermore an important step towards interpretable andsafely applied artificial intelligence.

Interpretable PID Parameter Tuning for Control Engineering using General Dynamic Neural Networks: An Extensive Comparison