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

## TL;DR

This paper explores extending traditional PID controllers with General Dynamic Neural Networks to improve control performance on complex systems while maintaining interpretability and stability, validated through extensive benchmarking.

## Contribution

It introduces neural PID controllers using GDNNs, demonstrating their superior performance and interpretability compared to standard and model-based controllers across multiple benchmarks.

## Key findings

- Neural PID controllers outperform standard PID in 15 of 16 tasks.
- Neural PID controllers outperform model-based control in 13 of 16 tasks.
- Bounded-input bounded-output stability analysis enhances interpretability of neural controllers.

## Abstract

Modern automation systems rely on closed loop control, wherein a controller interacts with a controlled process, based on observations. These systems are increasingly complex, yet most controllers are linear Proportional-Integral-Derivative (PID) controllers. PID controllers perform well on linear and near-linear systems but their simplicity is at odds with the robustness required to reliably control complex processes. Modern machine learning offers a way to extend PID controllers beyond their linear capabilities by using neural networks. However, such an extension comes at the cost of losing stability guarantees and controller interpretability. In this paper, we examine the utility of extending PID controllers with recurrent neural networks-namely, General Dynamic Neural Networks (GDNN); we show that GDNN (neural) PID controllers perform well on a range of control systems and highlight how they can be a scalable and interpretable option for control systems. To do so, we provide an extensive study using four benchmark systems that represent the most common control engineering benchmarks. All control benchmarks are evaluated with and without noise as well as with and without disturbances. The neural PID controller performs better than standard PID control in 15 of 16 tasks and better than model-based control in 13 of 16 tasks. As a second contribution, we address the lack of interpretability that prevents neural networks from being used in real-world control processes. We use bounded-input bounded-output stability analysis to evaluate the parameters suggested by the neural network, thus making them understandable. This combination of rigorous evaluation paired with better interpretability is an important step towards the acceptance of neural-network-based control approaches. It is furthermore an important step towards interpretable and safely applied artificial intelligence.