DiffLoop: Tuning PID controllers by differentiating through the feedback loop

TL;DR

This paper introduces DiffLoop, a novel method for tuning PID controllers by differentiating through the feedback loop using automatic differentiation, enabling gradient-based optimization of control parameters.

Contribution

It presents a new framework for PID tuning via back-calculation and differentiation, linking disturbance feedback policies with gradient-based optimization.

Findings

Effective PID tuning via gradient descent demonstrated on linear systems.

Theoretical analysis of non-convex optimization in PID tuning.

Numerical experiments show improved controller performance with the proposed method.

Abstract

Since most industrial control applications use PID controllers, PID tuning and anti-windup measures are significant problems. This paper investigates tuning the feedback gains of a PID controller via back-calculation and automatic differentiation tools. In particular, we episodically use a cost function to generate gradients and perform gradient descent to improve controller performance. We provide a theoretical framework for analyzing this non-convex optimization and establish a relationship between back-calculation and disturbance feedback policies. We include numerical experiments on linear systems with actuator saturation to show the efficacy of this approach.