DiffLoop: Tuning PID controllers by differentiating through the feedback loop

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.