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Deep reinforcement learning (DRL) has seen several successful applications to process control. Common methods rely on a deep neural network structure to model the controller or process. With increasingly complicated control structures, the closed-loop stability of such methods becomes less clear. In this work, we focus on the interpretability of DRL control methods. In particular, we view linear fixed-structure controllers as shallow neural networks embedded in the actor-critic framework. PID controllers guide our development due to their simplicity and acceptance in industrial practice. We then consider input saturation, leading to a simple nonlinear control structure. In order to effectively operate within the actuator limits we then incorporate a tuning parameter for anti-windup compensation. Finally, the simplicity of the controller allows for straightforward initialization. This makes our method inherently stabilizing, both during and after training, and amenable to known operational PID gains.