Abstract: A controller circuit implements an interpretable neural-network-based proportional integral derivative (PID) control function. The controller circuit comprises a controller output signal for input to a nonlinear plant, a controller input signal representing an error in an output of the nonlinear plant, and a neural network configured to calculate the controller output signal from the controller input signal by summing a first signal depending on a current value of the controller input signal, a second signal generated at least in part by a first neural network estimating a differential of the controller input signal, and a third signal generated at least in part by a second neural network estimating an integral over time of the controller input signal.