Rate limits in control surface actuators are a key culprit behind pilot-induced oscillations: a class of problematic handling qualities issues that have plagued aviators since the dawn of piloted flight. When repeatedly saturated, these rate limit nonlinearities induce time delays that rapidly form in the control system and cause the aircraft response to fall out of phase with pilot inputs, rendering the vehicle extremely difficult to control. This paper proposes a model reference control architecture to compensate for these rate limits using a neural network controller. The goal of the nonlinear compensation is to make the combined controller-plant system exhibit a closed-loop response similar to that of an ideal system: one immune to the effects of rate limits, and therefore less prone to pilot induced oscillations. This paper discusses the methods used to train the model reference controller and details results from a pair of case studies. Controllers are designed and applied to two aircraft models, one unaugmented and one augmented, that can be driven to encounter pilot induced oscillations. Results show that the model reference control scheme reduces pilot-induced oscillation tendencies throughout the tested maneuvering envelopes and improves closed-loop tracking performance in both cases.