Understanding how animals use sensory information to control locomotion is an important area of study in biology, control engineering, and robotics. The weakly electric glass knifefish Eigenmmania virescens is an ideal model to study sensorimotor control and integration since it naturally tries to track a one degree of freedom fore-aft moving refuge and exhibits smooth, rapid movement, allowing the analysis of how the fish converts sensory input into motor output. Previous studies applied simplified linear modeling of the controller and plant, but linear models are unable to capture the categorical differences in the fish’s responses to “predictable” vs. “unpredictable” moving refuge stimuli. Specifically, previous work (Roth et al., 2011) showed that these fish track individual single sinusoidal motions much better than when those sinusoids were embedded in pseudo-random sum-of-sines signals. Thus, linear models used to date cannot capture the fish’s real response as there are nonlinearities within the fish’s controller that are revealed using different types of stimuli. Here we focus on modeling the nonlinearities of fish tracking. We first coupled a harmonic oscillator with poles at the input frequency into the fish’s controller model so that the sinusoidal input can be nearly perfectly tracked at steady-state in theory. This linear control model, based on the internal model principle (IMP) in control engineering, only yields perfect tracking when the controller has an accurate model of the input frequency. However, the fish must infer the stimulus frequency in real time, adding nonlinearities to its controller. We developed a simple nonlinear control that takes advantage of the IMP, combined with a frequency identification process based on adaptive systems theory as a parsimoneous candidate that captures key elements of the nonlinear behavior, providing a more accurate model for future analyses.