This paper presents a Learning Feedback Linearization (LFL) based Nonlinear Auto-Regressive Moving Average (NARMA) controller design for a ROTary inverted PENdulum (ROTPEN) plant. The proposed NARMA controller comprises of a linear controller and an LFL block. The LFL block concatenated with the nonlinear plant constitutes a linear closed loop system so that linear control is applicable. An online learning algorithm is used for the data-dependent identification of the linearized plant and then for the data-dependent design of the linear part of the NARMA controller. The identification of the linearized plant starts with the determination of the LFL block in a supervised way by exploiting the input and the corresponding state data obtained from the nonlinear plant. The linearized plant is then identified as an ARMA model by the data generated with the combination of the already learned LFL block and the nonlinear plant. Robustness of the linearized system model is obtained by employing the insensitive loss function l(1,epsilon)(.,.) as the identification error of the linearized system. The Schur stability of the overall closed loop system is ensured by the linear inequality constraints imposed in the minimization of the l(1,epsilon)(.,.) tracking error for determining the linear controller parameters. The proposed LFL based NARMA controller is tested on ROTPEN model and its performance is compared with the Proportional-Derivative controller and Hammerstein based NARMA adaptive controller.