In this paper, a nonlinear proportional and integral (PI) controller based on Radial Basis Function Neural Network (RBFNN) is proposed for the speed control of electric drives. The Lyapunov function is employed in the design process to ensure system stability. The proposed nonlinear PI controller has a fixed proportional gain but a variable integral gain, which makes it outperforms than the conventional linear PI controller in terms of robustness to inertia variations. This paper’s design method distinguishes between an adaptive linear neuron (ADALINE) and an RBFNN with a hidden layer. The linear integrator in a traditional PI controller can be thought of as an ADALINE, whereas the nonlinear integrator can be activated by using a hidden layer. Various experiments on the dSPACE MicroLabBox-based test bench are conducted to verify the effectiveness of the proposed method.