Despite some research attempts, a general and comprehensive modeling means for inflatable robotic arms (IRAs) is yet to be established. To bridge this gap, this paper presents a novel approach to capturing the high nonlinearity of a large-scale (approximately 1.8 m long) and ultralight (only 191 g in weight) IRA, which is a trade-off between the computational accuracy and efficiency. The rigid-body kinematics and the piecewise constant curvature (PCC) assumption are compared to formulate the kinematic model that incorporates link compression and base errors. A dynamic model is derived leveraging the Cosserat rod theory recursively to predict the behavior of the IRA's thin-walled and incomplete continuum structure, and its inverse model is explicitly extended for error compensation. Thereafter, some prior-unknown parameters are primarily identified, and the real-time performance is also evaluated to assure the closed-loop tracking control. A comparative study amongst the modeling approach and its existing counterparts is quantitatively performed to verify the accuracy. Three model-based control schemes are contrasted to further demonstrate the viability of the proposed model, where an adaptive sliding mode control (ASMC) scheme is designed to handle the model uncertainties. Experimental results reveal the effectiveness of the modeling method and the superior performance of the ASMC.