In this work, we investigate the performance of nonlinear model predictive control (NMPC) and moving horizon estimation (MHE) in a feedback control system subject to different arrival cost (AC) approximation methods, process uncertainties with non-Gaussian distributions, and plant designs. In particular, we investigate the performance of an extended Kalman filter (EKF) as an AC estimator for large and complex applications. Considering the significant impact of state estimations as the initial condition of the NMPC problem, together with the importance of the AC approximation in the success of the MHE framework, it is expected that a poor approximation of the AC may lead to poor closed-loop performance. Different arrival cost estimation methods including the traditional EKF and constrained particle filtering were evaluated in this work- The closed-loop framework was tested on two industrial applications: a wastewater treatment plant and a high-impact polystyrene process. Error analysis on the convergence of the EKF-based AC estimator is presented in this work to provide insights into the performance of EKF as an AC estimator under different scenarios. The results show that an appropriate arrival cost estimation method such as EKF is adequate to maintain the operation of large and challenging systems in a closed-loop using an MHE-NMPC framework.