Strictures caused by esophageal cancer can narrow down the esophageal lumen, leading to dysphagia. Palliation of dysphagia has driven the development of a robotic soft esophagus (RoSE), which provides a novel in vitro platform for esophageal stent testing and food viscosity studies. In RoSE, peristaltic wave generation and control were done in an open-loop manner since the conduit lacked visibility and embedded sensing capability. Hence, in this work, RoSE version 2.0 (RoSEv2.0) is designed with embedded time of flight (TOF) and pressure sensors to measure conduit displacement and air pressure, respectively, for modeling and control. Model predictive control (MPC) of RoSEv2.0 is implemented to govern the peristalsis and air pressure profile autonomously. The implemented MPC used sparse identification of nonlinear dynamics with control (SINDYC) models to estimate the future states of ROSEv2.0. The dynamic models are discovered from the TOF and pressure sensor data. Peristalsis waves of speed 20 mm ⋅ s−1, wavelength 75 mm, and amplitudes 5, 7.5, and 10 mm were successfully generated by the MPC. Additionally, RoSEv2.0 with the MPC was employed to perform stent migration testing with various food boluses consistencies. The major contribution claimed in this article is the application of SINDYC-based MPC to solve the closed-loop control problem of RoSE for achieving desired peristaltic waves.