Soft robots are characterized by compliant elements that introduce heightened kinematic complexity compared to their rigid counterparts. Such systems, with infinite degrees of freedom, are inherently underactuated, making precise real-time shape regulation a challenging task. Model-based controllers, utilizing tractable reduced-order modelling methods, have emerged as promising solutions. However, practical implementations of these methods often rely on fully-actuated approximations, overlooking the underactuated nature of these continuum structures. In this study, we aim to experimentally validate model-based controllers that explicitly account for underactuation, surpassing the theoretical feasibility demonstrated in simulation. These controllers incorporate gravity cancellation and compliance compensation using the dynamic model of the robot to achieve superior real-time shape regulation compared to conventional PD/PID controllers. To facilitate this experimental validation, we have built a multi-segment soft robot research platform that includes a passively actuated segment, allowing for the utilization of both actuated and unactuated degrees of freedom in the control feedback loop. Through rigorous experimentation, we provide comprehensive evidence of the efficacy of this class of model-based controllers in controlling unconventionally actuated robotic systems. Consequently, our work bridges the gap between theory and practice, resulting in a practical real-time shape regulation framework that is adaptable to a vast variety of soft robotic systems.