This paper aims to experimentally validate the stochastic approximated model predictive control (MPC) called the random shooting (RS)-based control. This method was designed to address the computational challenges of standard MPC, mainly the computational complexity. However, RS-based approximated MPC in its original formulation lacks guarantees of recursive feasibility and closed-loop stability. Therefore, a modification of the RS-based approach, a recursive RS-based method, was also implemented to overcome these limitations. The recursive RS-based method features a dual-mode control strategy, which reduces the computational burden. The recursive feasibility and closed-loop stability are enforced through the integration of a support controller. The case study demonstrates a successful implementation of offset-free reference tracking by RS-based methods on a system with fast dynamics. The validated control methods were implemented under strict computational constraints, proving to be a fast, solver-free alternative that does not compromise stability or recursive feasibility.