The quality of model predictive control depends on the accuracy and reliability of the state and output predictions over the chosen time horizon. For poorly known processes, neural-network-based models offer predictions over long horizons based solely on measured data. However, the popular feedforward networks show little robustness to disturbances, measurement noise, and changing operating regimes, due to their high-order noise-sensitive input-output mapping. In recent work, the authors developed a reliable long-range predictor, comprising two neural networks with external feedback in series, and investigated its applicability for model predictive control on a simulation example. The networks use external feedback of the process state, yielding a state-space mapping that eliminates the drawbacks of the input-output mapping of the feedforward networks. These feedback networks also allow the inclusion of analytical state-space models to achieve a more realistic representation of the dynamic process, This renders them less prone to overlearning, thereby increasing the reliability and accuracy in the presence of noise, disturbances, and unforeseen process changes. This work applies the previously developed long-range predictor to the model predictive control of an experimental bench-scale semibatch chemical reactor. Examples of yield maximization for a reaction with complex kinetics are used to assess the proposed predictive control scheme. Control performance is compared for predictors based on the proposed external-feedback networks and on conventional feedforward networks. Results for various operating conditions, disturbances, and included analytical models demonstrate the superiority of the proposed control scheme in experiments. This demonstrates the feasibility of using neural networks as "intelligent" sensors and as long-range dynamic predictors.