Upper-limb exosuits are light wearable devices suitable for applications such as rehabilitation or assistance in industrial environments. One of the main drawbacks of these systems is the amount of uncertainties intrinsic to the nature of the device. Moreover, the direct interaction between the exosuit and its user adds disturbances to the system. Therefore, a robust control architecture to these phenomena is required for its appropriate control. In this article, a robust motion (position and speed) control architecture based on a cascade proportional-integral (PI) and a sliding mode controller (SMC), and a nonlinear disturbance observer (NDO) for the upper-limb cable-driven rehabilitation exosuit LUXBIT is designed. We call the proposed controller by the acronym CPISDO. The SMC nature allows to compensate the matched disturbances and uncertainties, while the NDO counteracts the unmatched ones. The PI component helps in reducing tracking error. Dynamic modelling, system architecture and control design are addressed. The CPISDO controller has been implemented over the exosuit and several experiments have been performed over 10 healthy subjects to evaluate the controller's tracking performance as well as the disturbance rejection. Supertwisting (a state-of-the-art SMC) and PI controllers have been implemented for CPISDO validation. Results are compared with other state-of-the-art solutions.INDEX TERMS Motion control, exoskeletons, control architectures, rehabilitation robotics, sliding-mode control.