Hybrid nonlinear model predictive and linear quadratic balance control for a two-wheeled self-balancing wheelchair

A two-wheeled self-balancing wheelchair is a highly nonlinear and underactuated wheeled inverted-pendulum system, which faces severe balance control challenges under large tilt angles, load variations, and external disturbances. A hybrid nonlinear model predictive control–linear quadratic regulator (NMPC–LQR) balance control scheme is presented that combines nonlinear optimal recovery and efficient local stabilization while reducing the computational burden. A reduced-order nonlinear dynamic model of the wheelchair–occupant system is derived via the Lagrange method. The proposed controller confines LQR to a locally valid region verified by linearization-error analysis, whereas NMPC is employed for large-deviation recovery. A linearization-error analysis is first used to determine the switching-threshold search range, and a normalized five-index criterion identifies 0.100 rad as the optimal nominal threshold. Mass-sensitivity tests further provide an empirical relation for estimating the optimal threshold within the tested mass range. Comparative simulations under initial tilt angles of 35, 40, and 45° show faster convergence than standalone LQR and standalone NMPC controllers. Benchmark comparisons with SMC demonstrate a larger recoverable initial-angle range. Robustness tests under parameter variations, pulse and step disturbances, and flat-ground friction changes, together with prototype experiments, validate the stability, disturbance rejection, and engineering applicability of the proposed control strategy.