State-feedback control of a Reaction-Wheel Inverted Pendulum prototype

Abstract

The Reaction-Wheel Inverted Pendulum (RWIP) is a nonlinear system with an unstable equilibrium point. We present a laboratory prototype built at the Industrial Automation and Control Laboratory of the Federal Institute of Education of Paraná – IFPR (campus Jacarezinho). The hardware consists of a rod mounted on a metal frame, a direct-current (DC) motor driving a reaction wheel, and a counterweight to reduce the required control torque. The control system uses an ESP32 interfaced with a computer running MATLAB/Simulink, with a 1 ms sampling period. Angular positions are measured with incremental encoders, and derivative filters provide the velocities required for state feedback. The dynamic model used to design the controllers was derived from Lagrange's equations and coupled with the DC-motor dynamics, yielding a state-space model that was linearized about the upright equilibrium. Two full-state feedback controllers were designed and tested: (i) a pole-placement (state feedback) and (ii) a Linear-Quadratic Regulator (LQR). A simplified bang-bang energy-injection swing-up raises the pendulum from the downward equilibrium, and an angle-based switching law hands control over to the state-feedback law once the pendulum nears the upright region. Both controllers were evaluated in simulation and implemented experimentally on the prototype under the same disturbance scenario. Performance was assessed through time-domain plots and the integral of the absolute error (IAE), the integral of the squared error (ISE), and their time-weighted counterparts (ITAE and ITSE). Over the full response, including the swing-up maneuver, the two controllers perform comparably, with experimental index differences below 5%. A repeatability campaign of fifteen runs per controller shows that the mean stabilization-phase indices of the two designs differ by 0.6% to 1.4%, against a run-to-run coefficient of variation of 5.6% to 13.4%, so the two controllers are equivalent in performance on this prototype. Across the sixty disturbance events of the campaign, all were rejected without loss of stabilization, with a largest angular excursion of 9.90◦and using at most 5.78 V of the available 12 V. The work provides practical validation and a didactic comparison of state-feedback synthesis methods applied to the RWIP, serving as a platform for teaching and applied research.