Nonlinear optimal control for the inertia wheel inverted pendulum

ABSTRACT Due to underactuation and nonlinearities, the control of the inertia wheel inverted pendulum is a non-trivial problem. The article proposes a nonlinear optimal control approach for the inertia wheel inverted pendulum. First, the dynamic model of the pendulum undergoes approximate linearisation around a temporary operating point which is recomputed at each time-step of the control method. The linearisation procedure makes use of first-order Taylor series expansion and requires the computation of the system’s Jacobian matrices. For the approximately linearised model of the pendulum, a stabilising H-infinity feedback controller is designed. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control scheme are proven through Lyapunov analysis. It is demonstrated that the control method satisfies the H-infinity tracking performance criterion, which signifies robustness against model uncertainty and external perturbations. Next, it is proven that the control loop is globally asymptotically stable. The nonlinear optimal control method retains the advantages of typical optimal control, that is fast and accurate tracking of the reference setpoints under moderate variations of the control input.