Output feedback stabilization of inverted pendulum on a cart in the presence of uncertainties

An output feedback controller is proposed for stabilization of the inverted pendulum on a cart in the presence of uncertainties. The output feedback controller has a multi-time-scale structure in which Extended High-Gain Observers are used to estimate system states and uncertainties in the first and fastest time scale; dynamic inversion is used to deal with uncertain input coefficients in the second time scale; the pendulum converges to a reference trajectory in the third time scale; and finally, the reference trajectory is designed such that both the pendulum and the cart converge to the desired equilibrium in the fourth and slowest time scale. The multi-time-scale structure allows independent analysis of the dynamics in each time scale and singular perturbation methods are effectively utilized to establish exponential stability of the equilibrium. Simulation results indicate that the output feedback controller provides a large region of attraction and experimental results establish the feasibility of practical implementation.