Sampled-data Fuzzy Control of Two-wheel Inverted Pendulums Based on Passivity Theory

In this paper, an aperiodically sampled-data control scheme is detailed for the two-wheel inverted pendulum using Takagi-Sugeno (T-S) fuzzy models. The passivity theory is applied in the presence of the disturbances in the actuator channel. A two-rule fuzzy model is utilized to represent the two-wheel inverted pendulum. By using the pendulum angle as the antecedent variable of the fuzzy rule, a passive sampled-data controller is established using the pendulum inclination angle and the mean value of the rim motors' rotary angles. A Lyapunov-like function based on the two fuzzy rules is constructed to develop criteria of passivity, by the utilization of very-strict passivity in terms of the pendulum angle. Then a solution to the gains of sampled-data controller is synthesized to ensure the very-strict passivity of the pendulum system. By the illustrative examples, the effectiveness of the variable-sampling control scheme is validated for the two-wheel inverted pendulum.