Fuzzy control of an inverted pendulum Driven by a reaction wheel using a trajectory tracking scheme

Abstract

In this work, the design of a Takagi-Sugeno Fuzzy controller with a trajectorytracking scheme for the reaction wheel pendulum is presented. By using the nonlinear state-space model, the system’s operating points are defined, then, the sector nonlinearity method is applied to obtain a linearized model of the system in order to implement linear local regulators. Once the reduced linearized models are obtained, and based on the desired closed loop response, local regulators are designed to generate the global control signal. This signal comprises two terms: The regulator and the reference tracking term. The proposed Fuzzy controller allows the pendulum to reach the upright position from its natural state by swinging it up with minimum tracking error. Once the upright position is reached, a regulator is implemented to operate over the linearized model around the operating point (i.e., upright position). Simulation results present both, the tracking of the angular trajectory and the controller behavior during small perturbations. It is shown that the control signal and the wheel speed remain within their boundaries. Although the control signal saturates, a tracking error less than 0.22 radians is observed.

Keywords

• Reaction wheel pendulum
• sector nonlinearity
• Takagi-Sugeno fuzzy control
• parallel distributed compensation
• trajectory tracking