Takagi–Sugeno Fuzzy Controller Design for an EV3 Ballbot Robotic System

In this paper, a Takagi–Sugeno Fuzzy Controller (TSFC) is proposed to control an EV3 Ballbot Robotic System (EV3BRS). The EV3BRS is a nonlinear underactuated robotic system having four generalized coordinates and two generalized torques. Such a robotic system may be seen as a system whose physical configuration has the form of an inverted pendulum mounted on a ball. In our work, the nonlinear model of the EV3BRS is linearized around different operation points near from the upright position of its body. The TSFC is then designed via Parallel Distributed Compensation (PDC) technique from the linearized models, where the Linear Matrix Inequalities (LMIs) approach is used to get the feedback gains for the local linear controllers, and whose performance is validated and contrasted with that from a Linear Quadratic Regulator (LQR) via numerical simulation.