Nonlinear Modeling and Control of 3-DOF Gyroscope Actuated Furuta Pendulum by Takagi-Sugeno Fuzzy Systems
Johannes Brunner, Nis Keilhauer, Vincent Vellguth, H. Brandtstädter, Horst Schulte · KIT Scientific Publishing eBooks · 2023
This paper presents the derivation of the equations of motion of a 3-DOF gyroscope with a pendulum attachment through the Euler-Lagrange approach, followed by a conversion into a Takagi-Sugeno Fuzzy Model. First, suitable coordinate frames and generalized coordinates are defined, followed by the definition of the kinetic energy of each body frame of the gyroscope. Next, the kinetic and potential energy of the pendulum attachment is described. The derived equations of motion are then validated by simulation and compared to the behavior of a testbed system (see Figure 1). The conversion to the Takagi-Sugeno fuzzy model is done by a weighted combination of locally valid linear models. A set of adequate premise variables and membership functions represent the nonlinear system. Finally, a controller synthesis through parallel distributed compensation and LMIs satisfying local quadratic Lyapunov functions is conducted and validated by simulation.