Modeling and sliding mode control of flexible structure

Modeling of flexible structure and its control using sliding modes is investigated in this paper. A system of Flexible Inverted Pendulum(FIP) with bobmass on its tip, cantilevered vertically on a cart, is taken as a representative case of flexible structures. Mechanical modeling of this system is proposed using a new approach. The pendulum is assumed to be made up of chain of multiple small sub-links. Torsional springs of different stiffnesses are then assumed at each joint (between successive links) in its structure. The flexibility of pendulum is accounted by specifying definite stiffness value to each torsional spring, in decreasing order from bottom to top. Complete mathematical model is derived considering multibody mechanical system using energy approach. The proposed model is validated with experimental data obtained from actual plant behavior. Sliding Mode Control (SMC) is then developed for this system. A stable sliding surface is designed. Controller is then synthesized using Gao´s power rate reaching law. Performance of this controller is tested in simulation. Robustness of this sliding mode controlled system, against disturbances, is confirmed from simulation results.