Multibody dynamic modeling and control of a flexible inverted pendulum

Effective control of flexible systems is a challenge in the design and implementation of control strategies. In this study, a systematic approach in the framework of multibody dynamic modeling was developed in order to control and stabilize a flexible inverted pendulum. In this approach, the dynamic behavior of the flexible inverted pendulum was replicated by an equivalent multibody system of rigid segments with rotational spring connections. Thus, it would be possible to derive an approximate nonlinear dynamic state space model for the flexible inverted pendulum and design a model-based control system. The state space model of the equivalent system was derived using Lagrange's equations, and the control system was designed using a linear-quadratic regulator along with a Kalman filter state observer. The dynamic behavior of the flexible inverted pendulum was simulated using the Simscape tools. Results of numerical simulations signify that the designed control system can effectively control the states of the flexible inverted pendulum. Moreover, increasing the number of rigid bodies enhances the effective flexibility of the equivalent multibody system and consequently improves the control performance.