Two-step modeling method of inverted pendulum considering Coulomb friction based on Lagrange equation and its model predictive control

Abstract

To overcome the shortcomings associated with modeling difficulty from Coulomb friction and low accuracy from traditional methods, this paper proposes a superposition modeling method based on Lagrange equation for the inverted pendulum. After establishing the high nonlinear dynamic model, the model predictive control (MPC) is adopted for the inverted pendulum control and the satisfactory results are obtained. Furthermore, those studies--the comparisons of simulation and experiment from literature, the statistics of averaged computation time, the responses of no Coulomb friction, the responses of having constraints of maximum control force, and the influences of MPC parameters--are respectively carried out. Compared with experimental results from the literature, simulation results are effective and reliable, which further explain the fluctuation phenomenon caused by Coulomb friction after entering the stable state and thereby illustrate the higher accuracy of the model proposed in this paper. Moreover, simulation results demonstrate that MPC has obvious advantages of dealing with highly nonlinear system with constraints and hence has a high value of practical application, and also reveal that the control and prediction horizon risen properly can improve the response performance.