Friction compensation of double inverted pendulum on a cart using locally linear neuro-fuzzy model

Abstract

Double inverted pendulum on a cart (DIPC) is a highly nonlinear system. Due to its complex dynamics, it is widely used as a test-bed plant for the verification of newly designed controllers. In DIPC, two pendulums are kept upward by linear movements of cart. Because of this linear motions and frequent switching of velocity directions, another nonlinearity caused by friction becomes dominant around the equilibrium point. Friction introduces limit cycles to the system and results in a poor steady-state response. To eliminate these negative effects, the locally linear neuro-fuzzy (LLNF) approach is used to build an inverse model for friction compensation. This model is compared with multilayer perceptron network in order to demonstrate the better performance of LLNF. To stabilize DIPC, a common optimal controller is used, and despite its limited performance, experimental results show that the application of inverse modeling for friction compensation improves the steady-state response outstandingly.