Identifying Friction in a Nonlinear Chaotic System Using a Universal Adaptive Stabilizer

TL;DR

This paper introduces a universal adaptive stabilizer-based method for accurately identifying friction parameters in highly nonlinear and chaotic systems like the Furuta pendulum, with significant reductions in computational time and high accuracy.

Contribution

The paper presents a novel friction parameter identification routine using a high-gain UAS observer, effective for nonlinear chaotic systems, with validated simulation and experimental results.

Findings

Converges to exact parameter values in simulation.

Achieves around 85% goodness of fit in experiments.

Reduces estimation time by over 99% compared to traditional methods.

Abstract

This paper proposes a friction model parameter identification routine that can work with highly nonlinear and chaotic systems. The chosen system for this study is a passively-actuated tilted Furuta pendulum, which is known to have a highly non linear and coupled model. The pendulum is tilted to ensure the existence of a stable equilibrium configuration for all its degrees of freedom, and the link weights are the only external forces applied to the system. A nonlinear analytical model of the pendulum is derived, and a continuous friction model considering static friction, dynamic friction, viscous friction, and the stribeck effect is selected from the literature. A high-gain Universal Adaptive Stabilizer (UAS) observer is designed to identify friction model parameters using joint angle measurements. The methodology is tested in simulation and validated on an experimental setup. Despite the high nonlinearity of the system, the methodology is proven to converge to the exact parameter values, in simulation, and to yield qualitative parameter magnitudes in experiments where the goodness of fit was around 85\% on average. The discrepancy between the simulation and the experimental results is attributed to the limitations of the friction model. The main advantage of the proposed method is the significant reduction in computational needs and the time required relative to conventional optimization-based identification routines. The proposed approach yielded more than 99\% reduction in the estimation time while being considerably more accurate than the optimization approach in every test performed. One more advantage is that the approach can be easily adapted to fit other models to experimental data.