Stability of controlled mechanical system with parametric uncertainties in a realistic friction model

• Main Author: Sun, Yun-Hsiang
• Other Authors: Wu, Christine Qiong (Mechanical Engineering) Sepehri, Nariman (Mechanical Engineering)
• Published: ASME 2016
• Subjects: Friction model comparison; Friction experimental setup design; Perturbation stability; LuGre friction model; Controlled mechanical system; Lyapunov exponents
• Online Access: http://hdl.handle.net/1993/31633

Friction compensation is challenging but imperative for control engineers. For high-performance engineering systems, a friction-model-based controller is typically required to accommodate the nonlinearities arisen from the friction model employed. It is well known that the parameters of the friction model used in the friction compensation are nearly impossible to be accurately identified. Therefore, the objective of this research is to study the effect of these parametric uncertainties on the stability of a set-point position control system. With the above goal in mind, a variety of aspects are investigated in this work. Firstly, several common friction features and friction models are surveyed to provide background knowledge which helps select the friction model with the highest accuracy for our study. Secondly, an experimental setup is proposed and fabricated to validate the levels of accuracy given by the candidate friction models. The comparisons between the numerical and experimental results confirm that the LuGre friction model is the best approximation of the observed friction behaviours among all models selected. Moreover, a series of profound discussions addressing the relation between the candidate models’ structures and their numerical friction feature predictions are provided and followed by a summary table that recapitulates the properties of the candidate friction models. Last but not least, the state space models of the proposed setup formulated by the improved version of the LuGre model and the two controllers of interest, namely input-output linearization controller and nominal characteristic trajectory following (NCTF) controller, are derived for the stability analysis under the parametric uncertainties. Two parameters in the friction model used, σ_0 and σ_1, are perturbed for the stability analysis in which the results applying the concept of Lyapunov exponents (LEs) clearly illustrate the significant effect of the varying σ_0 and σ_1 values on the system stability. The effect of parametric uncertainties can depend quite significantly on the incorporated controller, and the stability results obtained here are applicable to the design and analysis of other systems that are inherently similar to our setup. The stability analysis conducted is this work is recommended for other control systems to avoid unwanted qualitative behaviours under parametric perturbations. === October 2016