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

ABSTRACT

Parameters of friction model identified for a specific control system development are not constants. They vary over time and have a significant effect on the control system stability. Although much research has been devoted to the stability analysis under parametric uncertainty, less attention has been paid to incorporating a realistic friction model into their analysis. After reviewing the common friction models for controller design, a modified LuGre friction model is selected to carry out the stability analysis in this study. Two parameters of the LuGre model, namely σ₀ and σ₁, are critical to the demonstration of dynamic friction features, yet the identification of which is difficult to carry out, resulting in a high level of uncertainties in their values. Aiming at uncovering the effect of the σ₀ and σ₁ variations on the control system stability, a servomechanism with modified LuGre friction model is investigated. Two set-point position controllers are synthesised based on the servomechanism model to form two case studies. Through Lyapunov exponents, it is clear that the variation of σ₀ and σ₁ has an obvious effect on the stabiltiy of the studied systems and should not be overlooked in the design phase.

KEYWORDS:

• Stability analysis
• parametric uncertainties
• LuGre friction model
• Lyapunov exponents

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Natural Sciences and Engineering Research Council of Canada [grant number IRCPJ 441724-11].