International Journal of Control, Vol.91, No.4, 770-784, 2018
Stability analysis of a controlled mechanical system with parametric uncertainties in LuGre friction model
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 sigma(0) and sigma(1), 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 sigma(0) and sigma(1) 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 sigma(0) and sigma(1) has an obvious effect on the stabiltiy of the studied systems and should not be overlooked in the design phase.