Adaptive Robust Control of Servo Mechanisms With Compensation for Nonlinearly Parameterized Dynamic Friction

In this brief, an adaptive robust control (ARC) scheme with compensation for nonlinearly parameterized dynamic friction is proposed. Both parametric uncertainties and external disturbances are considered in this method. Our method takes advantage of a Lipschitzian property with respect to the parameters of nonlinearly parameterized model in the ARC design. The outcome is that the number of parameters to be updated in the ARC is equal to the number of unknown parameters in the plant, and thus the resulting control algorithm is convenient to be implemented. We have proved theoretically that the proposed method can not only guarantee desired transient performance for the system, but also make the magnitude of steady-state tracking error to be arbitrarily small in the presence of parametric uncertainties only. Experimental results are given to demonstrate the effectiveness of the proposed ARC scheme.

I. Introduction

In servo mechanisms, friction may cause many undesired phenomena such as large tracking errors, limit cycles, and stick-slip motion. Accordingly, it is important to compensate for the effects of friction, when high performance is needed for servo mechanisms. Many methods have been proposed to solve the friction compensation problem [1], [2]. Some control schemes (e.g., in [3], [4]) are based on an accurate offline friction estimation. The main drawback of this kind of methods is that, their design procedures need accurate models of friction, which are difficult to acquire. To overcome this problem, adaptive friction compensation techniques based on different friction models have been proposed in the literature [5]–[7]. In most of these results, friction is modeled as a static map between velocity and friction. However, in applications with high precision positioning and with low velocity tracking, friction compensation based on static models is not always satisfactory.