Differentiable Friction Model Research Articles

Adaptive Prescribed Performance Motion Control of Servo Mechanisms with Friction Compensation

This paper proposes an adaptive control for a class of nonlinear mechanisms with guaranteed transient and steady-state performance. A performance function characterizing the convergence rate, maximum overshoot, and steady-state error is used for the output error transformation, such that stabilizing the transformed system is sufficient to achieve the tracking control of the original system with a priori prescribed performance. A continuously differentiable friction model is adopted to account for the friction nonlinearities, for which primary model parameters are online updated. A novel high-order neural network with only a scalar weight is developed to approximate unknown nonlinearities and to dramatically diminish the computational costs. Comparative experiments on a turntable servo system are included to verify the reliability and effectiveness.

Adaptive Robust Motion Control of Direct-Drive DC Motors with Continuous Friction Compensation

Uncertainties including the structured and unstructured, especially the nonlinear frictions, always exist in physical servo systems and degrade their tracking accuracy. In this paper, a practical method named adaptive robust controller (ARC) is synthesized with a continuous differentiable friction model for high accuracy motion control of a direct-drive dc motor, which results in a continuous control input and thus is more suitable for application. To further reduce the noise sensitivity and improve the tracking accuracy, a desired compensation version of the proposed adaptive robust controller is also developed and its stability is guaranteed by a proper robust law. The proposed controllers not only account for the structured uncertainties (e.g., parametric uncertainties) but also for the unstructured uncertainties (e.g., unconsidered nonlinear frictions). Furthermore, the controllers theoretically guarantee a prescribed output tracking transient performance and final tracking accuracy in both structured and unstructured uncertainties while achieving asymptotic output tracking in the absence of unstructured uncertainties, which is very important for high accuracy control of motion systems. Extensive comparative experimental results are obtained to verify the high-performance nature of the proposed control strategies.

Lyapunov-Based Tracking Control in the Presence of Uncertain Nonlinear Parameterizable Friction

Modeling and compensation for friction effects has been a topic of considerable mainstream interest in motion control research. This interest is spawned from the fact that modeling nonlinear friction effects is a theoretically challenging problem, and compensating for the effects of friction in a controller has practical ramifications. If the friction effects in the system can be accurately modeled, there is an improved potential to design controllers that can cancel the effects; whereas, excessive steady-state tracking errors, oscillations, and limit cycles can result from controllers that do not accurately compensate for friction. A tracking controller is developed in this paper for a general Euler-Lagrange system that contains a new continuously differentiable friction model with uncertain nonlinear parameterizable terms. To achieve the semi-global asymptotic tracking result, a recently developed integral feedback compensation strategy is used to identify the friction effects online, assuming exact model knowledge of the remaining dynamics. A Lyapunov-based stability analysis is provided to conclude the tracking and friction identification results. Experimental results illustrate the tracking and friction identification performance of the developed controller.