Asymmetric and chaotic responses of dry friction oscillators with different static and kinetic coefficients of friction

The responses of a simple harmonically excited dry friction oscillator are analysed in the case when the coefficients of static and kinetic coefficients of friction are different. One- and two-parameter bifurcation curves are determined at suitable parameters by continuation method and the largest Lyapunov exponents of the obtained solutions are estimated. It is shown that chaotic solutions can occur in broad parameter domains—even at realistic friction parameters—that are tightly enclosed by well-defined two-parameter bifurcation curves. The performed analysis also reveals that chaotic trajectories are bifurcating from special asymmetric solutions. To check the robustness of the qualitative results, characteristic bifurcation branches of two slightly modified oscillators are also determined: one with a higher harmonic in the excitation, and another one where Coulomb friction is exchanged by a corresponding LuGre friction model. The qualitative agreement of the diagrams supports the validity of the results.

Research on Adaptive Friction Compensation of Digital Hydraulic Cylinder Based on LuGre Friction Model

This paper aims to eliminate nonlinear friction from the performance of the digital hydraulic cylinder to enable it to have good adaptive ability. First, a mathematical model of a digital hydraulic cylinder based on the LuGre friction model was established, and then a dual-observer structure was designed to estimate the unobservable state variables in the friction model. The Lyapunov method is used to prove the global asymptotic stability of the closed-loop system using the adaptive friction compensation method. Finally, Simulink is used to simulate the system performance. The simulation results indicate that the addition of adaptive friction compensation control can effectively reduce system static error, suppress system limit loop oscillation, “position decapitation,” “speed dead zone,” and low-speed creep phenomena, and improve the overall performance of the digital hydraulic cylinder. The control method has practical application value for improving the performance index of the digital hydraulic cylinder.

Valve Deadzone/Backlash Compensation for Lifting Motion Control of Hydraulic Manipulators

In this paper, a novel nonlinear model and high-precision lifting motion control method of a hydraulic manipulator driven by a proportional valve are presented, with consideration of severe system nonlinearities, various uncertainties as well as valve backlash/deadzone input nonlinearities. To accomplish this mission, based on the independent valve orifice throttling process, a new comprehensive pressure-flow model is proposed to uniformly indicate both the backlash and deadzone effects on the flow characteristics. Furthermore, in the manipulator lifting dynamics, considering mechanism nonlinearity and utilizing a smooth LuGre friction model to describe the friction dynamics, a nonlinear state-space mathematical model of hydraulic manipulation system is then established. To suppress the adverse effects of severe nonlinearities and uncertainties in the system, a high precision adaptive robust control method is proposed via backstepping, in which a projection-type adaptive law in combination with a robust feedback term is conducted to attenuate various uncertainties and disturbances. Lyapunov stability analysis demonstrates that the proposed control scheme can acquire transient and steady-state close-loop stability, and the excellent tracking performance of the designed control law is verified by comparative simulation results.

Investigation of longitudinal friction characteristics of an omnidirectional wheel via LuGre model

SUMMARY In recent years, omnidirectional wheels have found more applications in the design of automated guided vehicles (AGV). In this work, LuGre friction model is used for an omnidirectional wheel. A test setup that includes a single omnidirectional wheel is designed and constructed to identify the model parameters. With the help of the constructed test setup, the longitudinal friction characteristic of the omnidirectional wheel is obtained, and the model is verified via validation tests. In addition, for the first time, the effect of lateral frictional force on longitudinal motion is examined for an omnidirectional wheel through experiments.