Motion stabilization in the presence of friction and backlash: a hybrid system approach

In this paper a hybrid system approach is considered to deal with backlash and friction induced nonlinearities in mechanical control systems. To describe the low velocity frictional behaviour a linearized friction model is proposed. The novelty of this study is that based on the introduced friction model, the stability theorems developed for hybrid systems can directly be applied for controller design of mechanical systems in the presence of Stribeck friction and backlash. During the controller design it is assumed that the size of the backlash gap is unknown and the load side position and velocity cannot be measured. For motion control an LQ controller is applied. A condition is formulated for the control law parameters to guarantee the asymptotic stability of the control system. Simulation measurements were performed to confirm the theoretical results

Nonlinear Modeling and Verification of a Heaving Point Absorber for Wave Energy Conversion

Although the heaving Point Absorber (PA) concept is well known in wave energy conversion research, few studies focus on appropriate modelling of non-linear fluid viscous and mechanical friction dynamics. Even though these concepts are known to have non-linear effects on the hydrodynamic system, most research studies consider linearity as a starting point and in so doing have a weak approach to modelling the true dynamic behaviour, particularly close to resonance. The sole use of linear modelling leads to limited ability to develop control strategies capable of true power capture optimisation and suitable device operation. Based on a 1/50 scale cylindrical heaving PA, this research focuses on a strategy for hydrodynamic model development and experimental verification. In this study, nonlinear dynamics are considered, including the lumped effect of the fluid viscous and mechanical friction forces. The excellent correspondence between the derived non-linear model and wave tank tested PA behaviours provides a strong background for wave energy tuning and control system design

Dynamic and tribological study of a planetary gearbox with local nonlinearities

A planetary gearbox model comprising five spur gears (sun, ring and three planets) and the carrier has been developed and analysed. The influence of gear teeth backlash and friction during mixed regime of lubrication has been taken into consideration. Greenwood and Tripp model is employed, while viscous friction is calculated analytically using the functions of Evans and Johnson. A combined tribodynamics modeling approach has been implemented and modal analysis is performed in order to predict the coupled mechanism of tribological and dynamic behavior, subjected to backlash and excited at the gear meshing frequency. The software used for the simulations is ADAMS MSc (Student Edition), where the model variables (concerning gear geometry and forcing functions) have been added in a parametric way. The results showed that small variations of the dynamic transmission error affect notably the viscous friction through changing the contact load between the engaged teeth pairs. Also, higher values of the Stribeck oil parameter due to higher film thickness or lower surface roughness in the mixed lubrication regime lead to reduction of the boundary friction, whereas a reduction of the total generated friction occurs when increasing the angular velocity of the input gear body (due to higher film thickness and smaller asperity interactions). The above lead to reduced power loss of the mechanism. Finally, a characterization of the system dynamics is presented using the calculated eigenvalues and eigenmodes of the corresponding linearized system. Potential interactions with the gear meshing frequency of the system are also examined

Velocity dependence of joint friction in robotic manipulators with gear transmissions

This paper analyses the problem of modelling joint friction in robotic manipulators with gear transmissions at joint velocities varying from close to zero until their maximum appearing values. It is shown that commonly used friction models that incorporate Coulomb, (linear) viscous and Stribeck components are inadequate to describe the friction behaviour for the full velocity range. A new friction model is proposed that relies on insights from tribological models. The basic friction model of two lubricated discs in rolling-sliding contact is used to analyse viscous friction and friction caused by asperity contacts inside gears and roller bearings of robot joint transmissions. The analysis shows different viscous friction behaviour for gears and pre-stressed bearings. The sub-models describing the viscous friction and the friction due to the asperity contacts are combined into two friction models; one for gears and one for the pre-stressed roller bearings. In this way, a new friction model [1] is developed that accurately describes the friction behaviour in the sliding regime with a minimal and physically sound parametrisation. The model is linear in the parameters that are temperature dependent, which allows to estimate these parameters during the inertia parameter identification experiments. The model, in which the Coulomb friction effect has disappeared, has the same number of parameters as the commonly used Stribeck model [2]. The model parameters are identified experimentally on a St ¨aubli RX90 industrial robot

Implementation of a friction estimation and compensation technique

This thesis reports implementation of a friction estimation and compensation technique on a special laboratory apparatus. In this work, experimental results are reported for the Coulomb friction observer. The Coulomb friction observer estimates the total friction present in a system, assuming it to be a constant function of velocity. An extension of the observer, utilizing a coupled velocity observer, is used when velocity is not measurable. A modification to the velocity observer is also implemented. Experimental results show a remarkable improvement in the friction estimates which are also compared to the actual friction measurements. The estimates are qualitatively similar to the actual friction, demonstrating the ability of the modified design to track a non-constant friction. Finally, extremely low velocities are experimentally obtained by using the friction compensation technique mentioned above, further proving that accurate control at low velocities is possible by friction estimation and compensation

Linear motor motion control using a learning feedforward controller

The design and realization of an online learning motion controller for a linear motor is presented, and its usefulness is evaluated. The controller consists of two components: (1) a model-based feedback component, and (2) a learning feedforward component. The feedback component is designed on the basis of a simple second-order linear model, which is known to have structural errors. In the design, an emphasis is placed on robustness. The learning feedforward component is a neural-network-based controller, comprised of a one-hidden-layer structure with second-order B-spline basis functions. Simulations and experimental evaluations show that, with little effort, a high-performance motion system can be obtained with this approach