Academic literature on the topic 'LuGre friction model'

Friction compensation is challenging but imperative for control engineers. For high-performance engineering systems, a friction-model-based controller is typically required to accommodate the nonlinearities arisen from the friction model employed. It is well known that the parameters of the friction model used in the friction compensation are nearly impossible to be accurately identified. Therefore, the objective of this research is to study the effect of these parametric uncertainties on the stability of a set-point position control system. With the above goal in mind, a variety of aspects are investigated in this work. Firstly, several common friction features and friction models are surveyed to provide background knowledge which helps select the friction model with the highest accuracy for our study. Secondly, an experimental setup is proposed and fabricated to validate the levels of accuracy given by the candidate friction models. The comparisons between the numerical and experimental results confirm that the LuGre friction model is the best approximation of the observed friction behaviours among all models selected. Moreover, a series of profound discussions addressing the relation between the candidate models’ structures and their numerical friction feature predictions are provided and followed by a summary table that recapitulates the properties of the candidate friction models. Last but not least, the state space models of the proposed setup formulated by the improved version of the LuGre model and the two controllers of interest, namely input-output linearization controller and nominal characteristic trajectory following (NCTF) controller, are derived for the stability analysis under the parametric uncertainties. Two parameters in the friction model used, σ_0 and σ_1, are perturbed for the stability analysis in which the results applying the concept of Lyapunov exponents (LEs) clearly illustrate the significant effect of the varying σ_0 and σ_1 values on the system stability. The effect of parametric uncertainties can depend quite significantly on the incorporated controller, and the stability results obtained here are applicable to the design and analysis of other systems that are inherently similar to our setup. The stability analysis conducted is this work is recommended for other control systems to avoid unwanted qualitative behaviours under parametric perturbations.<br>October 2016

<p>All mechanical systems with moving parts are affected by friction, including industrial robots. Being able to design an accurate friction model would further increase the performance of todays robots. Friction is a complex dynamic phenomena that is constantly changing depending on the state and environment of the robot. It is therefore beneficial to update the parameters of the friction model online. An estimate of the friction will be made using the feedback control signal with the help of a feedforward control scheme in a two axis simulation setup. The friction estimate is then used for an offline identification of three friction model parameters in a static Lugre friction model. Improvements on the identification will be done by introducing some shut-off rules that will improve the estimate. The normalized least mean square method (NLMS) will then be used to update the parameters online. A simulation of friction compensation with a fixed friction model, and with an adaptive friction model will be studied. The method will also be simulated using experimental data taken from a real industrial robot.</p>

Accurate characterization and evaluation of tire/pavement friction is critical in assuring runway and highway safety. Historically, Pavement Friction Measurement Devices (PFMDs) employing different measuring mechanisms have been used to evaluate tire/pavement friction. They yield significantly disparate friction coefficients under the same contact conditions. Currently, an empirically developed data harmonization method based on a reference device (Dynamic Friction Tester (DFT)) is used in an attempt to overcome the disparities between the measurements using various different PFMDs. However, this method, which has been standardized by the American Society for Testing and Materials (ASTM E1960), has been criticized for its inconsistency by researchers and runway/highway operations personnel. The objective of this dissertation research was to develop a systematic and physically intuitive harmonization method for PFMDs that will improve the comparability of their data. As a foundation for such a harmonization, the LuGre tire model that employs physically meaningful parameters to represent the main attributes of tire/pavement friction was evaluated and validated. Measurements of tire/pavement friction by three widely used PFMDs; Locked Wheel Skid Trailer (LWST), Runway Friction Tester (RFT) and DFT, were accurately predicted using nonlinear optimization of LuGre model parameters. The LuGre model was found to be superior compared to the model used in the current ASTM E1960 standardization procedure for predicting PFMD measurements. A sensitivity analysis was performed to identify the relative significance of the LuGre model parameters in characterizing tire/pavement friction, and to study the effects of variation of those parameters on predicted frictional behavior. A set of laboratory tire experiments was designed and performed to validate the physical significance of LuGre tire model parameters and to study how they behave under typical load, inflation pressure, excitation frequency, and amplitude conditions. An empirical method was developed to accommodate the effects of water film thickness on tire/pavement friction in the LuGre model. The results of the sensitivity analysis and the experiments to directly estimate the model parameters were used to identify and quantify appropriate modifications to the measurement mechanisms of PFMDs that can be introduced to improve the comparability of their results. Friction experiments performed after introducing such modifications to the LWST showed an average reduction of 20% in the deviations between the results of LWST and RFT measurements. The research carried out in this dissertation is significant because it: (i) identified the deficiencies in the current method for harmonizing PFMD measurements and the underlying reasons for these deficiencies, (ii) emphasized the importance of a standardization approach that regulates the physical condition of PFMDs, in order to achieve universal comparability of tire/pavement friction measurements, (iii) validated that the LuGre tire model is a tire/pavement friction model capable of facilitating a better standardization approach, and, (iv) initialized the development of a physically meaningful harmonization procedure for PFMDs.

<p>The objective of this thesis is to develop a model that represents the dynamics of a hydraulically operated forestry crane. The model was derived with the traditional Euler-Lagrange formalism and considers the crane mechanics, three double-acting hydraulic cylinders and the valve control unit. On the basis of the derived model we reproduced the entire crane model in MATLAB in order to run simulations herewith. This gave us the possibility to do parameter changes for further studies of the crane in motion.</p><p>Another major goal within the thesis work was to estimate cylinder friction of the hydraulic actuators. We built up a test rig and used double-acting cylinders for determing their frictional behaviour. For this, we ran open-loop experiments in order to create velocity-friction maps that represented the static friction force of the cylinders. In this concern, we varied system pressure and cylinder load to study their influence on the friction force. By means of the derived static friction maps we approached the cylinder’s dynamic friction behaviour and applied both step and ramp control inputs to examine the spring-damping characteristics of the microspoic bristles in the contacting area. The dynamic friction experiments have been exerted in the fashion of the LuGre model. As a result we acquired different nominal friction parameters that we necessarily used to develope adequate friction models.</p><p>A third objective of this thesis was to establish a crane-tip control. Instead of a traditional control, providing a direct relationship between joystick input and cylinder extension, the focus was to build up a control for the end-effector’s trajectory in a two-dimensional frame. This could be achieved by using inverse kinematics in order to determine the required joint angles that corresponded to the desired position of the crane-tip.</p><p>The work also contains a CD including all developed MATLAB models that have been written within this project.</p>

Este trabalho discute o problema do controle preciso do seguimento de trajetórias de um servoposicionador pneumático. Um modelo matemático para o servoposicionador pneumático é apresentado, com atenção especial sendo dada à modelagem dos efeitos do atrito. Para a representação desses efeitos, é proposta uma modificação da estrutura matemática de um modelo de atrito amplamente utilizado no contexto dos algoritmos de controle em tempo real de servomecanismos (o modelo LuGre). A validade da aproximação proposta é justificada por meio de argumentos tanto analíticos como baseados em simulações. Com base no modelo para o atrito resultante da modificação proposta, apresenta-se um novo algoritmo de controle para o servoposicionador pneumático. Esse algoritmo é desenvolvido de acordo com a metodologia do controle em cascata, associada à técnica do controle a estrutura variável, sendo dotado de um esquema de compensação adaptativa dos efeitos do atrito e das forças externas aplicadas ao sistema. Uma análise de estabilidade completa é realizada para o sistema em malha fechada, onde são estabelecidas condições suficientes para que seja assegurada a convergência assintótica dos erros de seguimento para zero e dos parâmetros estimados a valores limitados. Também é apresentada uma análise de robustez do sistema controlado frente a incertezas nos parâmetros do modelo matemático do mesmo. O controlador proposto é avaliado por meio de testes por simulação e por aplicação a uma bancada experimental.<br>This work discusses the problem of the precise control of the trajectory tracking executed by a pneumatic positioning system. A mathematical model of the pneumatic positioning system is presented, with special emphasis given to the modeling of friction effects. For representing such effects, it is proposed a modification in the mathematical structure of a friction model that is widely employed in the context of the real-time control of servomechanisms (the LuGre model). The validity of the proposed approximation is justified by means of analytical arguments as well as simulation results. Based on the friction model that results from the proposed modification, a new control algorithm to be applied to the pneumatic positioning system is presented. Such algorithm is developed according to the cascade methodology, in association with the variable structure control technique and equipped with an adaptive compensation scheme of the effects of friction and external forces applied to the system. A complete stability analysis of the closed loop system is developed, and sufficient conditions are determined so that the asymptotic convergence of the tracking errors of the system to zero and of the estimated parameters to limited values is ensured. The robustness properties of the controlled system with respect to parametric uncertainties in its mathematical model are also analyzed. The performance of the controller is studied by means of simulation and experimental tests.

The objective of this study is to develop a high-fidelity physics-based flexible tire model that can be fully integrated into multibody dynamics computer algorithms for use in on-road and off-road vehicle dynamics simulation without ad-hoc co-simulation techniques. Despite the fact detailed finite element tire models using explicit finite element software have been widely utilized for structural design of tires by tire manufactures, it is recognized in the tire industry that existing state-of-the-art explicit finite element tire models are not capable of predicting the transient tire force characteristics accurately under severe vehicle maneuvering conditions due to the numerical instability that is essentially inevitable for explicit finite element procedures for severe loading scenarios and the lack of transient (dynamic) tire friction model suited for FE tire models. Furthermore, to integrate the deformable tire models into multibody full vehicle simulation, co-simulation technique could be an option for commercial software. However, there exist various challenges in co-simulation for the transient vehicle maneuvering simulation in terms of numerical stability and computational efficiency. The transient tire dynamics involves rapid changes in contact forces due to the abrupt braking and steering input, thus use of co-simulation requires very small step size to ensure the numerical stability and energy balance between two separate simulation using different solvers. In order to address these essential and challenging issues on the high-fidelity flexible tire model suited for multibody vehicle dynamics simulation, a physics-based tire model using the flexible multibody dynamics approach is proposed in this study. To this end, a continuum mechanics based shear deformable laminated composite shell element is developed based on the finite element absolute nodal coordinate formulation for modeling the complex fiber reinforced rubber tire structure. The assumed natural strain (ANS) and enhanced assumed strain (EAS) approaches are introduced for alleviating element lockings exhibited in the element. Use of the concept of the absolute nodal coordinate formulation leads to various advantages for tire dynamics simulation in that (1) constant mass matrix can be obtained for fully nonlinear dynamics simulation; (2) exact modeling of rigid body motion is ensured when strains are zero; and (3) non-incremental solution procedure utilized in the general multibody dynamics computer algorithm can be directly applied without specialized updating schemes for finite rotations. Using the proposed shear deformable laminated composite shell element, a physics-based flexible tire model is developed. To account for the transient tire friction characteristics including the friction-induced hysteresis that appears in severe maneuvering conditions, the distributed parameter LuGre tire friction model is integrated into the flexible tire model. To this end, the contact patch predicted by the structural tire model is discretized into small strips across the tire width, and then each strip is further discretized into small elements to convert the partial differential equations of the LuGre tire friction model to the set of first-order ordinary differential equations. By doing so, the structural deformation of the flexible tire model and the LuGre tire friction force model are dynamically coupled in the final form of the equations, and these equations are integrated simultaneously forward in time at every time step. Furthermore, a systematic and automated procedure for parameter identification of LuGre tire friction model is developed. Since several fitting parameters are introduced to account for the nonlinear friction characteristics, the correlation of the model parameters with physical quantities are not clear, making the parameter identification of the LuGre tire friction model difficult. In the procedure developed in this study, friction parameters in terms of slip-dependent friction characteristics and adhesion parameter are estimated separately, and then all the parameters are identified using the nonlinear least squares fitting. Furthermore, the modified friction characteristic curve function is proposed for wet road conditions, in which the linear decay in friction is exhibited in the large slip velocity range. It is shown that use of the proposed numerical procedure leads to an accurate prediction of the LuGre model parameters for measured tire force characteristics under various loading and speed conditions. Furthermore, the fundamental tire properties including the load-deflection curve, the contact patch lengths, contact pressure distributions, and natural frequencies are validated against the test data. Several numerical examples for hard braking and cornering simulation are presented to demonstrate capabilities of the physics-based flexible tire model developed in this study. Finally, the physics-based flexible tire model is further extended for application to off-road mobility simulation. To this end, a locking-free 9-node brick element with the curvature coordinates at the center node is developed and justified for use in modeling a continuum soil with the capped Drucker-Prager failure criterion. Multiplicative finite strain plasticity theory is utilized to consider the large soil deformation exhibited in the tire/soil interaction simulation. In order to identify soil parameters including cohesion and friction angle, the triaxial soil test is conducted. Using the soil parameters identified including the plastic hardening parameters by the compression soil test, the continuum soil model developed is validated against the test data. Use of the high-fidelity physics-based tire/soil simulation model in off-road mobility simulation, however, leads to a very large computational model to consider a wide area of terrains. Thus, the computational cost dramatically increases as the size of the soil model increases. To address this issue, the component soil model is proposed such that soil elements far behind the tire can be removed from the equations of motion sequentially, and then new soil elements are added to the portion that the tire is heading to. That is, the soil behavior only in the vicinity of the rolling tire is solved in order to reduce the overall model dimensionality associated with the finite element soil model. It is shown that use of the component soil model leads to a significant reduction in computational time while ensuring the accuracy, making the use of the physics-based deformable tire/soil simulation capability feasible in off-road mobility simulation.

Luge is an Olympic sport in which athletes ride feet-first on sleds down an ice-covered track. Competitors spring from the starting position and accelerate their sled by paddling with spiked gloves against the ice surface. Once the Luger leaves the starting section, their downhill motion is solely propelled by the effects of gravity. Athletes compete, one after the other, for the fastest time. Runs can differ by as little as a thousandth of a second, meaning that every minor sled adjustment, change of line choice, and shift of body position is critical. In the past, the sport of Luge has progressed through a series of steps involving trial and error, where changes to the sled and strategy rely more on intuition and race results, rather than in-depth, mathematical analysis. In an effort to try and improve track times for the US Olympic Luge team, a track and driver model is in development in order to simulate a sled going down the track. By doing this, the hope is to be able to pinpoint areas of possible improvement to the sled and see how adjustments can affect the optimum line down the track. A part of this model, which is the focus of the following paper, is the inclusion of an analysis to identify the frictional relationship between the ice surface and the steels of the sled. The model created of the ice-steel interaction was put in the form of a function file, which includes inputs of down force, ice temperature, sled velocity, and steel geometry. Creation of this model and completion of a set of parametric studies allowed for further understanding the interaction between the sled steels and ice surface, specifically applying to the sport of Luge. The model predicts for lower temperatures that at slower sled velocities the coefficient of friction is greater compared to faster sled velocities. This relationship inverts as the ice temperature moves closer to the melting temperature. A sharper steel edge radius was found to be beneficial in lowering the coefficient of friction at lower sled velocities. The sharp edge radius friction benefit decreases as the sled speed increases and is predicted to actually increase friction slightly compared to duller blades at greater velocities. A flat as possible rocker radius lowers friction at all sled velocities, as well as in banked turns where two contact patches are possible. On curves, the pressure on the steel is increased due to the effects of centripetal accelerations. A 1 g versus 5 g normal loading, experienced on the last turns of the track, increases the coefficient of friction on the blade, but also increases the allowable lateral force on the sled before side slip occurs. Understanding the relationships of these parameters, along with the information that may be gained from the driver model, may prove to be useful in choosing optimum sled characteristics and line choice.

碩士<br>國立交通大學<br>電控工程研究所<br>101<br>Micro-motion control in the 3C industry is operated in the relatively high-frequency range compared with traditional CNC processing. The control commands are difficult to precisely follow mainly because the motion command is relatively small and it passes through zero velocity frequently to cause the problem of friction. Traditional static friction compensation, which is obtained from a constant speed operation, is suitable only when the motion command is slowly-varying in a low frequency range. Experimental results indicate that the axis is nearly stop by applying linear controllers if the motion command is small. In this Thesis, the LuGre model is adopted and a practical and systematic approach to obtain the coefficients for the LuGre model is proposed. The DSP microcontroller TMS320F28335 is adopted for the AC servo driver of permanent synchronous motor (PMSM) in this study. All the static friction compensator, dynamic friction compensator, adaptive disturbance observer (DOB) are integrated and realized in this servo driver. By applying the present controller with the LuGre model, the bandwidth of the velocity loop is improved from 394Hz to 663.7Hz, and the position loop is improved from 9.5 Hz to 113.8 Hz, separately. The LuGre model has also been realized on DYNA 1007 CNC machine and results also show that the tracking error is improved 67.5% in RMS and the tracking peak error improvement is 72.0%.