Nonlinear Friction Research Articles

Friction Parameters Dynamic Change and Compensation for a Novel Dual-Drive Micro-Feeding System

This paper introduces a novel dual-drive micro-feeding system (DDMS) to obtain precise micro-feed synthetic motion by rotating both the screw and the nut, which eliminates the effects of nonlinear friction at low micro-feeding speeds and has good resistance to external disturbances. For the DDMS system, firstly, the frictional force of the screw–ball–nut contact surface is analyzed, and the dynamic system model based on the unique frictional coupling model is established for the DDMS. Secondly, a velocity squared term is added to the Stribeck model to characterize the influence of the frictional coupling on the system. The correctness of the modified model is verified through experiments and frictional parameters identification by combining with the genetic algorithm (GA). The dynamic trend of the frictional parameters with different speed combinations is studied, and the method of fitting parameters using the modified Stribeck model is proposed. Finally, the DDMS three closed-loop error compensation model and the proportional derivative position controller with the friction feedforward compensator are put forward to realize the accurate position-tracking function. Experiment results show that the method reduces the average tracking error by about 60% compared to the conventional PD controller.

Compound flooding in convergent estuaries: insights from an analytical model

Abstract. We investigate here the effects of geometric properties (channel depth and cross-sectional convergence length), storm surge characteristics, friction, and river flow on the spatial and temporal variability of compound flooding along an idealized, meso-tidal coastal-plain estuary. An analytical model is developed that includes exponentially convergent geometry, tidal forcing, constant river flow, and a representation of storm surge as a combination of two sinusoidal waves. Nonlinear bed friction is treated using Chebyshev polynomials and trigonometric functions, and a multi-segment approach is used to increase accuracy. Model results show that river discharge increases the damping of surge amplitudes in an estuary, while increasing channel depth has the opposite effect. Sensitivity studies indicate that the impact of river flow on peak water level decreases as channel depth increases, while the influence of tide and surge increases in the landward portion of an estuary. Moreover, model results show less surge damping in deeper configurations and even amplification in some cases, while increased convergence length scale increases damping of surge waves with periods of 12–72 h. For every modeled scenario, there is a point where river discharge effects on water level outweigh tide/surge effects. As a channel is deepened, this cross-over point moves progressively upstream. Thus, channel deepening may alter flood risk spatially along an estuary and reduce the length of a river estuary, within which fluvial flooding is dominant.

Observer-Based Backstepping Adaptive Force Control of Electro-Mechanical Actuator with Improved LuGre Friction Model

A dynamic load simulator, which can reproduce on-ground aerodynamic hinge moment of control surface, is an essential rig for the performance and stability test of an aircraft actuation system. In this paper, an observer-based backstepping adaptive control (OBAC) strategy with an improved friction model is proposed to deal with the force tracking problem of an electro-mechanical actuator under the influence of nonlinear friction and lumped disturbances. First, The LuGre friction model is improved by introducing the load effect of electrical linear load simulator (ELLS), and both dynamic and static parameters are identified with experimental data. Then, the ELLS system is divided into a loading subsystem and actuation subsystem for backstepping controller deign. The estimation of the position disturbance is obtained using an extended state observer and used for feedforward compensation for the loading subsystem. To reject the disturbance of friction parameter uncertainties for actuation subsystem, a friction scale factor with a reasonable adaptive updating law is introduced during the friction compensation process. Finally, the stability of the whole closed-loop system is demonstrated using a Lyapunov-based method, and experiments are performed to validate the effectiveness of the developed algorithm.

An accurate identification method based on double weighting for inertial parameters of robot payloads

AbstractThe inertial parameters of payloads attached to the end effector of robots benefit to several robotics applications, such as the model-based control, the task optimization, and so on. These applications require the accurate estimation of the inertial parameters. In the existing payload estimation approaches, however, the data weighting technique, which can reduce the adverse effects of outliers and significantly improve the final results, has not been applied yet. In this article, an accurate identification method based on double weighting for inertial parameters of robot payloads is proposed. In order to obtain the weighting matrices, a modified dynamic parameter identification method with two loops is firstly proposed. Then, based on the identified results of dynamic parameters, a payload identification model based on double weighting is constructed. In addition, the variations of both nonlinear friction parameters and linear friction parameters caused by the payload are considered in this model. Finally, experimental comparisons between our method and another four methods are conducted. The results confirm that our method shows the best performance, especially on improving the identification accuracy of mass and center of mass of the payload.

A Review of Key Technologies for Friction Nonlinearity in an Electro-Hydraulic Servo System

In a high-precision servo system, the nonlinear friction link is the key factor affecting the system performance. Reasonable solving of the friction link in servo systems has become a focus of current research. This paper summarizes the friction nonlinearity that affects the control performance of servo systems. First, the characteristics of friction are summarized, and the advantages and disadvantages of typical friction models in recent years are analyzed. Subsequently, existing friction model parameter identification methods are introduced and evaluated. On this basis, the development level of the friction nonlinear control strategy is analyzed from three aspects: friction model-based control, friction model-free control, and compound control. Finally, the objective advantages and disadvantages of the existing technology are summarized, and the future development direction of the friction model and selection reference for the nonlinear friction control strategy are comprehensively discussed.

Modeling and analysis of nonlinear axial friction forces of tripod joints considering roughness characteristics of contact pairs

The nonlinear axial friction force (NAFF) induced by contact and friction between components of tripod joints constitutes an important dynamic characteristic of drive-shaft systems, which will lead to deterioration of the NVH (noise, vibration and harshness) performance of the vehicle. Based on the fractal theory, this paper proposes a novel modeling and analysis method for accurate estimation of NAFF considering micro contact and friction characteristics of contact pairs. An analytical model is developed for estimating the NAFF of tripod joints considering micro contact and friction characteristics of contact pairs. In the process of modeling, a modified distribution function is proposed to describe distributions of contact asperities between the curved surfaces to describe the contact and friction states between the rollers and the tracks inside tripod joints more accurately. The developed analytical model suggests that NAFF is related to the fractal parameters, the material parameters, the operating conditions and the distribution of asperities. The effectiveness of the analytical model is demonstrated by comparing the model-predicted NAFF with the measured data. Based on the developed model of NAFF, the influences of important input parameters on the magnitude of NAFF are qualitatively analyzed. Subsequently, Sobol' global sensitivity analysis method is used to further investigate the influences of important input parameters on the magnitude of NAFF. The results show that the proposed modeling and analysis method for estimating NAFF are essential to characterize relationships among NAFF and fractal parameters, material properties and distribution of asperities from a micro level, which could facilitate design optimization of the tripod joints.

Neural network robust control of a 3‐DOF hydraulic manipulator with asymptotic tracking

AbstractMultiaxial hydraulic manipulators are complicated systems with highly nonlinear dynamics and various modeling uncertainties, which hinders the development of high‐performance controller. In this paper, a neural network feedforward with a robust integral of the sign of the error (RISE) feedback is proposed for high precise tracking control of hydraulic manipulator systems. The established nonlinear model takes three‐axis dynamic coupling, hydraulic actuator dynamics, and nonlinear friction effects into consideration. A radial basis function neural network (RBFNN) is synthesized to approximate the uncertain system dynamics and external disturbance, which can greatly reduce the dependence on accurate system model. In addition, a continuous RISE feedback law is judiciously integrated to deal with the residual unknown dynamics. Since the major unknown dynamics can be estimated by the RBFNN and then compensated in the feedforward design, the high‐gain feedback issue in RISE feedback control will be avoided. The proposed RISE‐based neural network robust controller theoretically guarantees an excellent semi‐global asymptotic stability. Comparative simulation is performed on a 3‐DOF hydraulic manipulator, and the obtained results verify the effectiveness of the proposed controller.

The Use of Deep Learning Model for Effect Analysis of Conventional Friction Power Confinement.

Nonlinear friction could affect the high-precision motion system, resulting in poor tracking accuracy in the end. This is due to the fact that the Lugre friction model's parameter identification process comprises both static and dynamic parameter identification. The convolutional neural network (CNN) model is used in this study to create the friction identification system. We suggest a hybrid methodology that combines the CNN method and the classic least-squares technique. The convolutional layer (CONV), which is defined by a convolutional kernel, analyzes and extracts features from an input image. In terms of accuracy and convergence, the results reveal that the upgraded CNN friction model outperforms the original CNN friction model. You may successfully reduce the influence of friction on your system while improving its performance by applying the feedforward correction.

Dynamic modeling and control for dual-flexible servo system considering two-dimensional deformation based on neural network compensation

A variable-length dual-flexible servo system is a complex nonlinear system that consists of a servo motor, a flexible joint, and a variable-length flexible load. In order to describe the mechanical behavior of the servo system more accurately, the two-dimensional (2D) deformation of flexible load needs to be considered. The coupled nonlinear terms, friction torque, and time variation of parameters in the dynamic equations constitute the uncertain part of the servo system. These mentioned factors will cause fluctuations in the flexible load's rotation angle. In this paper, a sliding mode control strategy based on neural network compensation is proposed to control the servo system. Firstly, the dynamic equations of the dual-flexible servo system considering the 2D deformation are established according to Lagrange's theorem. Then the control law of the sliding mode controller based on neural network is designed. The adaptive law of weight coefficients in the neural network is designed by the Lyapunov stability theorem. Finally, the numerical simulation analysis and control experiments are carried out. The experiment results prove that the control strategy can reduce the tracking error by 43.6%.

Non-Linear Bandwidth Extended-State-Observer Based Non-Smooth Funnel Control for Motor-Drive Servo Systems

This article proposes a non-smooth funnel control (NSFC) strategy based on the extended state observer (ESO) for motor-drive servo systems with unknown dynamics. These unknown dynamics, including the modeling error, the external disturbances, and the non-linear friction, are considered as a lumped disturbance. For estimating the unknown states and the lumped disturbance, a non-linear bandwidth extended state observer (NLB-ESO) is developed. The NLB designed using the Gaussian function and the position observation error can deal with the “peaking value problem” caused by the high observer gains. Furthermore, a funnel error surface is proposed based on the non-smooth error transformation (NSET) and incorporated into the dynamic surface control design procedure, where the NSFC can prescribe the position tracking error in a funnel region with small steady-state error and overshoot and short adjustment time. The non-smooth funnel error surface also avoids the singular problem in controller design by selecting the non-smooth parameter. Moreover, the stability of the closed-loop control system with the NLB-ESO is guaranteed by the Lyapunov theory. Comparative simulations and experiments show that the proposed NSFC can prescribe the tracking error in a funnel and ensure better tracking performance.

High-Precision Speed Control for Low-Speed Gimbal Systems Using Discrete Sliding Mode Observer and Controller

The high-precision control of angular speed in low-speed gimbal servo systems is an essential topic in the operation of the single gimbal control moment gyro (SGCMG). This article proposes a discrete control algorithm to suppress the influence of various disturbances on the low-speed gimbal servo system and the constraint between controller parameters and sampling time is established to ensure the stability of the system. To begin with, the disturbance analysis of the low-speed gimbal servo system is presented, including the torque ripple in the permanent magnet synchronous motor (PMSM), nonlinear friction, coupling torque caused by the spacecraft motion, and the parameter uncertainties. Then, a composite control method combining the sliding mode controller (SMC) with sliding mode observer (SMO) is applied to the speed loop and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> -axis current loop. The interferences are estimated by two SMOs, while SMCs are designed to eliminate the influence brought by the residual disturbances. The stability of the overall system is proven based on the Lyapunov criterion. Finally, simulation and experimental results verify the effectiveness of the proposed composite control method.

Generalized Langevin equationwith a nonlinear potential of mean force and nonlinear memory friction from a hybrid projection scheme.

We introduce a hybrid projection scheme that combines linear Mori projection and conditional Zwanzig projection techniques and use it to derive a generalized Langevin equation(GLE) for a general interacting many-body system. The resulting GLE includes (i) explicitly the potential of mean force (PMF) that describes the equilibrium distribution of the system in the chosen space of reaction coordinates, (ii) a random force term that explicitly depends on the initial state of the system, and (iii) a memory friction contribution that splits into two parts: a part that is linear in the past reaction-coordinate velocity and a part that is in general nonlinear in the past reaction coordinates but does not depend on velocities. Our hybrid scheme thus combines all desirable properties of the Zwanzig and Mori projection schemes. The nonlinear memory friction contribution is shown to be related to correlations between the reaction-coordinate velocity and the random force. We present a numerical method to compute all parameters of our GLE, in particular the nonlinear memory friction function and the random force distribution, from a trajectory in reaction coordinate space. We apply our method on the dihedral-angle dynamics of a butane molecule in water obtained from atomistic molecular dynamics simulations. For this example, we demonstrate that nonlinear memory friction is present and that the random force exhibits significant non-Gaussian corrections. We also present the derivation of the GLE for multidimensional reaction coordinates that are general functions of all positions in the phase-space of the underlying many-body system; this corresponds to a systematic coarse-graining procedure that preserves not only the correct equilibrium behavior but also the correct dynamics of the coarse-grained system.

Friction-free approach for a servo system: Design of a robust sliding-mode control based on a recurrent fuzzy neural network

Uncertainties such as disturbance and nonlinear friction always exist in physical motion control systems and degrade the precision of their tracking performance. In this research, a practical control strategy is integrated with a continuously differentiable friction model for a high-performance AC servo motor that performs with a continuous control input and is, hence, more properly suited for industrial applications. To further lessen the external disturbance and improve the tracking accuracy, a recurrent fuzzy neural network scheme was developed to approximate the system uncertainties, and its stability was guaranteed by the design of robust laws. The proposed controller was implemented on a high-performance digital signal processor (TMS320C6727). The results of the tracking simulations and experiments show that the proposed control scheme has a feasible and effective design for engineering servo system. In comparison with other algorithms, our approach has smaller values for both the peak and the root mean square of the tracking error while maintaining friction compensation, and it can potentially have a software implementation.

Modeling of a quasi-zero static stiffness mount fabricated with TPU materials using fractional derivative model

Static behaviors of quasi-zero static stiffness (QZSS) mounts have been widely studied to isolate low frequency vibrations. However, Dynamic behaviors contributed by the damping of QZSS mounts are simplified as a linear viscous damping, leading to a misestimate of isolation performances at low frequencies. In this paper, dynamic behaviors of a novel QZSS mount are modeled and analyzed. Firstly, a mount with QZSS characteristic is designed using finite element method and then fabricated with Thermoplastic polyurethanes (TPU). Secondly, reacted forces of the fabricated mount under static, harmonic and random excitations are measured through the MTS device. Thirdly, a mechanical model consisting of nonlinear elastic, friction and fractional derivative force elements arranged in parallel is presented to capture the measured mount’s nonlinear static, frequency-dependent and amplitude-dependent behaviors. Finally, a single degree of freedom system with a QZSS mount is used to investigate the influences of friction and fractional derivative models on the mount isolation performances.

Experimental study on nonlinear friction behavior of granular flow lubrication

Solid granules have good lubrication performance and load-bearing capacity, which has been concerned by researchers. However, the correlation mechanism between lubrication performance and granular medium dynamics is hardly focused on. In this study, the characteristics of two parallel friction pairs lubricated by the granular medium are experimentally investigated to study the nonlinear friction behavior during this process. The experimental results showed that the fluctuation behavior of friction force and friction coefficient with time shows a more flat nonlinear trend with the increase of the shear velocity and the pressure load. The discrete element simulation results corresponding to the experiment revealed that the change of nonlinear behavior of measured friction and friction coefficient is closely related to the evolution of force chains and dynamic characteristics of this granular flow lubrication system. The shear dilatancy amplitude of this granular flow lubrication system decreases obviously with the increase of the shear velocity and the pressure load. The flow states of granular medium is the main reason influencing the nonlinearity of shear gap. This study reveals the key factors affecting the friction nonlinearity and provides an evidence for the formation of granular shear dilatancy between two friction pairs lubricated by granular medium.

Measurement and Modelling of a Cycloidal Gearbox in Actuator with Permanent Magnet Synchronous Machine

Compact geared servo drives are a common part of modern industrial automation; thus, their proper modelling is a necessary part for the application and control design. The presented paper focuses on the mathematical model of the cycloidal gearbox, which is used in the compact actuator with a permanent magnet synchronous motor. A measurement procedure to obtain the necessary gearbox parameters is presented along with its mathematical model. A new approach was used to model the stiction and nonlinear gearbox friction behaviour in all four quadrants. A simulation of the actuator with the modelled gearbox is described and its results are compared with the real system measurement. Obtained results show a high match between simulation and experimental results and confirm the correctness of the simulation model.

Dynamic modeling and parameter identification for a gantry-type automated fiber placement machine combined with hydraulic balance system and nonlinear friction

A dynamic model considering hydraulic balance system and nonlinear friction is established for a gantry-type automated fiber placement (AFP) machine. To facilitate a comprehensive understanding, the AFP machine is introduced firstly. Due to the vertical movement of large masses, the AFP machine is equipped with a hydraulic balance system, thus a hydraulic model is secondly proposed to reveal the relationship between hydraulic pressure and the movement of the vertical axis. Then, a dynamic equation of the AFP machine is built by the Newton-Euler method, which is subsequently converted into the form of linearized minimum inertia parameters. In addition, the problems of nonlinear friction are also studied, and a segmented friction model is developed. To identify the parameters, issues regarding excitation trajectory, filtering, and identification algorithm are discussed. Corresponding experiments are performed, and the experimental results suggest that the prediction of the dynamic model is highly coincident with measurement data, and their relative error rates are less than 5%, proving the effectiveness of the established model and the identified parameters. Further analysis indicates that the proposed friction model is more in line with the actual situation, and can provide guidance for other friction research.

Advanced Contouring Compensation Approach via Newton-ILC and Adaptive Jerk Control for Biaxial Motion System

To achieve the precision contouring performance, this article presents a contouring compensation approach for the biaxial motion system even under extreme contour tasks. Two permanent magnet linear synchronous motors are installed in the biaxial motion platform. First, the dynamics of the biaxial motion servo system with the uncertainties such as model parameter variations, additive disturbance, and nonlinear friction are introduced. Since Newton algorithm is provided to realize dynamic contouring error estimation, accurate estimation of the contouring error can be achieved, even for the high velocity and complex contour with sharp corners and large curves. Then, iterative learning control (ILC) is used to control the contouring error for contouring performance improvement. An adaptive PD-type learning law based on an asymmetric Gaussian-like function is applied to improve the performance of the system. Moreover, adaptive jerk control (AJC) integrated with adaptive feedback gain is designed to address the negative effect of the uncertainties and enhance the robustness. The adaptive feedback gain is dominated and tuned by a novel adaptation law without the need for prior bound knowledge of the uncertainties. Meanwhile, parameter estimation is employed to handle the model parameter variations. Finally, the experimental results are presented to validate the efficiency and the achievable contouring performance of the proposed Newton-ILC and AJC approach.

Natural characteristic and vibration analysis of nonlinear articulated multi-beam ring structure for modeling ring truss antenna under base excitation

The investigation of natural characteristic and dynamic response of the ring truss antenna is essential for its design and vibration control since its high flexibility and nonlinearity. This paper investigates the dynamic properties of the articulated multi-beam ring structure for modeling the ring truss antenna under base excitation. The mathematical model of the multi-beam ring structure is established based on the global mode method. The matching conditions of force and displacement at connected points and boundary conditions of the ring structure are obtained. The global mode method and separation of variables method are applied to derive the analytical characteristic equation. Then natural frequency and global mode of the system are obtained. The orthogonality of global modes is proved. Based on the Galerkin procedure, the global modes which are explicitly functions are truncated to be substituted into the nonlinear partial differential equations of the system to yield the low dimensional discrete dynamic model with high accuracy described by ODEs which is useful for designing active vibration controllers. Afterwards the validity of the dynamic model is verified by comparing natural frequencies and mode shapes with those obtained by FEM. Finally, the effects of system parameters including external excitation, linear stiffness, third-order nonlinear stiffness, damping and friction torque on natural characteristic and dynamic response for the first resonance are analyzed. The results show that parameters of the structure have a significant effect on the whole system. The dynamic analysis in the paper is meaningful for design and vibration control of the antenna for the future study.

Tracking control strategy for space flexible manipulator considering nonlinear friction torque based on adaptive fuzzy compensation sliding mode controller

Space flexible manipulator (SFM) is one of the most promising development directions of space mechanism, which is attributed to more and more spacecraft on-orbit using it to perform maintenance, capture, and assembly operations. The SFM is a complex multi-output dynamic system with nonlinear friction torque. Nonlinear friction torque makes it difficult for precise tracking control of space flexible manipulators. In this paper, nonlinear friction torque in dynamics equations of the SFM is identified by the fuzzy rules based on the universal approximation property. The nonlinear friction torque is identified to improve the preciseness of the control torque in the SFM servo system. Thus, the accuracy of the rotation angle is improved, and the tracking errors of end-effectors are reduced. Firstly, the dynamic equations of the SFM considering nonlinear friction torque are established by the Hamilton principle. Then the sliding mode control strategy is proposed to control the SFM based on adaptive fuzzy compensation. Besides, the stability of the closed-loop servo system in the SFM is proved by the Lyapunov theorem. Finally, numerical simulation analysis and ground control experiments of the SFM are carried out. The results of control experiments show that the tracking error can be reduced in this control strategy. Therefore, the control strategy can improve the control accuracy of the SFM.