Nonlinear Friction Effects Research Articles

Model Predictive Control of Aero-Mechanical Actuators with Consideration of Gear Backlash and Friction Compensation

To address the issues of low positional accuracy and significant torque pulsation caused by gear backlash and nonlinear friction in the mechanical transmission mechanism of aeronautical flap electromechanical actuators, we propose a model predictive control method for flap electromechanical actuator considering gear backlash and friction compensation. Firstly, we model the gear backlash in the electromechanical actuator’s mechanical transmission mechanism and design a corresponding torque current compensation method using a simplified dead zone model. Secondly, the LuGre compensation friction model is introduced, and a friction torque current compensation method is developed to address the nonlinear friction torque generated during system operation. Finally, the proposed current compensation strategies are employed to mitigate the adverse effects of gear backlash and nonlinear friction on system control performance. The simulation results demonstrate that the proposed method enhances position tracking accuracy, reduces torque pulsation, and significantly improves the overall control performance of the system.

INFLUENCE OF EXTERNAL CUBIC VISCOSITY ON THE DYNAMICS OF A CANTILEVER ROD LOADED WITH A TRACKING FORCE

The analysis of the influence of external nonlinear cubic viscosity on the behavior of a cantilever rod loaded with a compressive tracking force is performed. The Bernoulli – Euler beam model is used for the describing of the rod bending deformations. After the transition to dimensionless variables, we obtained the form of notation in which the coefficients of the equation do not depend on the coefficient of cubic viscous friction. This indicates the independence of the critical load and system frequency characteristics from the level of nonlinear attenuation. Using the standard procedure of the Bubnov – Galerkin method, taking into account the first two forms of eigen oscillations, the problem is reduced to the analysis of a fourth order nonlinear system of ordinary differential equations with respect to generalized coordinates and generalized velocities. For the linear version of the equations with low attenuation, the values of the critical load are obtained in dependence on the ratio of the damping coefficients of the eigenforms. The behavior of the system is analyzed taking into account the considered cubic nonlinearity using the method of nonlinear normal forms. The problem is reduced to the analysis of a nonlinear dynamical system with one degree of freedom. There are constructive analytical methods of qualitative and approximate quantitative research for this class of problems. The critical value of the compressive force was determined by the analysis of the dependence of the first Lyapunov magnitude on the load parameter. It turned out to be less than the value corresponding to the system without damping (the destabilizing effect of external nonlinear friction). A bifurcation occurs in the system at the critical load value. Therefore, the zero equilibrium becomes an unstable complex focus of the first order and a limit cycle is born. The function of the self-oscillations amplitude of the load magnitude is constructed using the harmonic linearization method.

Integrated Controller Design and Application for CNC Machine Tool Servo Systems Based on Model Reference Adaptive Control and Adaptive Sliding Mode Control.

In order to reduce the effect of nonlinear friction and time-varying factors on the servo system of a computer numerical control (CNC) machine tool and improve its motion control accuracy, this paper uses an adaptive sliding mode control (ASMC) method based on model reference adaptive control (MRAC). The method adopts ASMC in the control outer loop and obtains the optimal control parameters by making the sliding mode control (SMC) law continuous and adaptively estimating the control parameters. At the same time, MRAC is used in the control inner loop to enhance the "invariance" of the controlled object so that the switching gain of SMC can satisfy the disturbance matching condition even under lesser conditions. Simulation and experimental results show that compared with the traditional SMC, the ASMC based on MRAC proposed in this paper effectively reduces the influence of nonlinear friction on the system performance, and the reduction in following error reaches 71.2%, which significantly improves the motion control accuracy of the control system. The spectral analysis of the following errors shows that the maximum magnitude reduction rate of the high-frequency chattering is 89.02%, which significantly reduces the effect of the high-frequency chattering and effectively improves the stability performance of the control system.

Interaction of flutter and forced response in a low pressure turbine rotor with friction damping and mistuning effects

In modern LPT designs, which typically can assume a tolerable level of flutter, the simultaneous presence of forced response and flutter in different operation regimes becomes unavoidable. Current design rules rely on the linear superposition of vibration levels from the isolated problems. However, recent evidence from reduced order model calculations and from experiments suggests that this may be an over conservative approach. In order to check this finding, this study examines the flutter and forced response interaction in a realistic low pressure turbine rotor. A high fidelity model is used, and an efficient numerical method is implemented for the computation of the aeroelastic vibrations of the rotor with nonlinear friction effects at the blade-disk contact interfaces. A hybrid approach is used that combines a traveling wave description for the linear modes with a physical space representation for the displacement of the nonlinear contacts. The resulting equations are integrated in the time domain in order to account for the unknown flutter frequencies present in the response. Both tuned and mistuned configurations are considered, and it is confirmed that the actual response of the system is much smaller than that coming from the linear superposition of the separated effects.

Integrated Disturbance Observer-Based Robust Force Control

For robotic tasks that involve combined transmitting and contact force control, achieving high-performance motion control while ensuring stable environment contact is difficult. Among the factors that affect the quality of this force control, we may account vibrations due to misalignment in the mechanical components, actuator inaccuracies, non-linear effects of friction, and backlash. All the above factors can be collectively considered as force disturbances. Towards high-performance motion control and contact stability, a novel integrated disturbance observer (IDOB) is proposed. The IDOB uses force sensor measurements with position measurements and a plant model to isolate and robustly suppress the effects of force disturbances within the plant without compromising contact stability. This is applied here to a force control system to demonstrate the enhanced force control performance in free space and in contact. The passivity, robust stability, and disturbance rejection of the proposed IDOB are compared with those of existing force controllers, with and without force-based DOBs. Finally, actual experiments are conducted in free space and contact under various interaction conditions, showing that the IDOB improves transmitting force control and disturbance suppression performances. Moreover, peak collision force is reduced while maintaining contact stability with stiff environments.

Tidal energy extraction modifies tidal asymmetry and transport in a shallow, well-mixed estuary

Tidal energy extraction is increasingly being studied as a potential renewable energy resource in estuaries worldwide. Although it is understood that energy extraction via tidal stream turbines can modify currents and transport within estuaries, it is not clear how the underlying nonlinear physical mechanisms dictating tidal hydrodynamics are modulated. This research investigates the influence of a hypothetical tidal stream turbine array on barotropic tidal processes in a shallow, well-mixed system: the Piscataqua River – Great Bay (PRGB) estuary, using a numerical model. The modeled turbine farm includes 180 turbines which would extract an estimated 44.7 GWh of energy, annually. The tidal hydrodynamic model for the existing condition is validated with in-situ observations of currents and water level before analyzing tidal asymmetry and transport with and without tidal turbines. Results indicate that the tidal turbine array will decrease tidal elevation and current magnitudes system-wide, but generally reduce ebb currents and transport more than flood over most of the estuary footprint, thereby diminishing tidal asymmetry. The smaller asymmetric distortion compared to the no-turbine case is attributed to reductions in the storage volume of water over the estuary’s extensive tidal flat regions between low and high waters which decreases the associated nonlinear intertidal storage mechanism up to 25%. This leads to weakened ebb dominance over estuary sections from the mouth to mid-reaches, where depths are deep enough to keep the combined nonlinear shallow water and frictional effects from asserting control over the storage mechanism. Even in upstream shallow regions where depth-dependent friction controls asymmetry in both cases, the frictional mechanism is reduced only by 10% with turbines. Some environmental considerations of this work are discussed, with focus on sediment transport, water quality, and ecology.

Experimental passive and reactive control of a Laboratory Scale WEC Point Absorber

Scaled testing is an important and valuable step in the process of determining best practices of WEC development, validating numerical models of WEC systems, and/or preparing for larger scale testing. Validation and verification of numerical models are very important as there are physical phenomena that are hard to numerically model such as non-linear frictional effects. This paper builds on the 2021 EWTEC paper [1] in performing and evaluating experimental testing of the Laboratory Upgrade Point Absorber (LUPA). Since this last paper, LUPA has been fabricated and deployed and an initial characterization has been performed. Particularly passive (damping), and reactive (damping and stiffness) control methodologies are employed in regular waves to characterize and evaluate the mechanical power extracted from the waves. Reactive control allows us to invest energyin the system to get a greater average energy out as compared to damping control.
 The LUPA project has just finished its first deployment in the Large Wave Flume at the O.H. Hinsdale Wave Research Laboratory at Oregon State University as shown in Figure 1. Three modes of operation were tested, namely one body heave only, two body heave only, and six degrees of freedom. The one body heave only mode restricts the motion to linear and vertical and fixes the spar body so that the float is the only body free to move. The two body heave only maintains the vertical linear motion, but unlocks the float such that the float and spar are free to heave. The six degrees of freedom case is a floating moored mode with no restrictions on motion.
 This paper will focus on comparing passive and reactive control for the one body heave only case and the six degreesof freedom case with preliminary results shown in Figure 2. Regular waves were tested, focusing on a single wave heightand sweeping the wave period. Results will be presented in power (W) units and in capture width (m). Fig. 2. Top shows max power output vs input wave period for one body and two body configurations and just damping and damping and stiffness cases.Take note of differing input wave height. Bottom shows capture width.
 The LUPA project will provide a valuable testing platform for students and researchers. It will also provide a publicly available open source design and dataset for the research community here: https://github.com/PMECOSU/LUPA. This paper will serve as documentation of the initial testing of the system, providing baseline control results to be compared in future testing.

Tracking Control of Robot Manipulator with Friction Compensation Using Time-Delay Control and an Adaptive Fuzzy Logic System

This paper aims to highlight the critical role of robot manipulators in industrial applications and elucidate the challenges associated with achieving high-precision control. In particular, the detrimental effects of nonlinear friction on manipulators are discussed. To overcome this challenge, a novel friction compensation controller (FCC) that combines time-delay estimation (TDE) and an adaptive fuzzy logic system (AFLS) is proposed in this paper. The friction compensation controller is designed to take advantage of the time-delay estimation algorithm’s strengths in eliminating and estimating unknown dynamic functions of the system using information from the previous sampling period. Simultaneously, the adaptive fuzzy logic system compensates for the hard nonlinearities in the system and suppresses the errors generated by time-delay estimation, thus improving the accuracy of the robotic arm’s tracking. The numerical experimental results demonstrate that the proposed friction compensation controller can significantly enhance the tracking accuracy of the robotic arm, with the addition of the adaptive fuzzy logic system improving time delay estimation’s performance by an average of 90.59%. Moreover, the proposed controller is more straightforward to implement than existing methods and performs exceptionally well in practical applications.

Data-driven modeling for damping and positioning control of gantry crane

Flexible structural vibrations of large gantry cranes are a well-known issue. Several control strategies were proposed for this problem, which require a detailed dynamical model. Since the modeling of large-scaled structures, as well as of significant nonlinear friction effects is complicated and time consuming, a direct data-driven dynamic reconstruction based on the Koopman operator theory is proposed. Such identification results in a higher order linear state-space model, which reflects the nonlinear behavior in the broad dynamical range of the system and does not depend on a specific operating point. In this paper, a data-driven linear model identification is investigated for a simulation model, as well as for an experimental laboratory crane. The damping and positioning control dynamics based on the identified model were studied and it was shown, that the resulting performance is comparable to model-based nonlinear approaches.

Application of Adaptive Integral Robust Controller in Laser Galvanometer Motor

High-speed motion control of the galvanometer has become a very important part of laser processing. Due to the parameter uncertainty of the galvanometer itself, non-linearity can affect the friction compensation effect. In this paper, we propose to reduce the steady-state tracking error of the galvanometer system by means of an integral control term, while estimating the friction behavior using a nonlinear modified LuGre observer. Then an adaptive integral robust control scheme is used to eliminate the effects of nonlinear friction and external disturbances. And the stability of the galvanometer system is proved by the Lyapunov theorem. Simulation verification by MATLAB shows that the control scheme proposed in this paper can accurately follow the system commands. And the controller can effectively suppress the effects of unknown disturbances and parameter uncertainties compared with traditional control strategies. The simulation results show that the proposed control scheme significantly improves the response speed and tracking accuracy of the galvanometer system.

Nonlinear Model-Based Control of a Pneumatically Driven Robot

In robotics, pneumatic drives are an interesting alternative to classic electric drives, as their physical properties enable the design of safe, lightweight and intuitively operable robots. In this work, a nonlinear model-based feedback control concept for a robot with 4 compressed-air-driven rotary joints is presented. The robot model comprising kinetics and pressure dynamics is formulated. For this drive type, significant nonlinear friction effects are present, which is known to be challenging for controller design, especially since there is no output-side measurement of the effective drive torque after subtracting friction. A control concept based on differential flatness, here with the particular case of feedback linearization, is derived, which is particularly well suited for a system with such effects. The algorithm contains both kinetics and pressure dynamics in one central controller, and its working principle and practical implications are discussed. With experimental results, the effectiveness of the trajectory tracking controller is demonstrated and insights into the components of this controller are provided.

Adaptive LuGre Friction Compensation for Servo System Based on Backstepping Control and Feedforward Control

Aims: The study aims to improve the position control accuracy of a class of permanent magnet synchronous motors under friction. Background: Permanent magnet synchronous motor and servo system are important parts of modern industry, in which the friction effect is a typical nonlinear factor. To overcome the nonlinear friction effect, it is necessary to design a compound feedforward algorithm to improve the motion control accuracy. Objective: The objective of the study is to design a compound adaptive friction feedforward controller to overcome the nonlinear friction effect in the servo system while ensuring tracking accuracy. Methods: A compound algorithm combining velocity-acceleration double feedforward and adaptive friction feedforward is proposed to ensure the control accuracy, and then the backstepping control is used to ensure strict convergence. Finally, the friction parameter observer is used to estimate the parameters, and the performance of the control system is simulated in the Simulink module Results: Compared to Pure Friction Feedforward Compensation (PFFC) and Adaptive Friction Compensation (AFC), Adaptive Backstepping Feedforward Friction Compensation (ABFFC) has a faster convergence speed, higher steady-state accuracy, and less friction nonlinear effect Conclusion: The servo system with adaptive backstepping and feedforward friction compensation improves the accuracy and convergence of control performance. Moreover, the adaptive permanent magnet synchronous motor control system can effectively overcome the nonlinear friction effect.

Modeling, Identification, and Compensation Control of Friction for a Novel Dual-Drive Hydrostatic Lead Screw Micro-Feed System

This paper investigates the transmission performance of a novel dual-drive hydrostatic lead screw micro-nano feed system (DDHLS) that can obtain extremely low speed. Firstly, the oil film liquid friction of hydrostatic transmission is modelled, and the calculation model of oil film dynamic friction is proposed based on the variable viscosity theory. Secondly, on this basis, combined with the LuGre friction model, a novel all-components refinement friction identification method (ACRFIM) for DDHLS was developed. The friction parameters of the feed drive components such as LM guide and hydrostatic lead screw can be identified independently using the proposed method, ensuring precise friction force modelling in all components. Then, an all-component adaptive friction compensation control algorithm (AACA) was designed by introducing the temperature and disturbance influence factors into the friction model and considering the influence of the dynamic friction of liquid. The experiments illustrate that the calculation accuracy of the oil film friction model based on the variable viscosity theory is substantially improved. DDHLS can effectively suppress the adverse effects of nonlinear friction, and the proposed AACA has an obvious compensation effect for the friction of the time-varying system.

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.

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.

Micromorphological transformation and frictional nonlinearity at a graphite powder lubricated sliding interface with low speed and heavy load

PurposeThis study aims to investigate the microtopography transformation at a low-speed heavy-load interface with the lubrication of powder particles and its nonlinear friction effect on the sliding pair in contact.Design/methodology/approachBased on the universal mechanical tester (UMT) tribometer and VK shape-measuring laser microscope, comparative friction experiments were conducted with graphite powder lubrication. The friction coefficient with nonlinear fluctuations and the three-dimensional morphology of the boundary layer at the interface were observed and analyzed under different operating conditions. The effects on lubrication mechanisms and frictional nonlinearity at the sliding pair were focused on under different surface roughness and powder layer thickness conditions.FindingsAt a certain external load and sliding speed, the initial specimen surface with an appropriate initial roughness and powder thickness can store and bond the powder lubricant to form a boundary film readily. The relatively flat and firm boundary layer of powder at the microscopic interface can reduce the coefficient of friction and suppress its nonlinear fluctuation effectively. Therefore, proper surface roughness and powder layer thickness are beneficial to the graphite lubrication and stability maintenance of a friction pair.Originality/valueThis research is conducive to developing a deep understanding of the microtopography transformation with frictional nonlinearity at a low-speed heavy-load interface with graphite powder lubrication.

Effects of nonlinear friction of passive heave compensator on drilling operation — Part II: Active robust control

Hydropneumatic Passive Heave Compensator (PHC) for offshore drilling may exhibit undesirable effects due to nonlinearities of the friction seal, causing the so called Compensator-Induced Vibration (CIV) phenomenon, which induces longitudinal oscillations of frequencies higher than the heave motion. In this paper, a control system is proposed to attenuate the heave motion and to mitigate the CIV and compared to common practice, such as a linear feedforward controller. The proposed control is composed of a nonlinear feedforward to mitigate the nonlinear seal friction of PHC and a feedback CRONE (French acronym for fractional order robust control) controller to address the CIV. The CRONE control is designed based on a reduced order model of the drill sting and the linearized model of the PHC. This control drastically reduces the CIV and the transmission of heave motion, highlighting the limitation of the linear feedforward. Furthermore, it is shown that the proposed control strategy can satisfactory attenuate the heave motion (by 95%) and the CIV phenomenon (by 88%), despite noisy measurements by the inclusion of a Kalman and a Butterworth filters.

Robust and high fidelity real-time hybrid substructuring

In many engineering applications, mechanical contact leads to unwanted dynamic phenomena, such as excitation of high frequency modes. To investigate the induced dynamics, systems need to be tested already in the early development stage. Real-Time Hybrid Substructuring (RTHS) is a Hardware-in-the-Loop approach, that enables testing of critical components with realistic boundary impedance. In RTHS, the critical components are tested experimentally, while the remaining system is simulated numerically in a co-simulation. The dynamics of the transfer system, which couples the experimental part with the numerical simulation render the test outcome inaccurate or even make it unstable unless they are compensated for. The aim of this work is to tackle two major shortcomings of RTHS, namely stability and fidelity of RTHS tests. This is achieved by the combined use of Normalized Passivity Control and Iterative Learning Control. Normalized Passivity Control guarantees passivity of the transfer system and Iterative Learning Control improves the actuator tracking performance iteratively in order to increase the fidelity of the test outcome. Furthermore, a convergence condition is proposed for Iterative Learning Control in this setup such that an optimal tuning of the learning law can be achieved. We tested the proposed compensation scheme experimentally for an RTHS test, where contact occurs. A special focus is put on investigating unstable RTHS tests, as their stabilization and accurate testing is a particular challenge. The results show that the test fidelity, which is measured by the relative root-mean-square error, can be improved by a factor of about 6.5. In addition, it is shown that the combination of velocity feedforward, Iterative Learning Control and Normalized Passivity Control improves the tracking and thus the test fidelity even further. The results reveal that the proposed method has the potential not only to overcome the nonlinear effects of friction in the actuator, but also to improve the tracking accuracy in highly dynamic motion tasks. The main advantages over existing compensation techniques are that only little knowledge about the transfer dynamics of the actuator and experimental part is needed and that the implementation is simple. Hence, it is assumed that this method will be of interest for testing with RTHS in many engineering applications, with or without contact.

Synchronization Control With Adaptive Friction Compensation of Treadmill-Based Testing Apparatus for Wheeled Planetary Rover

This article studies synchronization control of a novel devised treadmill-based testing apparatus for wheeled planetary rover roaming at low speed. To offer satisfactory tracking performance and to ameliorate internal conflicts amongst individual treadmills during rover-treadmill interaction, a decentralized synchronization control strategy integrating an adaptive friction compensation scheme is proposed. To overcome the nonlinear friction effect at low-velocity scenarios, the LuGre model based friction compensation scheme is constructed with a dual-observer structure that can handle parametric uncertainties without recourse to the high-resolution encoder-required parameter identification. With the proposed control design, asymptotic stability of the closed-loop system is guaranteed with the tracking error and synchronization error converging to zero in presence of parametric uncertainties. Experimental results demonstrate the effectiveness of the proposed control strategy, which significantly improves the tracking performance in comparison with the existing proportional differential (PD)-type controller and synchronization controller without friction compensation.

Corotational 3D joint finite element tailored for the simulation of bistable deployable structures

The 3D deployable frames studied in this work are structures composed of elastic beam elements connected by complex joints. During transformation a controlled snap-through allows the instantaneous stabilization of the structure in an open and in a closed, compact configuration. The mechanics of the transformation is highly nonlinear, since it relies on finite rotations of the structural elements. It is also strongly influenced by geometrical features required for a manufacturing-ready design, such as the finite size of structural elements and sufficient spacing between the beams. These features are generally disregarded in the usual wireframe-based design, but they are taken into account in this work by applying a tailor-made corotational 3D joint finite element, developed to incorporate naturally finite joint size, finite nonlinear joint stiffness and friction effects. The formulation of the proposed joint FE is presented and the performance of the numerical implementation is verified using computational benchmarks. The joint FE is then applied to the numerical investigation of the transformation response of bistable deployable structures from a single module case to large, complex structures. Among other findings, it is shown that the incorporation of finite joint size and beam spacing in the numerical model leads to a different snap-through mechanism that significantly reduces the peak force required for transformation, which could be a basis for future design strategies. Additionally the performance of structures applying the bistable structural pattern on the whole structure or following an entirely modular design (interconnected single modules) is also compared, as a function of the structural size.