Nonlinear Friction Effects Research Articles

RBF Networks-Based Adaptive Inverse Model Control System for Electronic Throttle

An electronic throttle is a dc-motor-driven valve that regulates air inflow into the combustion system of the engine. An effective controller for electronic throttle is not easy to accomplish since the plant is burdened with strong nonlinear effects of stick-slip friction, spring, and gear backlash. In this brief, an adaptive inverse model control system (AIMCS) is designed for the plant, and two radial basis function (RBF) neural networks are utilized in the AIMCS. The plant is identified by a RBF networks identifier, which provides the sensitivity information of the plant to the control input. And another RBF networks is utilized as inverse model controller established by inverse system method. The RBF networks are offline learned firstly and are online trained using back propagation algorithms. To guarantee convergence and for faster learning, adaptive learning rates are developed. Simulation and experiment results show the effectiveness of the AIMCS.

Dynamic Modeling of a Two-Axis, Parallel, H-Frame-Type XY Positioning System

XY positioning is an important task in industrial applications. This paper addresses the dynamic modeling of a belt-driven, parallel-type XY positioning system constructed in the form of a capitalized H. The system uses one long timing belt to transmit the rotation of two stationary motors to end-effector motion. Due to less moved masses, the studied H-frame system is potentially capable of fast acceleration, and therefore, faster positioning than traditional stacked systems. The use of an elastic transmission element also causes the biggest disadvantage of the system, which is an uncertainty of end-effector position due to stretching in the belt. Thus, the objective of this paper is to develop a dynamic model that can capture the response of this system. Using Lagrange's method, an eighth-order lumped parameter dynamic model of the stage motion is derived. The effect of nonlinear friction in the pulleys and cart motion is added to the model. The response of the model was simulated in MATLAB Simulink, and the model prediction is compared with real data obtained from the developed system. The results show that the model can accurately predict the dynamics of the developed H-frame positioning system.

Modeling and control of a pneumatically actuated inverted pendulum

This paper presents the results of modeling of an inverted pendulum system driven by a linear pneumatic motor and equipped with relatively low-cost potentiometer-based position measurement system. Based on the nonlinear model of the overall pendulum system, which also includes notable friction effects, a linearized model is derived. The linearized model is used as a basis for the design of state feedback controller based on LQ and LQG optimization procedures. The linear state feedback controllers are augmented by a compensator of nonlinear friction effects whose design is based on the results of experimental identification of an appropriate static friction model. The proposed pendulum controller structures have been verified by means of computer simulations and experimentally on the experimental setup of a pneumatically actuated inverted pendulum.

Improved dynamic identification of robotic manipulators in the linear region of dynamic friction

Conventional dynamic identification procedures for robotic manipulators make use of the linearity of the dynamic model with respect to the parameters. With these identification procedures, only a simple friction model such as Coulomb and viscous friction can be incorporated while other dynamic and nonlinear friction effects cannot be considered. This paper proposes a simple and yet effective scheme to identify the dynamic friction region of robotic manipulators. These results are then incorporated into the excited trajectory designing process. The proposed scheme has been verified on the first four link of the Mitsubishi PA10 manipulator, an improved dynamic model was obtained which proves the effectiveness of the proposed identification procedures.

Sliding mode control for an electrohydraulic actuator system with discontinuous non-linear friction

This paper considers the application of a sliding mode controller (SMC) to a high-precision electrohydraulic actuator (EHA) system with non-linear discontinuous friction effects. An important consideration in such systems is the oscillations that occur in the system response owing to friction for small input signals at cross-over regions where the velocity changes sign. A new model for a high-precision hydrostatic actuation system is developed to investigate the effects of discontinuous and non-linear friction. This model is used in the development of a sliding mode control strategy. A significant result from this study is that the SMC can suppress such oscillations. In addition, the paper uses a linear quadratic approach for defining a discrete-time sliding surface for non-linear systems. A comparative study involving the application of the proposed SMC versus a gain-scheduled proportional controller is presented.

AN ASYMPTOTIC TRACKING CONTROL STRATEGY FOR MECHANICAL SYSTEMS WITH UNCERTAIN NONLINEAR FRICTION

Modeling nonlinear friction effects is a challenging problem. In this paper, a tracking controller is proposed for a system with uncertain nonlinear friction dynamics. Instead of using a specific friction model, we assume that the friction dynamics are represented by a function, which is unknown except its being continuously differentiable and Lipschitz continuous with known Lipschitz constants. It is shown that the scheme results in friction identification and trajectory position and velocity tracking. The analysis is done using Lyapunov-based stability method.

Generalized capstan problem: Bending rigidity, nonlinear friction, and extensibility effect

A theoretical model of the capstan problem including the extensibility and the Poisson's ratio of the rod is established in this study. Several cases were examined to investigate the effects of important parameters on the tension transmission efficiency. As a result, the rod extensibility turned out to enhance the tension ratio, competing with the effects of rod bending rigidity and the frictional behaviors of the system. In case of no frictional modification ( n=1, the simple Amonton's law), larger initial strain renders greater tension ratio. This effect becomes more remarkable at high radius ratio. However, the effect of the modified frictional law may oppress the effect of rod extensibility if the initial tension T 0 grows larger. The effect of Poisson's ratio also tends to increase the tension ratio. But the amount was almost negligible since the maximum decrease was at most 7.8%. We also calculated the average strain throughout the rod by solving the governing equation and iterating the value of λ avg. Calculated strain throughout the rod was up to 2.6 times larger than initial strain. But this contribution leaded to at most 1.078 times larger radius ratio than the initial rod radius. Thus, it is well enough to consider only the extensibility effect on the increase of the tension ratio. We also presented several prerequisites to establish the model. Three major concerns about this model were introduced and clarified.

Numerical Study of Tsunami Waves with Sloping Bottom and Nonlinear Friction

In this paper we investigate the breaking of long-waves propagating on shallow water with nonlinear friction on the sloping bottom. A complete set of equations is presented and a numerical method is developed to simulate the wave propagation. The method uses an up-wind difference scheme for the nonlinear convective term and the central difference scheme for other derivative terms. Various numerical examples have been conducted to investigate the effect of nonlinear friction and drag coefficient on wave propagation and breaking. By analyzing the numerical results, we find that in order to overcome wave breaking, nonlinear friction needs to be below certain level.

Lyapunov-Based Tracking Control in the Presence of Uncertain Nonlinear Parameterizable Friction

Modeling and compensation for friction effects has been a topic of considerable mainstream interest in motion control research. This interest is spawned from the fact that modeling nonlinear friction effects is a theoretically challenging problem, and compensating for the effects of friction in a controller has practical ramifications. If the friction effects in the system can be accurately modeled, there is an improved potential to design controllers that can cancel the effects; whereas, excessive steady-state tracking errors, oscillations, and limit cycles can result from controllers that do not accurately compensate for friction. A tracking controller is developed in this paper for a general Euler-Lagrange system that contains a new continuously differentiable friction model with uncertain nonlinear parameterizable terms. To achieve the semi-global asymptotic tracking result, a recently developed integral feedback compensation strategy is used to identify the friction effects online, assuming exact model knowledge of the remaining dynamics. A Lyapunov-based stability analysis is provided to conclude the tracking and friction identification results. Experimental results illustrate the tracking and friction identification performance of the developed controller.

Effect of nonlinear friction on the dynamics of electromechanical systems

A two-mass model of the electromechanical system (EMS) is proposed in which a new composition of the mechanical subsystem is provided. The transfer function of the system taking into account loads on the shaft of an actuating motor and an object and nonlinearity of the friction function are obtained. Frequency characteristics are determined that clearly show that the accurate values of the viscous friction factors have to be known to assess qualitative indicators of systems and wires

Hybrid Theory-Based Time-Optimal Control of an Electronic Throttle

An electronic throttle is a dc-motor-driven valve that regulates air inflow into the combustion system of the engine. The throttle control system should ensure fast and accurate reference tracking of the valve plate angle while preventing excessive wear of the throttle components by constraining physical variables to their normal-operation domains. These high-quality control demands are hard to accomplish since the plant is burdened with strong nonlinear effects of friction and limp-home nonlinearity. In this paper, the controller synthesis is performed in discrete time by solving a constrained time-optimal control problem for the piecewise affine (PWA) model of the throttle. To that end, a procedure is proposed to model friction in a discrete-time PWA form that is suitable both for simulation and controller design purposes. The control action computation can, in general, be restated as a mixed-integer program. However, due to the small sampling time, solving such a program online (in a receding horizon fashion) would be very prohibitive. This issue is resolved by applying recent theoretical results that enable offline precomputation of the state-feedback optimal control law in the form of a lookup table. The technique employs invariant set computation and reachability analysis. The experimental results on a real electronic throttle are reported and compared with a tuned PID controller that comprises a feedforward compensation of the process nonlinearities. The designed time-optimal controller achieves considerably faster transient, while preserving other important performance measures, like the absence of overshoot and static accuracy within the measurement resolution

非線形摩擦のモデル化と摩擦補償による位置決め制御系の高精度化

This paper presents a performance improvement approach for the fast and precise positioning using a 2-degrees-of-freedom (2DOF) controller. In the controller design, effects of nonlinear friction on the positioning performance are especially paid attention, where a precise nonlinear friction characteristic with rolling friction behaviors is mathematically modeled and considered. A disturbance observer with an initial value compensation, therefore, is adopted in order to improve the disturbance suppression characteristic in positioning. The proposed positioning control approach with the friction modeling and compensation has been verified by experiments using a prototype for industrial positioning devices.

Optimization of an impact drive mechanism based on real-coded genetic algorithm

The main objective of this study is to optimize the mass ratio and the driving waveform of an impact drive mechanism (IDM). The method based on real-coded genetic algorithm (RGA) has the advantages to optimize the parameters of the IDM model even if it owns both the hysteretic phenomenon and nonlinear frictional effects. Furthermore, the method is calculated by real codes without the operations of encoding and decoding, and promotes the calculation efficiency very much. The maximum amplitude of the main body and the optimal waveform of the applied voltage compared with the triangular waveform are obtained. Finally, the dynamic responses due to the optimal waveform and the triangular waveform are compared.

A Mechanism and Simple Dynamical Model of the North Atlantic Oscillation and Annular Modes

A simple dynamical model is presented for the basic spatial and temporal structure of the large-scale modes of intraseasonal variability and associated variations in the zonal index. Such variability in the extratropical atmosphere is known to be represented by fairly well-defined patterns, and among the most prominent are the North Atlantic Oscillation (NAO) and a more zonally symmetric pattern known as an annular mode, which is most pronounced in the Southern Hemisphere. These patterns may be produced by the momentum fluxes associated with large-scale midlatitude stirring, such as that provided by baroclinic eddies. It is shown how such stirring, as represented by a simple stochastic forcing in a barotropic model, leads to a variability in the zonal flow via a variability in the eddy momentum flux convergence and to patterns similar to those observed. Typically, the leading modes of variability may be characterized as a mixture of ‘‘wobbles’’ in the zonal jet position and ‘‘pulses’’ in the zonal jet strength. If the stochastic forcing is statistically zonally uniform, then the resulting patterns of variability as represented by empirical orthogonal functions are almost zonally uniform and the pressure pattern is dipolar in the meridional direction, resembling an annular mode. If the forcing is enhanced in a zonally localized region, thus mimicking the effects of a storm track over the ocean, then the resulting variability pattern is zonally localized, resembling the North Atlantic Oscillation. This suggests that the North Atlantic Oscillation and annular modes are produced by the same mechanism and are manifestations of the same phenomenon. The time scale of variability of the patterns is longer than the decorrelation time scale of the stochastic forcing, because of the temporal integration of the forcing by the equations of motion limited by the effects of nonlinear dynamics and friction. For reasonable parameters these produce a decorrelation time of the order of 5‐10 days. The model also produces some long-term (100 days or longer) variability, without imposing such variability via the external parameters except insofar as it is contained in the nearly white stochastic forcing.

A Stabilization Control of 2-Link Pneumatic Manipulator by Means of Neural Network

This paper develops with a stabilizing method for hunting of the 2-link pneumatic manipulator. In the pneumatic manipulator, the time-delay exists due to the air tube when air pressure signal is transmitted, and the effect of the pneumatic motor's nonlinear friction is easy to be received. The hunting of each arm is not prevented by the conventional PD control, and it is generally difficult to realize a good stability control. For above problems, the new control method using neural network (NN) is proposed. Through simulation and experiment, the validity and practicability are clarified by this control method.

The two-dimensional character of spin-up in a rectangular container

This study presents two-dimensional (2D) numerical simulations of the spin-up of a homogeneous fluid in a rectangular container, compared with the corresponding three-dimensional (3D) simulation presented by other authors. A 2D simulation is based on a recently derived model [Zavala Sansón and van Heijst, J. Fluid Mech. 412, 75 (2000)] including nonlinear Ekman friction effects, in addition to the well-known linear damping term. It is found that the inclusion of nonlinear Ekman terms provides a remarkable agreement between 2D and 3D simulations for times comparable with the Ekman timescale, which implies that this formulation is able to capture the essential viscous features of the 3D situation. In contrast, a simulation based on a 2D model with conventional linear friction is not able to represent the 3D case correctly.

Design and modeling of a flexible test bed for use in control system analysis and verification

This paper describes a test bed specifically designed for studying the effects of nonlinear friction, backlash, and drive train flexibility on structurally flexible electro-mechanical systems, and for developing control algorithms that will compensate for nonlinear friction, backlash, and drive train flexibility in structurally flexible electro-mechanical systems. The test bed has a modular and adjustable design. Friction, backlash, and flexibility can all be varied or disabled. A mathematical model of the dynamics of the test bed is also described. This model includes stiction, Coulomb friction, backlash and drive train, and link flexibility. The model is verified via comparisons of model-predicted and experimental responses.

Comparison of Balance and Out of Balance Main Battle Tank Armaments

It has been commonly thought that stabilising an out of balance gun on a moving platform (tank or ship) is very difficult or impossible to achieve. Using models of a balanced and out of balance gun on a main battle tank this is shown not to be the case. The models of the guns used, include the effect of non-linear friction and out of balance. To improve the stabilisation of the out of balance gun, trunnion vertical acceleration feedforward is used.

An Improved PID Controller for Machines with Friction

Non linear effects of friction at low velocities may lead to “stick slip motion”. A control scheme, which decreases this “stick slip” and increases position tracking accuracy of the servo system is described. This paper takes two previous results: A friction controller described in (Li and Cook, 1998) and position dependent friction characteristics described in (Armstrong-Helouvry, 1991)and (Popovic and Goldenberg, 1998), to give an improved friction controller. The controller uses a static friction lookup table to apply a series of pulses of varying widths and magnitudes. Experimental results show the friction controllers performance when implemented on an industrial robot.

Robust friction compensation for submicrometer positioning and tracking for a ball-screw-driven slide system

Ball-screw-driven slide systems are largely used in industry for motion control applications. Their performance using standard proportional-integral-derivative (PID) control algorithm is unsatisfactory in submicrometer motion control because of nonlinear friction effects. In this article, controllers based on a bristle-type nonlinear contact model are developed and implemented for submicrometer motion. For submicrometer positioning, a proportional-derivative (PD) control scheme with a nonlinear friction estimate algorithm is developed, and its performance is compared with that of a PID controller. For tracking, a disturbance observer was added to reject external disturbances and to improve robustness. The experimental results indicate that the proposed controller has consistent performance in positioning with under 1.5% of steady-state error in the submicrometer range. For tracking performance, the proposed controller shows good and robust tracking with respect to parameter variation.