Stick slip and control in low-speed motion

Dimensional and perturbation analysis are applied to the problem of stick slip encountered during the motion of machines. The friction model studied is motivated by current tribological results and is appropriate for lubricated metal contacts. The friction model incorporates Coulomb, viscous, and Stribeck friction with frictional memory and rising static friction. Through dimensional analysis an exact model of the nonlinear system can be formed using five parameters rather than ten, greatly facilitating study and explicitly revealing the interaction of parameters. By converting the system of differential equations into a set of integrations, the perturbation technique makes approximate analysis possible where only numerical techniques had been available before. The analysis predicts the onset of stick slip as a function of plant and controller parameters; these results are compared with experimental data     

Robust nonlinear task space control for 6 DOF parallel manipulator

This paper presents a robust nonlinear controller equipped with a friction estimator for a 6 degree of freedom (DOF) parallel manipulator in the task space coordinates. The requisite 6 DOF system states for the task space control are acquired by an alpha-beta tracker and a numerical forward kinematic solution. The Friedland-Park friction observer in the joint space coordinates provides friction estimates that help to improve the control performance. Finally, the RNTC turns out to outper form a nonlinear task space control and a popularly adopted PID control with the friction estimator in the joint space coordinates.     

基于时频域交替法的迟滞非线性振动系统的稳态响应分析

连接界面的黏滑、摩擦行为不仅是引起结构刚度和阻尼非线性的主要原因,而且是结构无源阻尼的主要来源.Iwan模型能够较好地复现连接界面的黏滑、摩擦行为.本文采用时频域交替法(Alternating Frequency/Time Domain Method,AFT)研究含Iwan非线性模型的单自由度振子系统的稳态响应.时频域交替法具有频域法求解线性系统响应的高效性和时域法判断非线性力的便捷性特点,采用离散傅里叶变换和傅里叶逆变换,在频域和时域内分别求解系统响应和对应的非线性恢复力,再反复迭代计算系统的稳态响应.将时频域交替法计算结果和中心差分法计算的结果进行对比,并研究激励幅值对系统非线性特征的影响.结果表明,时频域交替法计算的结果与中心差分计算的结果具有较好的一致性,且求解效率较高,计算耗时减少50%;随着激励幅值的增加,系统的能量耗散增加,刚度降低,固有频率降低.     

Dynamic analysis of planar multi-body systems with LuGre friction at differently located revolute clearance joints

In this paper, the dynamic response of a planar rigid multi-body system with stick?Cslip friction in revolute clearance joints is studied. LuGre friction law is proposed to model the stick?Cslip friction at the revolute clearance joints. This is because using this law, one can capture the variation of the friction force with slip velocity, thus making it suitable for studies involving stick?Cslip motions. The effective coefficient of friction is represented as a function of the relative tangential velocity of the contacting bodies, that is, the journal and the bearing, and an internal state. In LuGre friction model, the internal state is considered to be the average bristle deflection of the contacting bodies. By applying the LuGre friction law on a typical slider?Ccrank mechanism, the friction force in the revolute joint having clearance is seen not to have a discontinuity at zero slip velocity throughout the simulation unlike in static friction models. In addition, LuGre model was observed to capture the Stribeck effect which is a phenomenon associated directly with stick?Cslip friction. The friction forces are seen to increase with increase in input speed. The effect of stick?Cslip friction on the overall dynamic behavior of a mechanical system at different speeds was seen to vary from one clearance joint to another.     

A discrete model of a stochastic friction system

To investigate a random friction system must cost a large of time on computer. So appropriate modeling of this system is of significance in practice. In this paper, an average model on simple random system with friction is firstly developed which is a discrete model by a two-dimensional mean Poincaré map. It is applied to describe random stick–slip motion. The numerical example shows that external noise can change the system behavior. That model is extended to a MDOF system only with a friction interface. The example of 3-DOF system exhibits the interesting behavior due to influence of external noise.     

The analysis and simulation for three-dimensional impact with friction

This paper presents a full discussion on how to formulate and evaluate the problem of spatial impact with friction in multibody systems. By considering that impact is experiencing a very short but finite time, we have established the differential equations of motion with normal impulse as a ‘time-like’ independent differential variable to describe the process of impact. A reliable numerical formulation, which can deal with the complex motions appearing in impact such as slip, stick and resumption of slip, has been developed by using difference schemes. The results indicate that the formulation and the numerical method presented in this paper can well solve the problems of 3D impact with friction by a comparison with the theoretical results existing in literature.     

Adaptive Friction Compensation For Tracking Control Of Mechanisms

Because friction is a phenomenon that is present in the vast majority of mechanical systems producing some unwanted effects such as tracking errors, limit cycles, and stick‐slip motion, friction model based compensation has been previously proposed. We present a simple adaptive friction compensator, developed from a simple friction model, that achieves the control objective (friction compensation). This simple model was effectively used to obtain a friction compensator with smooth terms avoiding the use of signum and absolute functions presented in previously reported works on friction compensation. Considering that the velocity is bound away from zero and using Lyapunov stability analysis, exponential stability of the closed loop system is shown; i.e., the tracking errors and the parameter estimation error converge exponentially to zero. Because our friction compensator is based on a simple friction model, numerical experiments using a more representative friction model are given to support our theoretical findings.     

一种离散型非线性自适应反馈控制器的设计与实现

针对运动控制低速跟踪系统中存在的非线性摩擦力影响的实际问题, 采用结构和参数完全未知的离散时间不确定非线性系统的反馈控制策略, 具体地进行了控制器的设计, 并利用MATLAB环境下的SIMULINK仿真来检验其控制效果, 进而运用到实际的电机控制系统中, 分析其控制性能, 并将其控制效果与PID控制相比较, 最后得出结论.     

Numerical solution of potential flow equations with a predictor-corrector finite difference method

We develop a numerical solution algorithm of the nonlinear potential flow equations with the nonlinear free surface boundary condition.A finite difference method with a predictor-corrector method is applied to solve the nonlinear potential flow equations in a two-dimensional (2D) tank.The irregular tank is mapped onto a fixed square domain with rectangular cells through a proper mapping function.A staggered mesh system is adopted in a 2D tank to capture the wave elevation of the transient fluid.The finite difference method with a predictor-corrector scheme is applied to discretize the nonlinear dynamic boundary condition and nonlinear kinematic boundary condition.We present the numerical results of wave elevations from small to large amplitude waves with free oscillation motion,and the numerical solutions of wave elevation with horizontal excited motion.The beating period and the nonlinear phenomenon are very clear.The numerical solutions agree well with the analytical solutions and previously published results.     

Dynamics of a three-module vibration-driven system with non-symmetric Coulomb’s dry friction

In the present paper, a three-module vibration-driven system moving on a rough horizontal plane is modeled to investigate the relation among the system’s steady-state motion, external Coulomb’s dry friction force and internal excitations. Each module of the system represents a vibration-driven system composed of a rigid body and a movable internal mass. Major attention is focused on the primary resonance situation that the excitation frequency is close to the first-order natural frequency of the system. In the case that the external friction is low, the internal excitation is weak and the stick–slip motion is negligible, both methods of averaging and modal superposition are employed to study the steady-state motion of the system. Through a set of algebraic equations, an approximate value of the system’s average steady-state velocity is obtained. Several numerical examples are calculated to verify the validity of the analytical results both qualitatively and quantitatively. It is seen that big quantitative errors will appear if stick–slip motions occur. Then, two mechanisms for the possible stick–slip motions are put forward, which explain the errors on the average steady-state velocity. Numerical simulations verify our analysis on the stick–slip effects and their mechanisms. Finally, to maximize the average steady-state velocity of the system, optimal control problem is studied. It is shown that, in addition to modifying the friction coefficients, the improvement of the system’s efficiency can be provided by changing the initial phase shifts among the three internal excitations.     

A sliding-mode based smooth adaptive robust controller for friction compensation

In this paper, a new approach employing both adaptive and robust methodologies is proposed for stick–slip friction compensation for tracking control of a one degree-of-freedom DC-motor system. It is well known that the major components of friction are Coulomb force, viscous force, exponential force (used to model the downward bend of friction at low velocity) and position-dependent force. Viscous force is linear and Coulomb force is linear in parameter; thus, these two forces can be compensated for by adaptive feedforward cancellation. Meanwhile, the latter two forces, which are neither linear nor linear in parameters, can only be partially compensated for by adaptive feedforward cancellation. Therefore, a robust compensator with an embedded adaptive law to ‘learn’ the upper bounding function on-line is proposed to compensate the uncancelled exponential and position-dependent friction. Lyapunov's direct method is utilized to prove the globally asymptotic stability of the servo-system under the proposed friction compensation method. Numerical simulations are presented as illustrations. © 1998 John Wiley & Sons, Ltd.     

On multiple model control for multiple contact systems

Multiple contact interaction is common in many robotic applications. These include grasping, wheeled vehicles, and distributed manipulation. All of these applications are capable of experiencing stick/slip phenomena at the contact interfaces. In particular, when there are more kinematic constraints then there are degrees of freedom, some contact interfaces must slip. Moreover, this stick/slip behavior is difficult to predict a priori due to strong sensitivities with respect to friction modeling and normal forces. Motivated by a simple multi-point manipulation device, we discuss how these effects can be accounted for and mitigated using tools from hybrid systems theory and multiple model adaptive control both for analysis and control design. In the context of the multi-point manipulation example, we show how multiple model supervisor-based adaptive control can provide stabilizing controllers for such systems. Our results are validated with simulations that both illustrate the need for these techniques and show their effectiveness.     

Seismic analysis of base isolated buildings

Summary  This paper presents a survey of the numerical simulation of base isolation systems for the vibration control of buildings and their equipment, primarilly against earthquakes. Base isolation has received much attention in the recent twenty years and many buildings have been protected using this technology. The article focusses mainly on the different numerical methods used in the analysis of base isolated buildings. The conventional form of solving the equations of motion governing the seismic response of building structures with nonlinear base isolation consists of using monolithic step by step integration methods. As an efficient alternative static condensation and block iterative schemes can be applied. The particularities of the equations of motion of buildings equiped with various base isolation systems are described. The linear theory of base isolated buildings is then presented. After this, numerical solution techniques for the analysis of the seismic response of buildings with isolation systems are developed in detail in the paper. Finally, numerical results for elastic and inelastic structures are described. A complete set of references coverning a wide range of studies is included.     

A regularized approach for frictional impact dynamics of flexible multi-link manipulator arms considering the dynamic stiffening effect

The present study offers a regularized approach for multi-link flexible manipulator arms with frictional impacts. The complex risks of global dynamics simulation, which involve nonlinear frictional impact, stick–slip, and foreshortening deformation, as well as multi-scale numerical problems, were implemented. The system is described as an assembly of \(n\) flexible links connected by \(n\) rotary joints. The stretching, bending, and the torsional deformations of the flexible links were considered in addition to the flexibility and mass of the joint. The introduction of a contact force potential energy approach transformed the non-differentiable functions of the normal and tangential frictions into differentiable ones, thereby generating Lagrange equations for the general recursive formulation of the systems. A numerical simulation for the double pendulum and spatial manipulator arms collision with targets was generated, thereby allowing the calculation of the frequent switching between the stick/sliding and forward/backward sliding. Several normal contact and friction models were adopted, and their corresponding results were analyzed. The generated ordinary differential equations of the proposed smoothed algorithm were solved using explicit solvers to verify any improvements in the global computational efficiency of the frictional collision dynamics for the flexible manipulator arms.     

Constitutive and Geometric Nonlinear Models for the Seismic Analysis of RC Structures with Energy Dissipators

Nowadays, the use of energy dissipating devices to improve the seismic response of RC structures constitutes a mature branch of the innovative procedures in earthquake engineering. However, even though the benefits derived from this technique are well known and widely accepted, the numerical methods for the simulation of the nonlinear seismic response of RC structures with passive control devices is a field in which new developments are continuously preformed both in computational mechanics and earthquake engineering. In this work, a state of the art of the advanced models for the numerical simulation of the nonlinear dynamic response of RC structures with passive energy dissipating devices subjected to seismic loading is made. The most commonly used passive energy dissipating devices are described, together with their dissipative mechanisms as well as with the numerical procedures used in modeling RC structures provided with such devices. The most important approaches for the formulation of beam models for RC structures are reviewed, with emphasis on the theory and numerics of formulations that consider both geometric and constitutive sources on nonlinearity. In the same manner, a more complete treatment is given to the constitutive nonlinearity in the context of fiber-like approaches including the corresponding cross sectional analysis. Special attention is paid to the use of damage indices able of estimating the remaining load carrying capacity of structures after a seismic action. Finally, nonlinear constitutive and geometric formulations for RC beam elements are examined, together with energy dissipating devices formulated as simpler beams with adequate constitutive laws. Numerical examples allow to illustrate the capacities of the presented formulations.     

Motion and force control with a nonlinear force error filter for underwater vehicle-manipulator systems

This paper deals with a control scheme for autonomous underwater robots equipped with manipulators. Several motion and force controllers have been developed. Most of them were designed in disregard of the dynamics of marine thrusters to develop a controller with a simple structure. However, the robot body propelled by thrusters generally has a considerably slower time response than the manipulator driven by electrical motors. Therefore, it may be difficult to construct a high-gain feedback control system to achieve a good control performance, because the high gain may excite the slow thruster dynamics ignored in the controller design, and the excitation will degrade the control performance. In this paper, we develop a motion and force controller for mathematical models with the dynamics of thrusters. It includes a nonlinear force error filter which allows us to construct a stable motion and force control system. To investigate its control performance, we conducted numerical simulations for comparing the proposed control scheme with an existing control scheme designed in disregard of the thruster dynamics. Simulation results demonstrate the usefulness of the proposed controller.     

Dealing with multiple contacts in a human-in-the-loop application

This paper deals with continuous contact force models applied to the human-in-the-loop simulation of multibody systems, while the results are valid in general to all the real-time applications with contacts. The contact model proposed in this work is suited to collisions between massive solids for which the assumption of quasi-static contact holds, and it can be supposed that the deformation is limited to a small region of the colliding bodies while the remainder of them are assumed to be rigid. The model consists of two components: normal compliance with nonlinear viscoelastic model based on the Hertz law, and tangential friction force based on Coulomb’s law including sticktion and a viscous friction component. Furthermore, the model takes into account the geometry and the material of the colliding bodies. The tangential model is a novel contribution while the normal model is completely taken from previous works. For this work, the formulation of the equations of motion is an augmented Lagrangian with projections of velocities and accelerations onto their constraints manifolds and implicit integrator. The whole solution proposed is tested in three applications: the first one is the simulation of a spring–mass system with Coulomb’s friction, which is an academic problem with known analytical solution; the second one is the Bowden and Leben stick–slip experiment; the third one is a simulator of a hydraulic excavator Liebherr A924, which is a realistic application that gives an idea of the capabilities of the method proposed.     

Dynamic analysis of wind-excited truss tower with friction dampers

This paper presents a rational analytical method for determining dynamic response of wind-excited large truss towers installed with friction dampers and investigates the effectiveness of friction dampers. The analytical procedure involves two models of one truss tower: one is the two-dimensional lumped mass dynamic model and the other is the three-dimensional (3D) finite element static model. These two models are alternately used to fulfill control force transformation, displacement increment transformation, and the numerical integration of equations of motion of the coupled damper-tower system. A three-story truss structure under wind excitation is used to validate the proposed bi-model method through the comparison with a precise 3D dynamic analysis. After a satisfactory comparison, a large space steel television tower is used as an application to examine the feasibility of the bi-model method and the effectiveness of friction dampers. The case study shows that the bi-model method can efficiently compute wind-induced response of the large space television tower with friction dampers and the installation of the friction dampers of proper parameters can significantly reduce wind-induced vibration of the tower.     

Kinematic modeling of wheeled mobile robots with slip

This work presents a kinematic modeling method for wheeled mobile robots with slip based on physical principles. First, we present the kinematic modeling of a mobile robot with no-slip considering four types of wheels: fixed, centered orientable, off-centered orientable (castor) and Swedish (also called Mecanum, Ilon or universal). Then, the dynamics of a wheeled mobile robot based on Lagrange formulation are derived and discussed. Next, a quasi-static motion is considered to obtain the kinematic conditions that provide the slip modeling equations. Several types of traction models for the slip between the wheel and the floor are indicated. In particular, for a frictional force linearly dependent on the sliding velocity, the no-slip kinematic equation of the wheeled mobile robot is related, through the weighted least-squares algorithm, with the slip modeling equations. To illustrate the applications of the proposed approach a tricycle vehicle is considered in a real situation. The experimental results obtained for the slip kinematic model are compared with the ones obtained for the well-known Kalman filter.