Presence Of Nonlinear Friction Research Articles

Inertial active Ornstein–Uhlenbeck particle in a non-linear velocity dependent friction

We explore the self-propulsion of an active Ornstein–Uhlenbeck particle with a non-linear velocity dependent friction. Using analytical approach and numerical simulation, we have exactly investigated the dynamical behaviour of the particle in terms of particle trajectory, position and velocity distribution functions in both underdamped as well as overdamped regimes of the dynamics. Analyzing the distribution functions, we observe that for a confined harmonic particle, with an increase in duration of self-propulsion, the inertial particle prefers to accumulate near the boundary of the confinement rather than the mean position, reflecting an activity induced bistability in the presence of nonlinear friction. On the other hand, in the overdamped or highly viscous regime, where the inertial influence is negligible, the sharp peak structure in the distribution across the mean position of the well reveals as usual trapping of the particle with increase in the persistent duration of activity. Moreover, for a free particle, using perturbation method, we have analytically computed the velocity distribution function in the vanishing limit of noise. The distribution interestingly shows the similar attributes as in case of a harmonic well, thus providing an additional effective confining mechanism that can be explained as a decreasing function of effective temperature. In this limit, the analytically computed distribution agrees well with the simulation results.

Reduced description method in the kinetic theory of Brownian motion with active fluctuations

We develop a microscopic approach to the kinetic theory of many-particle systems with dissipative and potential interactions in the presence of active fluctuations. The approach is based on a generalization of the Bogolyubov–Peletminskii reduced description method applied to the systems of many active particles. It is shown that the microscopic approach developed allows us to construct the kinetic theory of two- and three-dimensional systems of active particles in the presence of nonlinear friction (dissipative interaction) and an external random field with active fluctuations. The kinetic equations for these systems in the case of a weak interaction between the particles (both potential and dissipative ones) and low-intensity active fluctuations are obtained. We demonstrate particular cases in which the derived kinetic equations have solutions that match the results known in the literature. In addition, analysis of particular solutions showed that in the case of a friction force linearly dependent on the speed of structural units, the manifestation of self-propelling properties in the process of evolution of an active medium may be due to the local nature of active fluctuations.

Robust adaptive tracking control for servo mechanisms with continuous friction compensation

In this paper, a robust adaptive tracking control scheme is developed for servo mechanisms with nonlinear friction dynamics. A continuously differentiable friction model is used to capture the friction behaviors (e.g. Stribeck effect, Coulombic friction and Viscous friction). The robust integral of the sign of the error (RISE) feedback term is employed to design an innovative adaptive controller to compensate nonlinear friction and bounded disturbances. To reduce the effect of noise pollution, the desired trajectory is employed to replace the output signal in controller design. The developed adaptive controller can guarantee the asymptotic tracking performance for nonlinear servo mechanisms in the presence of nonlinear friction and bounded disturbances. Comparative experimental results are used to validate the effectiveness of the developed control algorithm.

Robust adaptive integral backstepping control for opto-electronic tracking system based on modified LuGre friction model

This paper presents a robust adaptive integral backstepping control strategy with friction compensation for realizing accurate and stable control of opto-electronic tracking system in the presence of nonlinear friction and external disturbance. With the help of integral control term to decrease the steady-state error of the system and combining robust adaptive control approach with the backstepping design method, a novel control method is constructed. Nonlinear modified LuGre observer is designed to estimate friction behavior. Robust adaptive integral backstepping control strategy is developed to compensate the changes in friction behavior and external disturbance of the servo system. The stability of the opto-electronic tracking system is proved by Lyapunov criterion. The performance of robust adaptive integral backstepping controller is verified by the opto-electronic tracking system with modified LuGre model in simulation and practical experiments. Compared to the adaptive integral backstepping sliding mode control method, the root mean square of angle error is reduced by 26.6% when the proposed control method is used. The experiment results demonstrate the effectiveness and robustness of the proposed strategy.

Fuzzy control for Electric Power Steering System with assist motor current input constraints

Friction and disturbances of the road are the main sources of nonlinearity in the Electric Power Steering (EPS) System. Consequently, conventional linear controllers design based on a simplified linear model of the EPS system will result in poor dynamic performance or system instability. On the other hand, a brush-type DC motor is more used in EPS control with an input current that is limited in practice. The control laws designed without taking into account the saturation effect may have undesirable consequences on the system stability. In this paper, a Takagi–Sugeno (T−S) fuzzy is used to represent the nonlinear behavior of an EPS system, and stabilization conditions for nonlinear EPS system with both constrained and saturated control input cases are proposed in terms of linear matrix inequalities (LMI). Simulation results show that both the saturated and constrained controls can stabilize the resulting closed-loop EPS system and provide a stable driving in the presence of nonlinear friction, disturbance of the road and actuator saturation.

Robust tracking of robot manipulator with nonlinear friction using time delay control with gradient estimator

We propose an enhanced controller to improve the robustness of Time Delay Control (TDC) for a robot manipulator in the presence of nonlinear friction, such as Coulomb friction. The problem of TDC is first analyzed with TDC as a trajectory control for a robot manipulator in the presence of nonlinear friction. Gradient estimation is used to solve this problem. The proposed controller is called TDC with Gradient Estimator (TDCGE). Comparing with a prior research to improve the robustness of TDC, named TDCSA, the TDCGE is much simpler to design. Through 1 DOF linear motor experiment, it is verified that the TDCGE is more robust against nonlinear friction than TDC and the TDCGE has a similar robustness to the TDCSA. In addition, it is confirmed that the TDCGE is easily implemented in the multi degree-of-freedom robot manipulator through a 3 DOF spatial robot manipulator experiment.

Control of mechanical systems with Stribeck friction and backlash

In this paper the control of mechanical systems in the presence of nonlinear friction and backlash is treated in a hybrid system approach. To deal with friction induced nonlinearities, the Stribeck friction model is linearized and the resulting model of the controlled plant is a hybrid system, the dynamics of which is given by linear models in the different partitions of the state space. During controller design it is assumed that the size of the backlash gap is unknown and the load side position and velocity cannot be measured. For motion control an LQ controller is applied. A condition is formulated for the control law parameters to guarantee the asymptotic stability of the control system. The LQ control algorithm is also extended for trajectory tracking tasks. Simulation results are presented to show the applicability of the theoretical results.

Particle with internal dynamical asymmetry: chaotic self-propulsion and turning

We investigate model of a complex particle that consists of a rigid shell and a nucleus with spatial asymmetric interaction. The particle's dynamics with the nucleus driven by a time-periodic force is considered. It is shown that unidirectional self-propulsed motion of particle arises in the absence of spatial and temporary asymmetry of external potentials and influences. Transport regimes are generic for the particle dynamics in the presence of nonlinear friction or periodic external potential. The changes of transport velocity and direction are determined by qualitative changes of dynamics regimes: attractor bifurcations in the internal phase space of the complex particle. Finally, microbiological relevance of the proposed model is briefly discussed.

Dynamic characteristics of a flexible arm with a reduction gear in the presence of nonlinear friction.

In this paper, we investigate the system dynamics of a one-link flexible arm affected by reduction gear friction. The natural frequency of the flexible arm lessens when the friction is larger and approaches that of a cantilever beam. The system damping changes with its natural frequency. Experiments were done in cases of both small and large frictions. The friction torque was nonlinear with viscous and Coulomb damping. Nonlinear and linearized calculations were shown to be in good agreement with experimental results.

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