Global convergence for two-pulse rest-to-rest learning for single-degree-of-freedom systems with stick-slip Coulomb friction

Robotica ◽  
2006 ◽  
Vol 25 (3) ◽  
pp. 307-313
Author(s):  
Brian J. Driessen ◽  
Nader Sadegh
Keyword(s):  
Global Convergence ◽  
Coefficient Of Friction ◽  
Coulomb Friction ◽  
Sliding Friction ◽  
Input Pulse ◽  
Iterative Learning ◽  
Degree Of Freedom ◽  
Stick Slip ◽  
Single Degree Of Freedom ◽  
Single Degree

SUMMARYIn this paper, we consider the problem of rest-to-rest maneu-ver learning, via iterative learning control (ILC), for single-degree-of-freedom systems with stick-slip Coulomb friction and input bounds. The static coefficient of friction is allowed to be as large as three times the kinetic coefficient of friction. The input is restricted to be a two-pulse one. The desired input's first pulse magnitude is required to be five times the largest possible kinetic (sliding) friction force. The theory therefore allows the stiction force to be as large as the desired second input pulse. Under these conditions, we prove global convergence of a simple iterative learning controller. To the best of our knowledge, such a global-convergence proof has not been presented previously in the literature for the rest-to-rest problem with stick-slip Coulomb friction.

scholarly journals Experimental investigation of a single-degree-of-freedom system with Coulomb friction

2020 ◽  
Vol 99 (3) ◽  
pp. 1781-1799
Author(s):  
Luca Marino ◽  
Alice Cicirello
Keyword(s):  
Experimental Investigation ◽  
Degree Of Freedom ◽  
Experimental Results ◽  
Systematic Observation ◽  
Stick Slip ◽  
Friction Forces ◽  
Single Degree Of Freedom ◽  
Sdof System ◽  
Single Degree ◽  
Set Up

AbstractThis paper presents an experimental investigation of the dynamic behaviour of a single-degree-of-freedom (SDoF) system with a metal-to-metal contact under harmonic base or joined base-wall excitation. The experimental results are compared with those yielded by mathematical models based on a SDoF system with Coulomb damping. While previous experiments on friction-damped systems focused on the characterisation of the friction force, the proposed approach investigates the steady response of a SDoF system when different exciting frequencies and friction forces are applied. The experimental set-up consists of a single-storey building, where harmonic excitation is imposed on a base plate and a friction contact is achieved between a steel top plate and a brass disc. The experimental results are expressed in terms of displacement transmissibility, phase angle and top plate motion in the time and frequency domains. Both continuous and stick-slip motions are investigated. The main results achieved in this paper are: (1) the development of an experimental set-up capable of reproducing friction damping effects on a harmonically excited SDoF system; (2) the validation of the analytical model introduced by Marino et al. (Nonlinear Dyn, 2019. https://doi.org/10.1007/s11071-019-04983-x) and, particularly, the inversion of the transmissibility curves in the joined base-wall motion case; (3) the systematic observation of stick-slip phenomena and their validation with numerical results.

Iterative Learning Control for a Class of Modeling Undesirable Single Degree of Freedom System

2014 ◽  
Vol 538 ◽  
pp. 379-382
Author(s):  
Wei Zhou ◽  
Bao Bin Liu
Keyword(s):  
Iterative Learning Control ◽  
Learning Algorithm ◽  
Learning Control ◽  
Iterative Learning ◽  
Degree Of Freedom ◽  
Control Input ◽  
Convergence Properties ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Simulation Results

A class of modeling undesirable single degree of freedom system is studied by using iterative learning control. The proposed iterative learning algorithm constantly updates the control input according to output error until the desired output occurred. So the system with designed controller can achieve perfect accuracy. We have proved convergence properties in iteration domain and simulation results demonstrate the effectiveness of the presented method.

Phase-Space Reconstructions of Stick-Slip Systems

1995 ◽  
Author(s):  
B. F. Feeny ◽  
J. W. Liang
Keyword(s):  
Phase Space ◽  
Degree Of Freedom ◽  
Slip Systems ◽  
Stick Slip ◽  
Reconstruction Process ◽  
Single Degree Of Freedom ◽  
The Real ◽  
Single Degree ◽  
Friction Models ◽  
Method Of Delays

Abstract Nonsmooth processes such as stick-slip may introduce problems with phase-space reconstructions. We examine chaotic single-degree-of-freedom stick-slip friction models and use the method of delays to reconstruct the phase space. We illustrate that this reconstruction process can cause pseudo trajectories to collapse in a way that is unlike, yet related to, the dimensional collapse in the original phase-space. As a result, the reconstructed attractor is not topologically similar to the real attractor. Standard dimensioning tools are applied in effort to recognize this situation. The use of additional observables is examined as a possible remedy for the problem.

Forced Vibrations of a Single-Degree-of-Freedom System With Coulomb Bearing Friction

1969 ◽  
Vol 36 (4) ◽  
pp. 871-873 ◽  
Author(s):  
E. V. Wilms
Keyword(s):  
Coulomb Friction ◽  
Degree Of Freedom ◽  
Half Cycle ◽  
Piecewise Linearization ◽  
Single Degree Of Freedom ◽  
State Response ◽  
Single Degree ◽  
Forcing Function ◽  
Bearing Friction

The equation of motion of a single-degree-of-freedom mechanical system with Coulomb friction acting at two bearings is derived. The equation is nonlinear, but may be solved by piecewise linearization. For the case of transient oscillations, the amplitude decreases by a constant ratio every half cycle and, in this respect, the behavior resembles that of viscous damping rather than the type of Coulomb damping which has previously been investigated. The steady-state response with a forcing function is determined for the case of small damping. In addition to the amplitude and phase angle of the motion, a solution requires the determination of a second angle which defines the linearized regions.

Sign in / Sign up

Export Citation Format

Share Document