scholarly journals On the Stability of Digital Position Control with Viscous Damping and Coulomb Friction

2017 ◽  
Vol 61 (4) ◽  
pp. 266 ◽  
Author(s):  
Csaba Budai ◽  
László Kovács L.
Keyword(s):  
Discrete Time ◽  
Dry Friction ◽  
Coulomb Friction ◽  
Control Parameter ◽  
Position Control ◽  
Viscous Damping ◽  
Sampled Data ◽  
Stable Domain ◽  
The Stability ◽  
Parameter Values

In this paper, we investigate the combined effect of viscous damping and Coulomb friction on sampled-data mechanical systems. In these systems, instability can occur due the sampling of the applied discrete-time controller which is compensated by the two different physical dissipation effects. In order to investigate the interplay between these, we focus on how the stable domain of operation is extended by the dry friction compared to viscous damping. We also show that dry friction causes concave envelope vibrations in this extended region. The analytical results, presented in the form of stability charts, are verified by a detailed set of simulations at different representative control parameter values.

scholarly journals The Complex Adaptive Delta-Modulator in Sliding Mode Theory

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 814
Author(s):  
Dhafer Almakhles
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Sliding Mode ◽  
Stability Conditions ◽  
Mode Theory ◽  
Dynamical Behaviors ◽  
Complex Adaptive ◽  
The Stability ◽  
Parameter Values

In this paper, we consider the stability and various dynamical behaviors of both discrete-time delta modulator (Δ-M) and adaptive Δ-M. The stability constraints and conditions of Δ-M and adaptive Δ-M are derived following the theory of quasi-sliding mode. Furthermore, the periodic behaviors are explored for both the systems with steady-state inputs and certain parameter values. The results derived in this paper are validated using simulated examples which confirms the derived stability conditions and the existence of periodicity.

Parametric Identification of Systems With Dry Friction and Nonlinear Stiffness Using a Time Series Model

1996 ◽  
Vol 118 (2) ◽  
pp. 252-263 ◽  
Author(s):  
Q. Chen ◽  
G. R. Tomlinson
Keyword(s):  
Time Series ◽  
Dry Friction ◽  
Coulomb Friction ◽  
System Parameter ◽  
Parametric Identification ◽  
Time Series Model ◽  
Viscous Damping ◽  
Nonlinear Stiffness ◽  
Transform Method ◽  
New Type

A new type of time series model, the AVD model which accommodates the Acceleration, Velocity and Displacement simultaneously, has been used to estimate the characteristics of nonlinear single and multi-degree of freedom systems with dry Coulomb friction, viscous damping and nonlinear stiffness. Numerical results via simulation are compared with those from a Fourier transform method, which suggests that the AVD model is a powerful technique for nonlinear system parameter identification.

Stability Analysis of a Vibrational System Subject to Negative Viscous Damping and Displacement-Dependent Dry Friction Damping

2003 ◽  
Author(s):  
Aldo A. Ferri ◽  
Wayne E. Whiteman
Keyword(s):  
Stability Analysis ◽  
Friction Force ◽  
Dry Friction ◽  
Effective Means ◽  
Viscous Damping ◽  
Friction Damper ◽  
Friction Damping ◽  
Fan Blade ◽  
The Stability ◽  
Dry Friction Damping

A stability analysis is conducted of an autonomous single-degree-of-freedom system damped with negative viscous damping and a displacement-dependent Coulomb friction force. The geometry of the dry friction damping element yields a friction force that grows linearly with the system displacement. The most direct application of this system is in the study of a turbomachinery blade with shroud interfaces designed to achieve this geometry. Recent studies have shown that the damping of systems with this type of displacement-dependent dry friction force resembles linear structural damping and suggests that this arrangement may be an effective means of flutter suppression in these turbine and fan blade applications. For this study, the inclusion of negative viscous damping is used in order to approximate destabilizing aerodynamic forces. An exact analysis is conducted to determine the stability of this autonomous system. Results show that energy losses from the displacement-dependent dry friction damper are large enough to achieve local and even global stability under certain conditions.

scholarly journals Discrete dynamics of complex systems

1997 ◽  
Vol 1 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Hermann Haken
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
Difference Equations ◽  
Control Parameter ◽  
Multiplicative Noise ◽  
Critical Value ◽  
Discrete Dynamics ◽  
Nonlinear Difference Equations ◽  
Starting Point ◽  
The Stability

This article extends the slaving principle of synergetics to processes with discrete time steps. Starting point is a set of nonlinear difference equations which contain multiplicative noise and which refer to multidimensional state vectors. The system depends on a control parameter. When its value is changed beyond a critical value, an instability of the solution occurs. The stability analysis allows us to divide the system into stable and unstable modes. The original equations can be transformed to a set of difference equations for the unstable and stable modes. The extension of the slaving principle to the time-discrete case then states that all the stable modes can be explicitly expressed by the unstable modes or so-called order-parameters.

Sampled data output regulation of n-link robotic manipulator using a realizable reconstruction filter

Robotica ◽  
2014 ◽  
Vol 34 (4) ◽  
pp. 900-912 ◽  
Author(s):  
Muwahida Liaquat ◽  
Mohammad Bilal Malik
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
Feedback Linearization ◽  
Impulsive System ◽  
Observer Design ◽  
Control Input ◽  
Sampled Data ◽  
Control Scheme ◽  
Reconstruction Filter ◽  
The Stability

SUMMARYThis paper proposes a solution to the sampled-data regulation problem for feedback linearizable n-link robotic manipulators. The prime focus is on the development and stability analysis of the proposed control scheme in the presence of model uncertainties and external disturbances. A major constraint is the availability of sampled measurements of output signal. This leads to designing an impulsive observer for feedback linearization. The discrete-time control input is mapped into its continuous-time counterpart using a realizable reconstruction filter (RRF). The underlying control scheme relies on the sampled-data regulator theory based on the discrete-time equivalence of the plant and RRF modeled as impulsive system. This method leads to controller/observer design in discrete time. The working of the entire scheme is dependent on the stability of impulsive observer; hence a Lyapunov-based stability analysis is also included to ensure the stability of a closed-loop system. The working of the proposed scheme along with a comparison with conventional solution is presented, when applied to the control of a 3-degree-of-freedom PUMA 560 robot.

Car—caravan snaking: Part 1: The influence of pintle pin friction

2002 ◽  
Vol 216 (7) ◽  
pp. 707-722 ◽  
Author(s):  
R S Sharp ◽  
M A Alonso Fernández
Keyword(s):  
Mathematical Model ◽  
Linear System ◽  
Coulomb Friction ◽  
Reduced Form ◽  
Design Parameters ◽  
Friction Damping ◽  
Satisfactory Solution ◽  
The Stability ◽  
Parameter Values ◽  
Dependent Behaviour

A brief review of knowledge of car-caravan snaking is carried out. Against the background described, a fairly detailed mathematical model of a contemporary car-trailer system is constructed and a baseline set of parameter values is given. In reduced form, the model is shown to give results in accordance with literature. The properties of the baseline combination are explored using both linear and non-linear versions of the model. The influences of damping at the pintle joint and of several other design parameters on the stability of the linear system in the neighbourhood of the critical snaking speed are calculated and discussed. Coulomb friction damping at the pintle pin is then included and simulations are used to indicate the consequent amplitude-dependent behaviour. The friction damping, especially when its level has to be chosen by the user, is shown to give dangerous characteristics, despite having some capacity for stabilization of the snaking motions. It is concluded that pintle pin friction damping does not represent a satisfactory solution to the snaking problem. The paper sets the scene for the development of an improved solution. This involves actively braking the caravan wheels, which is treated in Part 2 of the paper.

scholarly journals On the Stability of the Endemic Equilibrium of A Discrete-Time Networked Epidemic Model

2020 ◽  
Vol 53 (2) ◽  
pp. 2576-2581
Author(s):  
Fangzhou Liu ◽  
Shaoxuan CUI ◽  
Xianwei Li ◽  
Martin Buss
Keyword(s):  
Discrete Time ◽  
Epidemic Model ◽  
Endemic Equilibrium ◽  
The Stability

scholarly journals Semiglobal exponential input-to-state stability of sampled-data systems based on approximate discrete-time models

Automatica ◽  
2021 ◽  
Vol 131 ◽  
pp. 109742
Author(s):  
Alexis J. Vallarella ◽  
Paula Cardone ◽  
Hernan Haimovich
Keyword(s):  
Discrete Time ◽  
Data Systems ◽  
Sampled Data ◽  
Discrete Time Models
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