Controlling friction-induced instability by recursive time-delayed acceleration feedback

The present article focuses on suppressing mode-coupling instability in frictional systems, which can cause unwanted vibrations such as squeal in braking systems. Mode-coupling instability occurs when two or more modes of a system approach each other. This article proposes the use of resonant velocity feedback control to eliminate friction-induced oscillations generated by mode-coupling instability. A two degree-of-freedom linear model is used to capture the instability due to friction-induced mode coupling. The efficacy of the control is demonstrated through linear stability analysis, and by optimizing control parameters using pole crossover method to minimize the transient time of the response. The robustness analysis demonstrates the ability of the control to effectively mitigate the instability even under parametric perturbations. The controlled system is simulated in MATLAB Simulink to validate analytical results. The effects of time delay, which is commonly present in feedback systems, are also investigated. Finally, the effectiveness of the control is studied in the presence of nonlinearity in the system. The nonlinear dynamics are analyzed by creating bifurcation diagrams with different bifurcation parameters.

Section: Introductionmentioning

confidence: 99%

Efficacy of velocity feedback control for suppression of the friction-induced oscillation due to mode-coupling instability in a two degrees-of-freedom mechanical system

Kumar

Malas

2023

“…Nechak (2019) adopted the nonlinear control scheme based on the feedback linearization approach to suppress the mode-coupling instabilities. Applications of time-delayed feedback control have been discussed recently (Chatterjee, 2007b; Chatterjee and Mahata, 2009a, 2009b; Das and Mallik, 2006). Adaptive fuzzy, neuro-fuzzy and data mining technique based compensation methods are proposed by Wang et al (2011, 2012, 2013) to suppress friction-induced instabilities.…”

Section: Introductionmentioning

confidence: 99%

Effect of high-frequency excitation on friction induced vibration caused by the combined action of velocity-weakening and mode-coupling

Sahoo

Chatterjee

2020

The present article studies the effects of both tangential and normal high-frequency excitations on a two-degree-of-freedom moving-mass-on-belt which represents a minimal model incorporating both velocity-weakening instability (so-called Stribeck effect) and mode-coupling instability (so-called binary flutter). The method of direct partition of motion is employed for studying the characteristics of the system in slow time scale. Linear stability analysis is performed near the equilibrium point of the system for both with and without sinusoidal high-frequency excitation. It is observed that the instability can be suppressed by the tangential high-frequency excitation only for a specific range of strength of excitation. However, stability does not improve under normal high-frequency excitations, though amplitude of the self-excited oscillation can be controlled to some extent. Direct numerical simulations are carried out in MATLAB SIMULINK to validate the analytical predictions.

“…Das and Mallik (2006) use an experimental setup of friction-driven system to propose the efficacy of a time-delayed PD feedback controlof forced vibration as well as friction-induced vibrations due to the Stribeck effect. The time-delayed displacement feedback control of different types of friction-induced instabilities (Chatterjee, 2007) and the ‘recursive time-delayed acceleration feedback control’ (Chatterjee and Mahata, 2009) are some of the valuable contributions in this field of active control. Heckl and Abrahams (1996) proposed a method of active control of friction-induced vibration by superimposition of a tangential force on the frictional force.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear control of stick-slip oscillations by normal force modulation

Nath

Chatterjee

2016

The present paper investigates the efficacy of controlling friction induced vibration by normal load modulation. Friction-induced self-excited vibration, attributed to the low-velocity drooping characteristics of friction (Stribeck effect), is modelled by a mass-on-belt model where the normal force of the mass is being modulated based on the acceleration feedback followed by a second order filtering. Polynomial model is employed to study the friction phenomenon between the mass and the belt. The pole crossover design (to ensure faster transient and greater relative stability) is implemented to optimize the filter parameters with an independent choice of the belt velocity and control gain. These sets of optimized parameter values are then used to construct local stability boundaries in the plane of control parameters. Numerical simulations in a MATLAB SIMULINK model and bifurcation diagrams obtained in AUTO (while using belt velocity as the bifurcation parameter) indicate that a significantly small-amplitude limit cycle resulting from a supercritical Hopf bifurcation stabilizes the extreme low velocity region at higher values of the control gain. With the increase of the control gain the subcritical nature of Hopf bifurcation changes to a supercritical one. The efficacy of this optimization (based on numerical results) in the delicate low velocity region is also enclosed.