A Modified Linear Integral Resonant Controller for suppressing jump-phenomenon and hysteresis in micro-cantilever beam structures

MacLean, J. D.; Aphale, Sumeet S.

doi:10.1016/j.jsv.2020.115365

Cited by 14 publications

(14 citation statements)

References 27 publications

(46 reference statements)

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“…The Time-Delayed Nonlinear Integral Resonant Controller (TDNIRC) is introduced within this work to control the nonlinear oscillation of a parametrically excited system for the first time. Accordingly, the whole system mathematical model can be expressed as follows [25,26]:…”

Section: Mathematical Model and Slow Flow Modulating Equationsmentioning

confidence: 99%

“…Accordingly, the stability chart of the considered system has been plotted depending on Eqs. (24,26) as shown in Fig. 10 for different values of the feedback signal gains ( 1 and 2 ).…”

Section: Nonlinear Integral Resonant Controller With Timedelays ( = + ≠ )mentioning

confidence: 99%

“…Linear and nonlinear forms of the Integral Resonant Controller (IRC) have been extensively introduced to suppress the nonlinear vibration of different nonlinear dynamical systems [21][22][23][24][25][26], where Diaz et al [21] applied the IRC to control the nonlinear vibrations of the lightweight civil engineering structures. Al-Mamun et al [22] utilized the nonlinear integral resonant controller to control the nonlinear oscillations of piezoelectric micro-actuator.…”

Section: Introductionmentioning

confidence: 99%

“…The authors concluded that the applied controller could suppress the system nonlinear vibration effectively. MacLean and Sumeet [26] applied the linear integral resonant control to the bifurcation behaviors of micro-cantilever beam structures. The authors concluded that the proposed control method can eliminate jumpphenomenon and hysteresis of the considered system via increasing the system linear damping coefficient.…”

Section: Introductionmentioning

confidence: 99%

“…In comparing the current work with the previously published articles, it is the first time to apply a linear and nonlinear combination of the integral resonant controller to mitigate the nonlinear oscillation of a parametrically excited system. In addition, the effect of loop-delays has not been discussed before regarding the integral resonant controller [21][22][23][24][25][26]. Finally, the main contribution of this article is introducing the NIRC as a new and effective control strategy in suppressing the nonlinear oscillations of the parametrically excited systems besides the cubicvelocity and cubic-acceleration feedback controllers.…”

Section: Introductionmentioning

confidence: 99%

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Time-Delayed Nonlinear Integral Resonant Controller to Eliminate the Nonlinear Oscillations of a Parametrically Excited System

et al. 2021

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In this work, a nonlinear integral resonant controller is utilized for the first time to suppress the principal parametric excitation of a nonlinear dynamical system. The whole system is modeled as a secondorder nonlinear differential equation (i.e., main system) coupled to a nonlinear first-order differential equation (i.e., controller). The control loop time-delays are included in the studied model. The multiple scales homotopy approach is employed to obtain an approximate solution for the proposed time-delayed dynamical system. The nonlinear algebraic equation that governs the steady-state oscillation amplitude has been extracted. The effects of the time-delays, control gain, and feedback gains on the performance of the suggested controller have been investigated. The obtained results indicated that the controller performance depends on the product of the control and feedback signal gains as well as the sum of the time-delays in the control loop. Accordingly, two simple objective functions have been derived to design the optimum values of the loop-delays, control gain, and feedback gains in such a way that enhances the efficiency of the proposed controller. The analytical and numerical simulations illustrated that the proposed controller could eliminate the system vibrations effectively at specific values of the control and feedback signal gains. In addition, the selection method of the loop-delays that either enhances the control performance or destabilizes the system motion has been explained in detail. INDEX TERMSNonlinear integral resonant controller, Parametric resonance; Linear and nonlinear feedback control; Time-delays; Objective function; Stability chart. LIST OF SYMBOLS ,̇1,̈1Displacement, velocity, and acceleration of the parametrically excited system. ,̇2Displacement and velocity of the nonlinear resonant controller. Linear damping coefficients of the parametrically excited system Linear natural frequency of the parametrically excited system , Cubic nonlinearity coefficients of the parametrically excited system. Excitation force amplitude of the parametrically excited system. Excitation frequency of the parametrically excited system. The control signal gains. , 2The linear and nonlinear feedback signal gains. Feedback gain of the nonlinear resonant controller.1 , 2 Time-delays of the closed loop.I.

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Section: Mathematical Model and Slow Flow Modulating Equationsmentioning

confidence: 99%

“…Accordingly, the stability chart of the considered system has been plotted depending on Eqs. (24,26) as shown in Fig. 10 for different values of the feedback signal gains ( 1 and 2 ).…”

Section: Nonlinear Integral Resonant Controller With Timedelays ( = + ≠ )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Time-Delayed Nonlinear Integral Resonant Controller to Eliminate the Nonlinear Oscillations of a Parametrically Excited System

et al. 2021

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On $$\frac{1}{2}$$-DOF active dampers to suppress multistability vibration of a $$2$$-DOF rotor model subjected to simultaneous multiparametric and external harmonic excitations

Saeed,

Awrejcewicz,

Elashmawey

et al. 2024

Nonlinear Dyn

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This article addresses the bifurcation characteristics and vibration reduction of a $$2$$ 2 -DOF dynamical system simulating the nonlinear oscillation of an asymmetric rotor model subjected to simultaneous multiparametric and external excitations. To suppress the system's vibrations, two $$1/2$$ 1 / 2 -DOF active dampers are attached to the system in linear and cubic nonlinear forms via a magnetic coupling actuator. The closed-loop system model is derived as two differential equations with multi-control terms, including cubic, quantic, and septic, coupled nonlinearly to two first-order systems. Applying perturbation theory, the system model is solved, and the autonomous system describing the closed-loop slow-flow dynamics is obtained. Through numerical algorithms, the motion bifurcation is analyzed using various tools such as 2D and 3D bifurcation diagrams, two-parameter stability charts, basins of attraction, orbit plots, and time response profiles. The analytical investigations confirm that the uncontrolled model behaves like a hardening Duffing oscillator with multistability characteristics, displaying simultaneous mono-stable, bi-stable, tri-stable, or quadri-stable periodic oscillations depending on both the asymmetric nonlinearities and angular velocity. Subsequently, the influence of different control parameters is analyzed to determine the threshold between mono and multi-stability conditions. Finally, optimal control parameters are designed to eliminate multistability characteristics and achieve minimum and safe vibration levels.

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Control of negative imaginary systems exploiting a dissipative characterization

2022

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A Modified Linear Integral Resonant Controller for suppressing jump-phenomenon and hysteresis in micro-cantilever beam structures

Cited by 14 publications

References 27 publications

Time-Delayed Nonlinear Integral Resonant Controller to Eliminate the Nonlinear Oscillations of a Parametrically Excited System

Time-Delayed Nonlinear Integral Resonant Controller to Eliminate the Nonlinear Oscillations of a Parametrically Excited System

On $$\frac{1}{2}$$-DOF active dampers to suppress multistability vibration of a $$2$$-DOF rotor model subjected to simultaneous multiparametric and external harmonic excitations

Control of negative imaginary systems exploiting a dissipative characterization

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