Vibration boundary control of Timoshenko micro-cantilever using piezoelectric actuators

Mehrvarz, Amin; Salarieh, Hassan; Alasty, Aria; Vatankhah, Ramin

doi:10.24200/sci.2017.4327

Cited by 8 publications

(4 citation statements)

References 29 publications

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“…In (23), L p (Ω) is a Lebesgue space which is the space of measurable functions whose L p norm is bounded, equation (24), and H k (Ω) is a Hilbert space that is defined in a Sobolev space W 2k (Ω) in (25).…”

Section: A Boundary Controlmentioning

confidence: 99%

“…In these methods, it is clear that the main system has been changed, and the infinite dimensions of the system are reduced to some finite dimensions of freedom, so the obtained controller is suitable when only a few specified modes of the system dynamics are excited which may not be guaranteed in realworld applications. Another group of controllers is boundary control methods that design the controller directly for the infinite dimensional main system and do not change it [22]- [24]. These controllers have many functions such as marine riser [25]- [27] and robotic [28].…”

Section: Introductionmentioning

confidence: 99%

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Boundary Vibration Control of Strain Gradient Timoshenko Micro-Cantilevers Using Piezoelectric Actuators

Mehrvarz¹,

Salarieh²,

Alasty³

et al. 2018

Preprint

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In this paper, the problem of boundary control of vibration in a clamped-free strain gradient Timoshenko microcantilever is studied. For getting systems closer to reality, the force/moment exertion conditions should be modeled. To this end, a piezoelectric layer is laminated on one side of the beam and the controlling actuation is applied through the piezoelectric voltage. The beam and piezoelectric layer are coupled and modeled at the same time and the dynamic equations and boundary conditions of the system are achieved using the Hamilton principle. To achieve the purpose of eliminating vibration of the system, the control law is obtained from a Lyapunov function using LaSalle's invariant set theorem. The control law has a form of feedback from the spatial derivatives of boundary states of the beam. The finite element method using the strain gradient Timoshenko beam element has been used and then the simulation is performed to illustrate the impact of the proposed controller on the microbeam.

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Section: A Boundary Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Boundary Vibration Control of Strain Gradient Timoshenko Micro-Cantilevers Using Piezoelectric Actuators

Mehrvarz¹,

Salarieh²,

Alasty³

et al. 2018

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, there has been little consideration of using GSMC for distributed parameter system (DPS). It is due to the existence of PDE form in the DPS dynamics, such that GSMC for DPS become more difficult and complicated In another hand, for the sake of Timoshenko beam, vibration control is achieved under input backlash [15], uncertainties [16], a cooperative control problem [17], input and output constraint [18], input dead zone [19], piezoelectric actuators [20], optimal piezoelectric vibration control [21], output constraint and input backlash [22], contact-force control problem [23].…”

Section: Introductionmentioning

confidence: 99%

Robust Global Boundary Vibration Control of Uncertain Timoshenko Beam With Exogenous Disturbances

Eshag

Sun

et al. 2020

IEEE Access

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In this paper, the dynamics solution problem and the boundary control problem for the Timoshenko beam under uncertainties and exogenous disturbances are addressed. The dynamics of the Timoshenko beam are represented by one non-homogenous hyperbolic partial differential equation (PDE), one homogenous hyperbolic PDE, and three ordinary differential equations (ODEs). The authors suggest a method of lines (MOL) for obtaining the dynamics of the Timoshenko beam in the form of the ODE formula instead of the PDE formula. A global sliding mode boundary control (GSMBC) is designed for vibration reduction of the Timoshenko beam influenced by uncertainties, distributed disturbance, displacement boundary disturbance, and rotation boundary disturbance. Chattering phenomena are avoided by using exponential reaching law reinforced by a relay function. Along the time and position axis: a) the boundary displacements and rotation of the Timoshenko beam are converged to equilibrium; b) the distributed vibrations on both displacements and rotation axis of the Timoshenko are attenuated; c) influence of the exogenous disturbances and system parameters uncertainties are compensated. By using the Lyapunov direct approach, exponential convergence and robustness of the closed-loop system are guaranteed. Finally, simulations are carried out to show that the proposed GSMBC-based MOL scheme is effective for vanishing the vibrations of the Timoshenko beam under uncertainties and external disturbances. INDEX TERMS Boundary control, distributed parameter system (DPS), global sliding mode control (GSMC), method of lines (MOL), partial differential equation (PDE), Timoshenko beam.

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“…Vibration analysis of piezoelectric materials has increased in recent years and various researches have been done in this field such as energy harvesting and piezoelectric sensors (Lundstrom and Jalili, 2018a, 2018b). Therefore, the piezoelectric sensor and actuator are used to apply force and for getting feedback from the boundary of the system (Mehrvarz et al., 2018a, Mehrvarz et al, 2018b).…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis and control of fluid containers using piezoelectrically-excited side wall

Mehrvarz

Ardekani

Khodaei

et al. 2019

Journal of Vibration and Control

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The vibration analysis and control of containers with heavy loaded fluid is undertaken in this paper. The problem of fluid–structure vibration is viewed and analyzed from several viewpoints including both analytical methods and numerical techniques. In order to effectively control the fluid–structure vibration, one of the side walls is made flexible where two piezoelectric patches are utilized to sense the distributed displacements resulting from fluid-structure movements, while the other one is used to actively control the vibration. For this, a boundary control technique is used to actively control the multi-modal vibration of fluid–structure. The simulation results for the analytical models are further validated using a comprehensive finite element method. Before applying the proposed controller, the results show that the fluid vibration is different in different heights and distances. However, the simulation results indicate that the piezoelectrically-excited beam is able to suppress the vibrations of all the positions very effectively and quickly. These results prove the feasibility of utilizing piezoelectrically-excited beams in vibration control of fluid–structure.

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Vibration boundary control of Timoshenko micro-cantilever using piezoelectric actuators

Cited by 8 publications

References 29 publications

Boundary Vibration Control of Strain Gradient Timoshenko Micro-Cantilevers Using Piezoelectric Actuators

Boundary Vibration Control of Strain Gradient Timoshenko Micro-Cantilevers Using Piezoelectric Actuators

Robust Global Boundary Vibration Control of Uncertain Timoshenko Beam With Exogenous Disturbances

Vibration analysis and control of fluid containers using piezoelectrically-excited side wall

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