Shape control of piezoelectric bimorph by piezo response function and global optimization algorithms: a comparative study

Sumit, .; Shukla, Rahul; Sinha, A. K.

doi:10.1088/1361-665x/abb06f

Cited by 9 publications

(8 citation statements)

References 94 publications

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“…Simulated annealing (SA), a non-traditional nature inspired optimization technique, is used to determine the electric field of piezoceramic actuators at each iteration. The superiority of SA over the other contemporary non-traditional nature inspired optimizations for the analysis of shape control problems can be found in our previous work [35]. Furthermore, the details of iPRF-based optimization can be found in our recent work [52].…”

Section: Problem Definition and Optimization Methodologymentioning

confidence: 93%

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Measurements for static shape control optimization of silicon mirror using nonlinear piezoceramic actuators

Sumit¹,

Kane²,

Ganguli³

et al. 2023

Smart Mater. Struct.

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In this paper, experimental study for shape control of silicon mirror is done by nonlinear piezoceramic actuator. A piezoelectric unimorph-based silicon mirror (PUSiM) is fabricated using APC 850 piezoceramic for shape control analysis. The piezo response function of all the actuators and profile of PUSiM are measured by confocal sensor at various applied electric fields to verify the nonlinearity of piezoceramic actuator. For comparison, electromechanical coupled finite element model of PUSiM is developed. Recently proposed iterative piezo response function-based optimization is used to calculate the electric field of piezoceramic actuators to achieve the target elliptical profile of PUSiM. At optimum voltage the achieved profile of PUSiM is quite close to the target elliptical profile with 193 nm root-mean-square error. Knowing the nonlinearity inherent in the piezoceramic actuators at high voltages the proposed measurement technique is a way forward for the shape control of structures and deformable mirrors.

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Section: Problem Definition and Optimization Methodologymentioning

confidence: 93%

“…Thus, the analytical/approximate solution is only needed to determine the PRF. The methodology of shape control using PRF-based optimization can be found in literature [35][36][37][38]. The target profile cannot be achieved at optimum electric potential by PRFbased approach in case piezoactuators are nonlinear.…”

Section: Introductionmentioning

confidence: 99%

Measurements for static shape control optimization of silicon mirror using nonlinear piezoceramic actuators

Sumit¹,

Kane²,

Ganguli³

et al. 2023

Smart Mater. Struct.

Self Cite

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“…Static solutions of the piezoelectric Timoshenko beam equations for ψ and w 0 are obtained by inserting ψ ,x + w 0,x x from ( 14) into (15). One finds for the rotation angle by integrating the outcome three times with respect to x…”

Section: General Solution Of a Piezoelectric Timoshenko Beammentioning

confidence: 99%

Shape control of moderately thick piezoelectric beams

Schoeftner

2023

Acta Mech

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The present contribution focuses on shape control of thick beam-type structures. First the governing equations of a multi-layered beam are derived by taking advantage of the Timoshenko assumptions and the constitutive relations of piezoelectric materials. The deflection curves are explicitly given for a piezoelectric cantilever subjected to a polynomial distribution of the vertical load and the applied electric voltage. In order to find a solution for the optimal shape control voltage an objective function, which depends on the quadratic deflection curve over the beam length, is minimized. Finally several benchmark examples are given for thick beams and the outcome is compared to finite element results and previously derived shape control results from the scientific literature that hold for thin piezoelectric beams. The presented shape control method shows a better agreement with the numerical outcome than the analytical shape control results within the Bernoulli-Euler theory, but the desired voltage distribution only slightly differs from the outcome for thin beams. Furthermore it is found that for a given total thickness-to-length ratio piezoelectric bimorph structures may be more difficult to be perfectly controlled than three-layer beams with thin piezoelectric layers. This is due to higher order piezoelectric effects which are not considered by the present theory (e.g. the thickness deformation caused by the thickness piezoelectric coupling constant).

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“…The details of coupling of the Java code with FEM model can be found in our recent work elsewhere. 36,37 The starting population (value of gains) is generated randomly and updated using Equations ( 1) and ( 2) in further iterations. The values of controller gains are replaced by the new updated values in the plant for each computation as presented in Figure 4.…”

Section: Fem Modelling Of Msd Systemmentioning

confidence: 99%

Study of PID controller gain for active vibration control using FEM based particle swarm optimization in COMSOL multiphysics

Sumit

Shukla

Sinha

2022

Journal of Micromanufacturing

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Proportional integral derivative (PID) controllers are widely used to solve different control engineering problems. To know the dynamic behaviour of a working plant by mathematical modelling is quite challenging. Finite element method (FEM) is a well-known technique and broadly used for the modelling of engineering systems. This article presents the FEM-based heuristic approach to design and optimize the PID controllers. The ‘allowed area method’ has been used for the formulation of the objective function followed by the tuning of the PID controller. First, the proposed approach is tested on 2-degree of freedom (DOF) mass-spring-damper (MSD) system. FEM modelling of 2-DOF MSD system with PID controller has been carried out in COMSOL Multiphysics and coupling of particle swarm optimization (PSO) has been carried out with the FEM model of the MSD system, for the optimization of PID controller gain. The FEM results are in good agreement with the analytical one. Next, the established method is applied to design and optimize the PID controller gain to control the vibration of a cantilever beam using piezoelectric actuator. Similar to the MSD system, FEM modelling of PID controller for the smart beam has been carried out in COMSOL Multiphysics, and the coupling of PSO is carried out with the FEM model of the smart beam for the optimization of PID controller gain. Simulation of the uncontrolled and controlled responses of the smart beam is carried out at the optimum controller gain for free vibration and step excitation. The piezoelectric actuator of smart beam has successfully damped the vibration within approximately 2.5 s.

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Shape control of piezoelectric bimorph by piezo response function and global optimization algorithms: a comparative study

Cited by 9 publications

References 94 publications

Measurements for static shape control optimization of silicon mirror using nonlinear piezoceramic actuators

Measurements for static shape control optimization of silicon mirror using nonlinear piezoceramic actuators

Shape control of moderately thick piezoelectric beams

Study of PID controller gain for active vibration control using FEM based particle swarm optimization in COMSOL multiphysics

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