Parametric optimal bounded feedback control for smart parameter-controllable composite structures

Ying, Z. G.; Ni, YQ; Duan, Yuanfeng

doi:10.1016/j.jsv.2014.11.018

Cited by 15 publications

(6 citation statements)

References 29 publications

(78 reference statements)

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“…Increasing structural damping is a common strategy for resonant response suppression. Damping produced by passive control is limited, whereas active feedback control can produce large artificial damping, which is incorporated in damping coefficient of system (9). The effect of the damping on vibration response characteristics will be explored for control at the midpoint.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…where the parameter β is set as a small value, e.g., 10 −5 . Equation (34) presents a general iteration algorithm for the harmonic balance solution to periodic vibration of the nonlinear system (9). However, a computational expense of the iterative Equation ( 34) is large due to coupling high dimensions.…”

Section: Iteration Procedures For Vibration Responsementioning

confidence: 99%

“…The controlled beam can be converted into a multi-degree-of-freedom (MDOF) nonlinear system. Feedback control of MDOF systems has been studied [5][6][7][8][9][10][11][12][13][14]. However, the control effectiveness of a large damping gain on vibration mitigation of the nonlinear meso beam needs to be studied further.…”

Section: Introductionmentioning

confidence: 99%

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Vibrational Amplitude Frequency Characteristics Analysis of a Controlled Nonlinear Meso-Scale Beam

Ying

2021

Actuators

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Vibration response and amplitude frequency characteristics of a controlled nonlinear meso-scale beam under periodic loading are studied. A method including a general analytical expression for harmonic balance solution to periodic vibration and an updated cycle iteration algorithm for amplitude frequency relation of periodic response is developed. A vibration equation with the general expression of nonlinear terms for periodic response is derived and a general analytical expression for harmonic balance solution is obtained. An updated cycle iteration procedure is proposed to obtain amplitude frequency relation. Periodic vibration response with various frequencies can be calculated uniformly using the method. The method can take into account the effect of higher harmonic components on vibration response, and it is applicable to various periodic vibration analyses including principal resonance, super-harmonic resonance, and multiple stationary responses. Numerical results demonstrate that the developed method has good convergence and accuracy. The response amplitude should be determined by the periodic solution with multiple harmonic terms instead of only the first harmonic term. The damping effect on response illustrates that vibration responses of the nonlinear meso beam can be reduced by feedback control with certain damping gain. The amplitude frequency characteristics including anti-resonance and resonant response variation have potential application to the vibration control design of nonlinear meso-scale structure systems.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Iteration Procedures For Vibration Responsementioning

confidence: 99%

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Vibrational Amplitude Frequency Characteristics Analysis of a Controlled Nonlinear Meso-Scale Beam

Ying

2021

Actuators

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“…The stochastic optimal control for linear and nonlinear systems has been studied and many control strategies have been pre-sented. [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] In general, the separation theorem is used to convert the original system with noisy observations into another system with complete observations and then the optimal control law is determined based on the stochastic dynamical programming principle. However, for the nonlinear stochastic system with noisy observations, the separation theorem yields an estimated system with infinite-dimensional probability density, such that the optimal control cannot be determined.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Minimax Vibration Control for Uncertain Nonlinear Quasi-Hamiltonian Systems with Noisy Observations

Ying¹,

Hu²,

Huan³

2019

The International Journal of Acoustics and Vibration

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A stochastic minimax control strategy for uncertain nonlinear quasi-Hamiltonian systems with noisy observations under random excitations is proposed based on the extended Kalman filter and minimax stochastic dynamical programming principle. A structure system with smart sensors and actuators is modeled as a controlled, excited and dissipative Hamiltonian system with noisy observations. The differential equations for the uncertain nonlinear quasi-Hamiltonian system with control and observation under random excitation are given first. The estimated nonlinear stochastic control system with uncertain parameters is obtained from the uncertain quasi-Hamiltonian system with noisy observation. In this case, the optimally estimated state is determined by the observation based on the extended Kalman filter. The dual dynamical programming equation for the estimated uncertain system is then obtained based on the minimax stochastic dynamical programming principle. The worst-case disturbances are determined for bounded uncertain parameters and the optimal control law is determined for the worst case by the programming equation. The proposed minimax control strategy is applied to two uncertain nonlinear stochastic systems with controls and noisy observations. The control effectiveness for the stochastic vibration response reductions of the systems is illustrated with numerical results. The proposed minimax control strategy is applicable to general uncertain nonlinear multi-degree-of-freedom structure systems with noisy observations under random excitations.

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“…29 The stochastic optimal controls for linear and nonlinear systems have been studied and many control strategies have been presented. [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] However, the stochastic optimal control for a nonlinear system with a noised observation was only considered in several studies. 43 Under a specified condition, the separation theorem was applied to convert the nonlinear stochastic system with a noised observation into a completely observable linear system for determining optimal control, but the application is strongly limited.…”

Section: Introductionmentioning

confidence: 99%

Optimal Vibration Control for Structural Quasi-Hamiltonian Systems with Noised Observations

Ying¹,

Hu²,

Huan³

2017

IJAV

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A structural control system with smart sensors and actuators is considered and its basic dynamic equations are given. The controlled, stochastically excited, and dissipative Hamiltonian system with a noised observation is obtained by discretizing the nonlinear stochastic smart structure system. The estimated nonlinear stochastic system with control is obtained, in which the optimally estimated state is determined by the observation based on the extended Kalman filter. Then the dynamical programming equation for the estimated system is obtained based on the stochastic dynamical programming principle. From this, the optimal control law dependent on the estimated state is determined. The proposed optimal control strategy is applied to two nonlinear stochastic systems with controls and noised observations. The control efficacy for stochastic vibration response reductions of the systems is illustrated with numerical results. The proposed optimal control strategy is applicable to general nonlinear stochastic structural systems with smart sensors, smart actuators and noised observations.

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Parametric optimal bounded feedback control for smart parameter-controllable composite structures

Cited by 15 publications

References 29 publications

Vibrational Amplitude Frequency Characteristics Analysis of a Controlled Nonlinear Meso-Scale Beam

Vibrational Amplitude Frequency Characteristics Analysis of a Controlled Nonlinear Meso-Scale Beam

Stochastic Minimax Vibration Control for Uncertain Nonlinear Quasi-Hamiltonian Systems with Noisy Observations

Optimal Vibration Control for Structural Quasi-Hamiltonian Systems with Noised Observations

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