Time-delay feedback control of a cantilever beam with concentrated mass based on the homotopy analysis method

Li, Jia-Xuan; Yan, Yan; Wang, Wen-Quan

doi:10.1016/j.apm.2022.04.016

Cited by 15 publications

(4 citation statements)

References 36 publications

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“…where q ∈ [0, 1]is an embedding parameter, h is a non-zero auxiliary function (denotes the convergence control parameter [23,26,27,44]), L is an auxiliary linear operator which has the property L (0) = 0, u 0 (x) is an initial guess of u (x) and ϕ (x; q) is an unknown function. The zero-order deformation equation of the operator H (ϕ, q) = 0 is considered as follow:…”

Section: Fundamental Of the Hammentioning

confidence: 99%

The Homotopy Analysis Method to Solve the Nonlinear System of Volterra Integral Equations and Applying the Genetic Algorithm to Enhance the Solutions

Ahmed¹,

Al-Hayani

Al-Bayati³

2023

Eur. J. Pure Appl. Math.

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This paper presents the application of the Homotopy Analysis Method (HAM) for solving nonlinear system of Volterra integral equations used to obtain a reasonably approximate solution. The HAM contains the auxiliary parameter h which provides a simple way to adjust and control the convergence region of the solution series. The results show that the HAM is a very effective method as well. The results were compared with the solutions obtained by developing a homotopy analysis method using the genetic algorithm (HAM-GA), considering the residual error function as a fitness function of the genetic algorithm.

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Section: Fundamental Of the Hammentioning

confidence: 99%

The Homotopy Analysis Method to Solve the Nonlinear System of Volterra Integral Equations and Applying the Genetic Algorithm to Enhance the Solutions

Ahmed¹,

Al-Hayani

Al-Bayati³

2023

Eur. J. Pure Appl. Math.

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“…They presented a suitable trend for determining the Lagrange multiplier by considering the effects of concentrated mass on natural frequencies in linear and nonlinear states. Xuan et al [ 30 ] investigated the strong nonlinear vibration of a cantilever beam system with a concentrated mass at an intermediate position controlled by displacement and velocity time delay.…”

Section: Introductionmentioning

confidence: 99%

Improved calculation method for dry modal analysis of four-stage centrifugal-pump rotor system based on concentrated-mass method

Li,

Wei,

Gao

et al. 2024

PLoS ONE

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To improve the accuracy of modal analysis for a four-stage centrifugal-pump rotor system with a balancing disc based on the concentrated-mass analytical method, a simplified concentrated mass mathematical model and an ANSYS simulation model are established. The results from these two models are compared to determine factors that cause significant differences in the mode shapes. Subsequently, an optimized mathematical model based on the corrected mass moment of an inertia matrix and stiffness correction coefficients is proposed, and the effectiveness of this optimized mathematical model is validated using a four-stage centrifugal pump with back blades. The results show that the natural frequencies obtained from the ANSYS simulations are consistently higher than those obtained using the analytical method. The simplification of the moment of inertia at the impeller and balancing disc contributes primarily to the calculated errors. The optimized mathematical model reduces the errors in the natural frequencies from 12.96%, 12.13%, 9.96%, 5.85%, and 8.74% to 2.45%, 1.56%, 0.65%, 5.34%, and 2.28%, respectively. The optimization of natural frequencies offers better performance at lower-order modes, whereas its effects on higher-order modes are less significant. The optimization method is applicable to centrifugal pumps with back blades and reduces the error in theoretical calculations, based on reductions in the concentrated mass from 13.11%, 12.85%, 9.91%, and 7.2% to 3.7%, 3.86%, 0.57%, and 2.87%, respectively, thus further confirming the feasibility of the optimized model design.

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“…Time delay is often encountered in various engineering and communication systems, and time delay in dynamic systems is often the main source of instability and performance degradation. Therefore, for T-S fuzzy systems with time delay, there are some controller design results [24][25][26][27] and FE results 8,[28][29][30][31][32] recently. Especially, by amending the composite Lyapunov approach, several fault-tolerant control laws for singularly perturbed systems with actuator faults and disturbances are proposed in literature 28 to overcome the fast-slow decomposition requirement conditions.…”

Section: Introductionmentioning

confidence: 99%

“…Figures 21,23 and 25 respectively show the output curves of the actual fault value and the observer estimation value when the perturbation parameters are different. It can be seen from the figure that when the perturbation parameters are 𝜀 = 𝜀 ver1 = 0.54(𝜀 ver1 ∈ (0, 𝜀 * ]) and 𝜀 = 𝜀 * opt = 0.55, the anti disturbance ability and stability performance are similar, but when 𝜀 = 𝜀 ver2 = 0.56(𝜀 ver2 ∉ (0, 𝜀 * ]), compared with the simulation track, the fault estimation error at 𝜀 = 𝜀 * opt = 0.55 is smaller, and the ability to suppress external disturbances is stronger.Figures 22,24 and 26 describe the corresponding system estimation error curves. As can be seen from the figure, the method proposed in this paper has a small state error…”

mentioning

confidence: 99%

Multi‐objective optimization‐based robust fault estimation observer design for fuzzy singularly perturbed systems with time‐varying state delays

Zeng

Sun

Huang

et al. 2022

Optim Control Appl Methods

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In this paper, the problem of multi-objective robust fault estimation based on observer is addressed for T-S fuzzy nonlinear singularly perturbed systems with time-varying state delay and external disturbance. Under H ∞ performance constraint, a fuzzy augmented fault estimation observer is introduced to improve the performance of actuator and sensor fault estimation simultaneously. The sufficient conditions for the existence of fault estimator are given in the form of LMIs, where 𝜀-dependent Lyapunov function is considered. The given multi-objective fault estimator design strategy has a good ability to suppress external disturbance and ensure the estimation accuracy and convergence rate work well for all 𝜀 ∈ (0, 𝜀]. Then the largest stability bound and the best attenuation capacity are guaranteed by deriving a modified optimal algorithm. Finally, two examples are given to illustrate the feasibility and correctness of the proposed design method.

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Time-delay feedback control of a cantilever beam with concentrated mass based on the homotopy analysis method

Cited by 15 publications

References 36 publications

The Homotopy Analysis Method to Solve the Nonlinear System of Volterra Integral Equations and Applying the Genetic Algorithm to Enhance the Solutions

The Homotopy Analysis Method to Solve the Nonlinear System of Volterra Integral Equations and Applying the Genetic Algorithm to Enhance the Solutions

Improved calculation method for dry modal analysis of four-stage centrifugal-pump rotor system based on concentrated-mass method

Multi‐objective optimization‐based robust fault estimation observer design for fuzzy singularly perturbed systems with time‐varying state delays

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