Pole assignment for control of flexible link mechanisms

Ouyang, Huajiang; Richiedei, Dario; Trevisani, Alberto

doi:10.1016/j.jsv.2013.01.004

Cited by 26 publications

(17 citation statements)

References 34 publications

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“…To emphasise the advantage of MMVSTDC for the vibration suppression of the smart beam, a conventional velocity feedback control (CVFC) (Ouyang et al, 2013) is designed based on the pole placement theory as a comparison to the MMVSTDC. Its control law is expressed aswhere boldv is the output velocity vector and boldR is the matrix designed by the pole placement theory.…”

Section: Simulation and Experimental Verificationmentioning

confidence: 99%

Adaptive modal vibration control for smart flexible beam with two piezoelectric actuators by multivariable self-tuning control

Zhang

2020

Journal of Vibration and Control

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It has been popular for decades that the vibrations of space structures are suppressed with smart actuators. However, the higher mode vibrations are often motivated when a control strategy is applied to attenuate the vibration for the smart structures. Moreover, if the multi-mode vibration of a smart structure is suppressed with multi-actuators, a proper multivariable control law will be adopted to solve the coupling problem caused by the multi-actuators of the smart structure. Therefore, in the paper, a decoupling technique for two modal vibrations of a smart flexible beam with two piezoelectric patches is adopted by adaptive control. The proposed control law is designed with a multivariable minimum variance self-tuning control. Considering the first two orders of modal vibrations, two piezoelectric patches are configured on the flexible beam according to the strain of the first two orders of modal vibrations along the longitudinal direction of the beam. A dynamical model for the flexible beam with two piezoelectric actuators is constructed by the mode superposition method. With the dynamical model, simulations are implemented to suppress the free vibration of the flexible beam. Moreover, experiments are carried out to verify the effectiveness of the multivariable minimum variance self-tuning control for vibration suppression of the flexible structure. The control results clearly show that the free vibration amplitude of the cantilevered beam with two control voltages applied to the two piezoelectric patches is less than that with one control voltage applied to the first piezoelectric actuator. Thus, multivariable minimum variance self-tuning control is a more efficient approach for suppressing multimodal vibration for a smart flexible beam with two piezoelectric actuators compared with the conventional velocity feedback control.

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Section: Simulation and Experimental Verificationmentioning

confidence: 99%

Adaptive modal vibration control for smart flexible beam with two piezoelectric actuators by multivariable self-tuning control

Zhang

2020

Journal of Vibration and Control

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“…The control gains have been computed through the method proposed by Ram and Mottershead (2007), and subsequently extended in Ouyang (2011) and Ouyang et al (2013) for asymmetric systems, which provides an effective and reliable solution for the case of rank-one control. However, any method could be used.…”

Section: Experimental Assessment Of the Eigenstructure Assignmentmentioning

confidence: 99%

Multi-domain optimization of the eigenstructure of controlled underactuated vibrating systems

Belotti

Richiedei

Trevisani

2020

Struct Multidisc Optim

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The paper proposes a multi-domain approach to the optimization of the dynamic response of an underactuated vibrating linear system through eigenstructure assignment, by exploiting the concurrent design of the mechanical properties, the regulator and state observers. The approach relies on handling simultaneously mechanical design and controller synthesis in order to enlarge the set of the achievable performances. The underlying novel idea is that structural properties of controlled mechanical systems should be designed considering the presence of the controller through a concurrent approach: this can considerably improve the optimization possibilities. The method is, first, developed theoretically. Starting from the definition of the set of feasible system responses, defined through the feasible mode shapes, an original formulation of the optimality criterion is proposed to properly shape the allowable subspace through the optimal modification of the design variables. A proper choice of the modifications of the elastic and inertial parameters, indeed, changes the space of the allowable eigenvectors that can be achieved through active control and allows obtaining the desired performances. The problem is then solved through a rank-minimization with constraints on the design variables: a convex optimization problem is formulated through the “semidefinite embedding lemma” and the “trace heuristics”. Finally, experimental validation is provided through the assignment of a mode shape and of the related eigenfrequency to a cantilever beam controlled by a piezoelectric actuator, in order to obtain a region of the beam with negligible oscillations and the other one with large oscillations. The results prove the effectiveness of the proposed approach that outperforms active control and mechanical design when used alone.

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“…The dynamic behavior of a mechanical system can be easily studied by means of modal analysis, which provides the system modal parameters or characteristics (i.e., natural frequencies, mode shapes, and damping ratios). The knowledge of the modal characteristics is a fundamental requirement for the implementation of several advanced model-based engineering techniques, such as motion planning [1], control design [2,3], stability analysis [4,5], model reduction [6][7][8][9][10], model updating [11][12][13], and structural modification [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Flexible-Link Multibody System Eigenvalue Analysis Parameterized with Respect to Rigid-Body Motion

Palomba¹,

Vidoni²

2019

Applied Sciences

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The dynamics of flexible multibody systems (FMBSs) is governed by ordinary differential equations or differential-algebraic equations, depending on the modeling approach chosen. In both the cases, the resulting models are highly nonlinear. Thus, they are not directly suitable for the application of the modal analysis and the development of modal models, which are very useful for several advanced engineering techniques (e.g., motion planning, control, and stability analysis of flexible multibody systems). To define and solve an eigenvalue problem for FMBSs, the system dynamics has to be linearized about a selected configuration. However, as modal parameters vary nonlinearly with the system configuration, they should be recomputed for each change of the operating point. This procedure is computationally demanding. Additionally, it does not provide any numerical or analytical correlation between the eigenpairs computed in the different operating points. This paper discusses a parametric modal analysis approach for FMBSs, which allows to derive an analytical polynomial expression for the eigenpairs as function of the system configuration, by solving a single eigenvalue problem and using only matrix operations. The availability of a similar modal model, which explicitly depends on the system configuration, can be very helpful for, e.g., model-based motion planning and control strategies towards to zero residual vibration employing the system modal characteristics. Moreover, it allows for an easy sensitivity analysis of modal characteristics to parameter uncertainties. After the theoretical development, the method is applied and validated on a flexible multibody system, specifically using the Equivalent Rigid Link System dynamic formulation. Finally, numerical results are presented and discussed.

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Pole assignment for control of flexible link mechanisms

Cited by 26 publications

References 34 publications

Adaptive modal vibration control for smart flexible beam with two piezoelectric actuators by multivariable self-tuning control

Adaptive modal vibration control for smart flexible beam with two piezoelectric actuators by multivariable self-tuning control

Multi-domain optimization of the eigenstructure of controlled underactuated vibrating systems

Flexible-Link Multibody System Eigenvalue Analysis Parameterized with Respect to Rigid-Body Motion

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