Optimal Design of Vibrating Systems Through Partial Eigenstructure Assignment

Belotti, Roberto; Richiedei, Dario; Trevisani, Alberto

doi:10.1115/1.4033505

Cited by 23 publications

(21 citation statements)

References 18 publications

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“…The crux is defining such a cost function, or performance index, that properly represents the physical problem and its relationship with the desired performances and should be easily solvable (Yan and Wang 2020). Other features, such as convexity to ensure that global optimal solutions can be found regardless of the initial guess (Belotti et al 2016), are also valuable to ensure meaningful results and actual optimal results. A reliable definition of the cost function imposes considering the presence of the controller too, whenever the structure operates with closed-loop controllers.…”

Section: Performance Optimization Through Concurrent Mechanical and Cmentioning

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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Section: Performance Optimization Through Concurrent Mechanical and Cmentioning

confidence: 99%

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

Belotti

Richiedei

Trevisani

2020

Struct Multidisc Optim

Self Cite

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“…where N ∈ R n do f ×n do f can be any nonsingular matrix; here it is considered N = M. The quadratic (Equations (12) and (13)) and the generalized (Equations (14) and (15)) eigenvalue problems have the same 2n do f eigenvalues, whereas the corresponding eigenvectors are correlated by the following relations,…”

Section: Modal Analysis For Systems With Nonsymmetric Matricesmentioning

confidence: 99%

“…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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“…Examples are resonant conveyors, employed for material moving [20,21] and ultrasonic horns, used for cleaning, welding, cutting, machining and drilling [22,23]. To obtain a perfect match between the desired motion and the resonator natural dynamics, the resonant system is typically modified through changes in mass and/or stiffness parameters [24,25]. Modifications of system parameters are generally needed also to make a robot resonant [26], as well as to exploit its free response.…”

Section: Introductionmentioning

confidence: 99%

Natural Motion for Energy Saving in Robotic and Mechatronic Systems

et al. 2019

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Energy saving in robotic and mechatronic systems is becoming an evermore important topic in both industry and academia. One strategy to reduce the energy consumption, especially for cyclic tasks, is exploiting natural motion. We define natural motion as the system response caused by the conversion of potential elastic energy into kinetic energy. This motion can be both a forced response assisted by a motor or a free response. The application of the natural motion concepts allows for energy saving in tasks characterized by repetitive or cyclic motion. This review paper proposes a classification of several approaches to natural motion, starting from the compliant elements and the actuators needed for its implementation. Then several approaches to natural motion are discussed based on the trajectory followed by the system, providing useful information to the researchers dealing with natural motion.

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Optimal Design of Vibrating Systems Through Partial Eigenstructure Assignment

Cited by 23 publications

References 18 publications

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

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

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

Natural Motion for Energy Saving in Robotic and Mechatronic Systems

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