Pole assignment in vibrating systems with time delay: An approach embedding an a-priori stability condition based on Linear Matrix Inequality

Belotti, Roberto; Richiedei, Dario

doi:10.1016/j.ymssp.2019.106396

Cited by 19 publications

(14 citation statements)

References 26 publications

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“…If τ f = τ g = 0 then P c (s) is a polynomial and therefore the system features 2N eigenpairs that completely describe the system dynamics. Conversely, as studied in this paper, if the time delays are not null, the characteristic equation has an infinite number of roots: 2N roots are the "primary roots", while an infinite number of "secondary roots" (often denoted as the "latent roots") arise [21,24].…”

Section: Definitionsmentioning

confidence: 95%

“…While, k h is the solution of the homogeneous equation Gk h = 0. Finally, the solution of Equation ( 8) is more conveniently formulated as follows [21,26,27]:…”

Section: Placement Of the N P Closed-loop Polesmentioning

confidence: 99%

“…The papers previously quoted require evaluating a posteriori the stability of the closedloop system. Recently, a two-stage method that embeds an a priori stability condition has been developed by Belotti and Richiedei in [21]. It relies on the powerful theory of Linear Matrix Inequalities (LMI) and ensures the placement of the dominant poles of interest while imposing stability of the remaining unassigned poles, either those due to the mechanical resonances and those induced by the time delay.…”

Section: Introductionmentioning

confidence: 99%

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Vibration Control of a Two-Link Flexible Robot Arm with Time Delay through the Robust Receptance Method

et al. 2021

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This paper proposes a method for active vibration control to a two-link flexible robot arm in the presence of time delay, by means of robust pole placement. The issue is of practical and theoretical interest as time delay in vibration control can cause instability if not properly taken into account in the controller design. The controller design is performed through the receptance method to exactly assign a pair of pole and to achieve a given stability margin for ensuring robustness to uncertainty. The desired stability margin is achieved by solving an optimization problem based on the Nyquist stability criterion. The method is applied on a laboratory testbed that mimic a typical flexible robotic system employed for pick-and-place applications. The linearization assumption about an equilibrium configuration leads to the identification of the local receptances, holding for infinitesimal displacements about it, and hence applying the proposed control design technique. Nonlinear terms, due to the finite displacements, uncertainty, disturbances, and the coarse encoder quantization, are effectively handled by embedding the robustness requirement into the design. The experimental results, and the consistence with the numerical expectations, demonstrate the method effectiveness and ease of application.

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Section: Definitionsmentioning

confidence: 95%

“…While, k h is the solution of the homogeneous equation Gk h = 0. Finally, the solution of Equation ( 8) is more conveniently formulated as follows [21,26,27]:…”

Section: Placement Of the N P Closed-loop Polesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Vibration Control of a Two-Link Flexible Robot Arm with Time Delay through the Robust Receptance Method

et al. 2021

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“…Active approaches exploit the energy introduced in the system by external actuators based on the information of some sensors to perform the EA. e state of the art in active control spans from model-based techniques (see, e.g., [5][6][7][8][9]) to receptance-based methods (see, e.g., [10][11][12][13]).…”

Section: Introductionmentioning

confidence: 99%

Robust Assignment of Natural Frequencies and Antiresonances in Vibrating Systems through Dynamic Structural Modification

Caracciolo

Richiedei

Tamellin

2021

Shock and Vibration

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This paper proposes a novel method for the robust partial assignment of natural frequencies and antiresonances, together with the partial assignment of the related eigenvectors, in lightly damped linear vibrating systems. Dynamic structural modification is exploited to assign the eigenvalues, either of the system or of the adjoint system, together with their sensitivity with respect to some parameters of interest. To handle with constraints on the feasible modifications, the inverse eigenvalue problem is cast as a minimization problem and a solution method is proposed through homotopy optimization. Variables lifting for bilinear and trilinear terms, together with bilinear and double-McCormick’s constraints, are exploited to provide a convexification of the problem and to boost the attainment of the global optimum. The effectiveness of the proposed method is assessed through four numerical examples.

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“…In [26], the problem of stabilization of linear systems with both input and state delays by observer-predictors was studied. In the paper [27], the assignment of the poles of a second-order vibrating system through state feedback with one lumped delay was studied by means of the linear matrix inequality (LMI) approach. A partial pole assignment approach was presented in [28] for second-order systems with time delay.…”

Section: Introductionmentioning

confidence: 99%

Arbitrary Coefficient Assignment by Static Output Feedback for Linear Differential Equations with Non-Commensurate Lumped and Distributed Delays

Зайцев

Kim

2021

Mathematics

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We consider a linear control system defined by a scalar stationary linear differential equation in the real or complex space with multiple non-commensurate lumped and distributed delays in the state. In the system, the input is a linear combination of multiple variables and its derivatives, and the output is a multidimensional vector of linear combinations of the state and its derivatives. For this system, we study the problem of arbitrary coefficient assignment for the characteristic function by linear static output feedback with lumped and distributed delays. We obtain necessary and sufficient conditions for the solvability of the arbitrary coefficient assignment problem by the static output feedback controller. Corollaries on arbitrary finite spectrum assignment and on stabilization of the system are obtained. We provide an example illustrating our results.

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Pole assignment in vibrating systems with time delay: An approach embedding an a-priori stability condition based on Linear Matrix Inequality

Cited by 19 publications

References 26 publications

Vibration Control of a Two-Link Flexible Robot Arm with Time Delay through the Robust Receptance Method

Vibration Control of a Two-Link Flexible Robot Arm with Time Delay through the Robust Receptance Method

Robust Assignment of Natural Frequencies and Antiresonances in Vibrating Systems through Dynamic Structural Modification

Arbitrary Coefficient Assignment by Static Output Feedback for Linear Differential Equations with Non-Commensurate Lumped and Distributed Delays

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