Active control of linear vibrating systems for antiresonance assignment with regional pole placement

Richiedei, Dario; Tamellin, Iacopo

doi:10.1016/j.jsv.2020.115858

Cited by 20 publications

(15 citation statements)

References 27 publications

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“…In addition, also combinations with sliding mode-type control procedures such as those in [ 36 ] can be investigated. Finally, it should be pointed out that the technique is readily applicable also to higher dimensional system models, such as the interconnection of multiple spring-mass-damper elements in the frame of mechanical vibration control or the interconnection of RLC networks, which may serve either as a representation of long electric transmission lines or as a finite-dimensional approximation of volume flow and pressure variations in fluidic networks [ 10 , 37 , 38 ]. In all of these applications, efficient output feedback control procedures are promising for the reduction of undesirable oscillations.…”

Section: Conclusion and Outlook On Future Workmentioning

confidence: 99%

“…For general references about the theory and possible applications of LMIs in the frame of control and observer synthesis, the reader is referred to the works of [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 ]. In addition, approaches for the assignment of admissible eigenvalue domains, partially with applications to the control and oscillation attenuation of mechanical systems with elastic spring elements, were considered recently in [ 9 , 10 ], where a continuous-time setting was taken into account. For the discrete-time counterpart, cf.…”

Section: Introductionmentioning

confidence: 99%

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Linear Matrix Inequalities for an Iterative Solution of Robust Output Feedback Control of Systems with Bounded and Stochastic Uncertainty

Rauh

Romig

2021

Sensors

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Linear matrix inequalities (LMIs) have gained much importance in recent years for the design of robust controllers for linear dynamic systems, for the design of state observers, as well as for the optimization of both. Typical performance criteria that are considered in these cases are either H2 or H∞ measures. In addition to bounded parameter uncertainty, included in the LMI-based design by means of polytopic uncertainty representations, the recent work of the authors showed that state observers can be optimized with the help of LMIs so that their error dynamics become insensitive against stochastic noise. However, the joint optimization of the parameters of the output feedback controllers of a proportional-differentiating type with a simultaneous optimization of linear output filters for smoothening measurements and for their numeric differentiation has not yet been considered. This is challenging due to the fact that the joint consideration of both types of uncertainties, as well as the combined control and filter optimization lead to a problem that is constrained by nonlinear matrix inequalities. In the current paper, a novel iterative LMI-based procedure is presented for the solution of this optimization task. Finally, an illustrating example is presented to compare the new parameterization scheme for the output feedback controller—which was jointly optimized with a linear derivative estimator—with a heuristically tuned D-type control law of previous work that was implemented with the help of an optimized full-order state observer.

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Section: Conclusion and Outlook On Future Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Linear Matrix Inequalities for an Iterative Solution of Robust Output Feedback Control of Systems with Bounded and Stochastic Uncertainty

Rauh

Romig

2021

Sensors

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“…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%

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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“…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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Active control of linear vibrating systems for antiresonance assignment with regional pole placement

Cited by 20 publications

References 27 publications

Linear Matrix Inequalities for an Iterative Solution of Robust Output Feedback Control of Systems with Bounded and Stochastic Uncertainty

Linear Matrix Inequalities for an Iterative Solution of Robust Output Feedback Control of Systems with Bounded and Stochastic Uncertainty

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

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