Pole Assignment for Active Vibration Control of Linear Vibrating Systems through Linear Matrix Inequalities

Belotti, Roberto; Richiedei, Dario; Tamellin, Iacopo; Trevisani, Alberto

doi:10.3390/app10165494

Cited by 15 publications

(11 citation statements)

References 31 publications

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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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“…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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“…We shall introduce a multi-step two-stage approach for solving the PZAP in the multi-input second-order control system based on the measured receptances, the system matrices M, C, K and linear matrix inequalities (LMIs). This is motivated by the two papers due to Ram and Elhay [32] and Belotti et al [4]. In [32], Ram and Elhay proposed a multi-step solution method for the multi-input PQEAP.…”

Section: 4)mentioning

confidence: 99%

“…In [32], Ram and Elhay proposed a multi-step solution method for the multi-input PQEAP. In [4], based on the receptance method and LMIs, Belotti et al presented a two-stage method for assigning the dominant poles to the desired locations and keep the remaining ones within a prescribed region in the complex plane for the single-input second-order control system. To our knowledge, there is no numerical method available for solving the PZAP for the multi-input second-order control system (1.4).…”

Section: 4)mentioning

confidence: 99%

On Pole-Zero Assignment of Vibratory Systems by Multi-Input Feedback Control

Bai,

Wang

2020

Preprint

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In this paper, we consider the pole-zero assignment problem for vibratory systems via multi-input feedback control. We propose a multi-step two-stage approach for solving the multi-input pole-zero assignment problem. We first reformulate the assignment problem as a multi-step single-input pole-zero assignment problem. Then, in each step, we propose a twostage approach for solving the single-input pole-zero assignment problem. In the first stage, based on the measured receptances, we replace the selected zeros of the prescribed open-loop point receptance to the desired locations, where we need to solve a small underdetermined linear equation for finding the corresponding columns of the feedback matrices. In the second stage, by using linear matrix inequalities, the complete closed-loop poles are assigned to the prescribed subregion of the complex left-hand plane. Finally, we give some numerical examples to demonstrate the effectiveness of our method.

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“…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%

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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Pole Assignment for Active Vibration Control of Linear Vibrating Systems through Linear Matrix Inequalities

Cited by 15 publications

References 31 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

On Pole-Zero Assignment of Vibratory Systems by Multi-Input Feedback Control

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

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