Performance boundary mapping for continuous and discrete time linear systems

Voßwinkel, Rick; Pyta, Lorenz; Schrödel, Frank; Mutlu, İlhan; Mihailescu-Stoica, Dinu; Bajçinca, Naim

doi:10.1016/j.automatica.2019.05.055

Cited by 14 publications

(11 citation statements)

References 13 publications

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“…Robust pole-placement controller for the uncertain polytopic systems (1) and ( 2) and the D R region defined by ( 5) can be directly computed from the LMI corresponding to the respective D R stability condition (6); see for example, [23]. A corresponding state feedback matrix defining the control law (3) is obtained by a solution to the following LMI…”

Section: Discrete-time Robust Pole-placement State Feedback Controlle...mentioning

confidence: 99%

“…Besides stability for all uncertain parameter values, a closed loop performance is an important factor in successful robust control design. Various approaches exist to consider performance both in state space and frequency domains; pole-placement belongs to efficient techniques for achieving the prescribed closed-loop dynamics, [4][5][6][7][8] and others.…”

Section: Introductionmentioning

confidence: 99%

“…The LMI formulation of generalized D R stability condition enables efficient computation of the corresponding feedback controller gains [2][3][4]10]. There is a tight connection between closed-loop poles and other performance indices, such as settling time and stability margin [5][6][7]. A major part of the published results on LMI based pole-placement; however, considers the continuous-time case, where standard pole regions for prescribed stability degree and relative damping are convex and can be directly applied to the developed robust state feedback control design schemes, [3,7,8,11].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Discrete-Time Pole-Region Robust Controller for Magnetic Levitation Plant

Hypiusova

Rosinová

2021

Symmetry

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Robust pole-placement based on convex DR-regions belongs to the efficient control design techniques for real systems, providing computationally tractable pole-placement design algorithms. The problem arises in the discrete-time domain when the relative damping is prescribed since the corresponding discrete-time domain is non-convex, having a “cardioid” shape. In this paper, we further develop our recent results on the inner convex approximations of the cardioid, present systematical analysis of its design parameters and their influence on the corresponding closed loop performance (measured by standard integral of absolute error (IAE) and Total Variance criteria). The application of a robust controller designed with the proposed convex approximation of the discrete-time pole region is illustrated and evaluated on a real laboratory magnetic levitation plant.

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Section: Discrete-time Robust Pole-placement State Feedback Controlle...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Discrete-Time Pole-Region Robust Controller for Magnetic Levitation Plant

Hypiusova

Rosinová

2021

Symmetry

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“…The boundaries between the different areas correspond to the values computed in Example 3 and 8. Alternatively, these sets can be calculated using parameter space methods, see [22,48] and references cited there.…”

Section: Eigenvalue Placement Real and Interval Stabilizationmentioning

confidence: 99%

Eigenvalue Placement by Quantifier Elimination - the Static Output Feedback Problem

Röbenack

Voßwinkel

2020

Acta Cybern

Self Cite

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This contribution addresses the static output feedback problem of linear time-invariant systems. This is still an area of active research, in contrast to the observer-based state feedback problem, which has been solved decades ago. We consider the formulation and solution of static output feedback design problems using quantifier elimination techniques. Stabilization, as well as more specified eigenvalue placement scenarios, are the focus of the paper.

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“…For uncertain system, stability and prescribed performance is required for the whole uncertainty domain. One of the frequently used approaches to guarantee the prescribed closed-loop system dynamics is pole-placement technique [7,[12][13][14][15] and others. In pole-placement, it can be advantageous to prescribe only a region, where the closed-loop poles should be placed instead of their exact position.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Nonlinear and Linear Controllers for Magnetic Levitation System

Rosinová

Hypiusova

2021

Applied Sciences

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Nonlinear system control belongs to advanced control problems important for real plants control design. Various techniques have been developed in this field. In this paper we compare two different approaches to a nonlinear unstable Magnetic levitation system control. The first control design approach further develops our recent results on robust discrete-time pole-placement, based on convex DR-regions. The second studied approach is based on feedback linearization and the simplified development of the corresponding nonlinear control law is provided. Both approaches are compared and evaluated. The efficiency of robust discrete-time pole-placement controller is shown as well as its competitiveness in comparison with nonlinear control for Magnetic levitation system.

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Performance boundary mapping for continuous and discrete time linear systems

Cited by 14 publications

References 13 publications

Discrete-Time Pole-Region Robust Controller for Magnetic Levitation Plant

Discrete-Time Pole-Region Robust Controller for Magnetic Levitation Plant

Eigenvalue Placement by Quantifier Elimination - the Static Output Feedback Problem

Comparison of Nonlinear and Linear Controllers for Magnetic Levitation System

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