Stable controller design of MIMO systems in real Grassmann space

Kim, Su-Woon; Boo, Chang-Jin; Kim, Sin; Kim, Ho-Chan

doi:10.1007/s12555-012-0202-2

Cited by 6 publications

(5 citation statements)

References 22 publications

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“…Nonetheless, it is feasible to approximately synthesize a controller that delivers a specific performance in terms of the structured single -µ-value. In this procedure known as (D, G-K) iteration [17][18][19][20][21][22], i.e., the difficulty in identifying a µ-optimal controller K so that µ(F(jω), K(jω)) ≤ β, ∀ω, is converted into the problem of identifying finding transfer function matrices D(ω)∈ and G(ω)∈ ∞ , such that,…”

Section: Controller Synthesis H-infinitymentioning

confidence: 99%

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Applications of the Order Reduction Optimization of the H-Infinity Controller in Smart Structures

Moutsopoulou,

Petousis,

Vidakis

et al. 2023

Inventions

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In this paper, our strategy is to look for locally optimum answers to a non-smooth optimization problem that has been constructed to include minimization goals and restrictions for smart structures’ vibration suppression. In both theoretical analysis and practical implementation, it is widely recognized that designing multi-objective control systems poses a considerable challenge. In this study, we assess the effectiveness of this method by employing the open-source Matlab toolbox Hifoo 2.0 and juxtapose our findings with established industry standards. We start by framing the control problem as a mathematical optimization issue and proceed to identify the controller that effectively addresses this optimization. This approach introduces the potential application of intelligent structures in tackling the challenge of vibration suppression. This study makes use of the most recent version of the freely available application Hifoo which tries to study vibration suppression with the limits outlined above in the context of multi-objective controller design. A controller directive is initially set, allowing for a lower order.

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Section: Controller Synthesis H-infinitymentioning

confidence: 99%

“…It connects H-infinity synthesis and µ-analysis generally, producing positive outcomes. The initial reference is a limit on µ expressed in relation to the adjusted singular value [22,23],…”

Section: Controller Synthesis H-infinitymentioning

confidence: 99%

Applications of the Order Reduction Optimization of the H-Infinity Controller in Smart Structures

Moutsopoulou,

Petousis,

Vidakis

et al. 2023

Inventions

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“…Dynamic systems can be actively controlled using distributed sensors and actuators composed of adaptable piezoelectric materials. The main considerations that structural control engineers need to keep in mind while creating reliable control techniques for assessing resilience, optimal placement, and structural modeling in the face of uncertainty are covered in this essay [27][28][29][30]. Because the controller provided is of order 56, sophisticated control techniques may be applied to simpler models, and we use the optimization method Hifoo to reduce the order of the controller.…”

Section: Introductionmentioning

confidence: 99%

μ-Analysis and μ-Synthesis Control Methods in Smart Structure Disturbance Suppression with Reduced Order Control

Moutsopoulou,

Petousis,

Stavroulakis

et al. 2024

Algorithms

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In this study, we created an accurate model for a homogenous smart structure. After modeling multiplicative uncertainty, an ideal robust controller was designed using μ-synthesis and a reduced-order H-infinity Feedback Optimal Output (Hifoo) controller, leading to the creation of an improved uncertain plant. A powerful controller was built using a larger plant that included the nominal model and corresponding uncertainty. The designed controllers demonstrated robust and nominal performance when handling agitated plants. A comparison of the results was conducted. As an example of a general smart structure, the vibration of a collocated piezoelectric actuator and sensor was controlled using two different approaches with strong controller designs. This study presents a comprehensive simulation of the oscillation suppression problem for smart beams. They provide an analytical demonstration of how uncertainty is introduced into the model. The desired outcomes were achieved by utilizing Simulink and MATLAB (v. 8.0) programming tools.

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“…The Schubert calculus on the Grassmannian [15] studies the linear subspaces that have specified positions with respect to fixed flags of linear spaces. This is a rich class of wellunderstood geometric problems that appear in applications such as the pole placement problem in linear systems theory [2,3,13,32] and in information theory [1]. Schubert problems serve as a laboratory for investigating new phenomena in enumerative geometry, such as possible numbers of real solutions [5,9,23,24,30] or monodromy/Galois groups [18,20,26].…”

mentioning

confidence: 99%

“…Figure 1. Stiefel coordinates corresponding to a checkerboard.n = 14 and k = 7, with permutation array π =(6,7,8,9,11,12,13,14,10,5,4,3,2,1). The entries 0 are forced by the requirement that the matrix be reduced.…”

mentioning

confidence: 99%

Numerical Schubert Calculus via the Littlewood-Richardson Homotopy Algorithm

Leykin¹,

Campo²,

Sottile³

et al. 2018

Preprint

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We develop the Littlewood-Richardson homotopy algorithm, which uses numerical continuation to compute solutions to Schubert problems on Grassmannians and is based on the geometric Littlewood-Richardson rule. One key ingredient of this algorithm is our new optimal formulation of Schubert problems in local Stiefel coordinates as systems of equations. Our implementation can solve problem instances with tens of thousands of solutions.

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Stable controller design of MIMO systems in real Grassmann space

Cited by 6 publications

References 22 publications

Applications of the Order Reduction Optimization of the H-Infinity Controller in Smart Structures

Applications of the Order Reduction Optimization of the H-Infinity Controller in Smart Structures

μ-Analysis and μ-Synthesis Control Methods in Smart Structure Disturbance Suppression with Reduced Order Control

Numerical Schubert Calculus via the Littlewood-Richardson Homotopy Algorithm

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