A geometric approach to the singular filtering problem

Schumacher, Johannes

doi:10.1109/tac.1985.1103859

Cited by 26 publications

(7 citation statements)

References 40 publications

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“…Because the examples in this article pertain only to a single-transducer, single-disturbance case, we merely refer the reader to Schumacher (1985) for a thorough treatment of this issue.…”

Section: Power Generation Limit For a Vibratory Energy Harvestermentioning

confidence: 99%

On the Causal Power Generation Limit for a Vibratory Energy Harvester in Broadband Stochastic Response

Scruggs

2010

Journal of Intelligent Material Systems and Structures

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This article illustrates that certain relatively well-known results from feedback control theory can be used to determine the maximum-attainable power generation for a vibratory energy harvester excited by a stationary broadband stochastic disturbance. For such applications, control techniques based on impedance matching theory cannot be used to optimize power generation, because the dynamic controller they prescribe is always anticausal. However, an optimal causal controller does exist, and can be derived using H 2 /LQG theory. Levels of power generation with this controller are compared to those of the anticausal optimal performance, as well as to traditional 'tuning' techniques which match the anticausal impedance only at the resonant frequency. It is demonstrated that tuning techniques can be significantly sub-optimal in broadband applications, especially when electronic conversion is relatively efficient. In addition to being useful in the design of controllers for energy harvesting applications, these results may also be used to ascertain the insurpassable power generation limits associated with a given combination of transducer and electronic hardware.

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“…Because the examples in this article pertain only to a single-transducer, single-disturbance case, we merely refer the reader to Schumacher (1985) for a thorough treatment of this issue.…”

Section: Power Generation Limit For a Vibratory Energy Harvestermentioning

confidence: 99%

On the Causal Power Generation Limit for a Vibratory Energy Harvester in Broadband Stochastic Response

Scruggs

2010

Journal of Intelligent Material Systems and Structures

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“…The early applications of this problem have been confined to the SISO case where the interpolation has been performed by a scalar transfer function [l], [3]. The extension to the multivariable case was first introduced in [2] and used by many others [7], [8]; it has imposed, however, the interpolation requirements on the whole matrix. Since the straightforward extension of the SISO interpolation problem has led to overdetermined solutions in the multivariable case, a directional interpolation problem has been presented in [9] which resolves the overdetermination.…”

Section: Discussionmentioning

confidence: 99%

“…M that leads, for a minimum value of X 2 0, to MTI -T 1 = XU (2) where U is an inner transfer function matrix in H,oO,, that satisfies the following:…”

Section: Given T1'hzl and Tzeh?xr Where Is Nonsingular And R'mentioning

confidence: 99%

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The structure of inner matrices that satisfy multiple directional interpolation requirements

Shaked

1989

IEEE Trans. Automat. Contr.

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1293By constructing the system matrix P of S(A, B, C) where SI -A -Bwe readily find that P (-l) [ z] = 0 and P(-1) [ = [ : ] where 9 = (3 -1 1 1)', XI = (10 0 5 5)', d' = (1 2)', and h = (5 5)'.Abstmct-The structure of an inner matrix that satisfies directional interpolation requirements for nondistinct d u e s at the right half-plane is derived explicitly, in closed form, in terms of the interpolation directions. The simple expression that is obtained for the required inner transfer function matrix has the same structure as the one that has already been found for distinct interpolation requirements, and it thus provides a comprehensive treatment, in the frequency domain, of interpolation problems that arise in many areas of linear system optimization.

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“…The first two conditions on Q m require that Q, is a rank-minimizing solution of a linear matrix inequality. The same linear matrix inequality is also appearing in the szngular filtering problem (see [26], this problem is dual to the singular linear quadratic control problem). It can be shown that the largest solution of the linear matrix inequality, whose existence is guaranteed since ( a ) C,,, has L, norm less than or equal to y.…”

Section: A T P M + P a = P B B T P M A -B B T P M Is Asymptoticalmentioning

confidence: 98%

New advances in H-infinity control - A tutorial paper

Stoorvogel

1992

Guidance, Navigation and Control Conference

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In this paper we present the by now classical solution of the H, control problem. T h e objective is to present the known results in a manner accessible to the nonexpert. We will conclude with a small design example to illustrate the results. -I l n e notation in chis paper is fairly standard. VVe caii i an invariant zero of the system ( A , B, C, D) if the matrix loses rank for s = S. For a rationai matrix G we denote by rankn( G the rank of G a s a rational matrix. It can J be shown that rankR(*,G is equal to the rank of G(sj for all but finitely many s E C. 2 Main result H, is defined as the linear space of matrix-valued functions which are analytic and bounded in the open righthalf complex plane. -4 rational transfer matrix is in H, if and oniy if the transfer matrix is stable and proper. We endow this space with the following norm: 858 A cv,.nn >.,,L-S I,,,-A 11 ..;A.,C , . O C~V . , J Downloaded by NANYANG TECHNICAL UNIVERSITY on August 24, 2015 | http://arc.aiaa.org |

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A geometric approach to the singular filtering problem

Cited by 26 publications

References 40 publications

On the Causal Power Generation Limit for a Vibratory Energy Harvester in Broadband Stochastic Response

On the Causal Power Generation Limit for a Vibratory Energy Harvester in Broadband Stochastic Response

The structure of inner matrices that satisfy multiple directional interpolation requirements

New advances in H-infinity control - A tutorial paper

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