Robust stability—degree assignment and its applications to the control of flexible structures

Kimura, Hidenori; Oike, Taro; Miura, Atsuyoshi; Akai, Kenju; Kida, Takashi

doi:10.1002/rnc.4590010303

Cited by 40 publications

(10 citation statements)

References 13 publications

(4 reference statements)

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“…In order to solve this problem we need to design a robust stabilizing controller, which requires an estimattion of the vibration characteristics in its uncertainty modeling. This is why we combine the H ∞ control [12][13][14][15] and closed loop identification (CLID) [16][17][18][19][20], which is similar to what we have done in a recent study [6]. This paper is a continuation of our recent research.…”

Section: Introductionmentioning

confidence: 87%

“…As is well-known, the H ∞ control theory has provided a sophisticated design method for robust control systems by explicitly incorporating modeling errors into design. Since its advent in the eighties [12], a variety of applications have been done particularly to control of flexible structures (see, e.g., [14,[21][22][23]). Nevertheless, the potential difficulty we face in the application of this theory is uncertainty modeling; this is conspicuous in the case of unstable systems like a magnetic levitation system as treated here.…”

Section: Introductionmentioning

confidence: 99%

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APPLICATION OF H_∞ CONTROL AND CLOSED LOOP IDENTIFICATION TO A MAGNETIC LEVITATION SYSTEM

Tsujino

Nakashima

Fujii

1999

Asian Journal of Control

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A systematic procedure for modeling and robust control of a multivariable magnetic levitation system is described. Our previous study revealed that an observer‐based LQ controller can stabilize the system, but generates spillovers in the presence of an impulse disturbance. To solve this problem, we apply an H∞ control to suppress the spillovers caused by unmodeled dynamics which we estimate using closed loop identification. First, an exactly linearized model is obtained to compensate for nonlinearities in the system, followed by estimation of the unmodeled dynamics using closed loop identification. Second, this information is used to design a two degree of freedom H∞ servo system for suppressing the spillover while tracking a step reference input. Finally, the desired robust performance of the resulting servo system is confirmed theoretically by γ‐analysis and also experimentally.

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Section: Introductionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

APPLICATION OF H_∞ CONTROL AND CLOSED LOOP IDENTIFICATION TO A MAGNETIC LEVITATION SYSTEM

Tsujino

Nakashima

Fujii

1999

Asian Journal of Control

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“…We obtain the 8th-order controller that satisfies the specifications for σ 0 = 0.3 and ω d = 2 with robust stability-degree assignment [3], using the MATLAB linear matrix inequalities (LMI) toolbox. …”

Section: __mentioning

confidence: 99%

Finite‐dimensional approximate modeling with error bounds of flexible vibrating systems based on partial eigenstructures

Imai

Wada

2006

Electrical Engineering Japan

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SUMMARYAn approach to control-oriented uncertainty modeling is presented for a class of elastic vibrating systems such as flexible structures, beams and strings, described by partial differential equations. Uncertainty bounding techniques are developed using the upper and lower bounds of the unknown eigenparameters. The result forms a basis for a finite-dimensional controller design in which closed loop stability and performance are guaranteed. A feasible set of systems is defined of all systems governed by a class of differential equations with certain norm bounds of the unknown input and output operators and with partially known bounds of the eigenparameters. Then the perturbation magnitude covering the feasible set is evaluated in the frequency domain where a standard truncated modal model is chosen as the nominal one. An upper bound to the truncated error magnitude which is calculated by linear programming is proposed. It is demonstrated that all the parameters formulating a feasible set are derived by finite element analysis for a flexible beam example, and feasibility of the proposed scheme is also illustrated by numerical bounding results.

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“…In addition, robust stability-degree assignment [15] is applied here to improve attenuation characteristics.…”

Section: Application Of Robust Stability-degree Assignmentmentioning

confidence: 99%

Robust damping control of power oscillation incorporating parametric resonance

Watanabe

Ohishi

Yasuda

2002

Electrical Engineering Japan

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SUMMARYIn this paper we consider a damping control of lowfrequency oscillations in an electric power system. On the basis of the hypothesis that an auto-parametric resonance model can explain a power oscillation, we propose a new model for a robust damping control, by which the system maintains stability even if some auto-parametric resonance happens. With this model, we can express a parametric variation of a principal oscillation mode and a class of uncertainties which cover neglected dynamics. Since the model has a certain structure of uncertain parameters, we design a robust controller via µ-synthesis. The robust controller which can be obtained from the presented design strategy has the property that the control performances are more sophisticated in comparison to controllers designed with other existing methods based on the H ∞ control.

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Robust stability—degree assignment and its applications to the control of flexible structures

Cited by 40 publications

References 13 publications

APPLICATION OF H_∞ CONTROL AND CLOSED LOOP IDENTIFICATION TO A MAGNETIC LEVITATION SYSTEM

APPLICATION OF H_∞ CONTROL AND CLOSED LOOP IDENTIFICATION TO A MAGNETIC LEVITATION SYSTEM

Finite‐dimensional approximate modeling with error bounds of flexible vibrating systems based on partial eigenstructures

Robust damping control of power oscillation incorporating parametric resonance

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Robust stability—degree assignment and its applications to the control of flexible structures

Cited by 40 publications

References 13 publications

APPLICATION OF H∞ CONTROL AND CLOSED LOOP IDENTIFICATION TO A MAGNETIC LEVITATION SYSTEM

APPLICATION OF H∞ CONTROL AND CLOSED LOOP IDENTIFICATION TO A MAGNETIC LEVITATION SYSTEM

Finite‐dimensional approximate modeling with error bounds of flexible vibrating systems based on partial eigenstructures

Robust damping control of power oscillation incorporating parametric resonance

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Product

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APPLICATION OF H_∞ CONTROL AND CLOSED LOOP IDENTIFICATION TO A MAGNETIC LEVITATION SYSTEM

APPLICATION OF H_∞ CONTROL AND CLOSED LOOP IDENTIFICATION TO A MAGNETIC LEVITATION SYSTEM