Recent advances in the study of distributed parameter systems

Tzafestas, Spyros G.; Stavroulakis, Peter

doi:10.1016/0016-0032(83)90055-8

Cited by 25 publications

(10 citation statements)

References 139 publications

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“…Compared to the control theory of FPDEs, the control theory of integer partial differential equations (IPDEs) has been has been developed for a long time [16][17][18] and two approaches have emerged: early and late lumping approaches [18][19][20]. The early lumping approach consists in reducing the infinite dimensional system (IPDEs) to a finite dimensional one, that is, a lumped parameter system (described by ordinary differential equations) using different model reduction techniques [18,19,21].…”

Section: Introductionmentioning

confidence: 99%

Distributed feedback control of a fractional diffusion process

Maidi

Corriou

2018

Int. J. Dynam. Control

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In this paper, a control law that enforces an output tracking of a fractional diffusion process is developed. The dynamical behavior of the process is described by a space-fractional parabolic equation. The objective is to force a spatial weighted average output to track its specified output by manipulating a control variable assumed to be distributed in the spatial domain. The state feedback is designed in the framework of geometric control using the notion of the characteristic index. Then, under the assumption that the fractional diffusion process is a minimum phase system, it is shown that the developed control law guarantees exponential stability in L 2-norm for the resulting closed loop system. Numerical simulations are performed to show the tracking and disturbance rejection capabilities of the developed controller. Keywords Distributed parameter system • fractional partial differential equation • fractional diffusion • late lumping • geometric control • characteristic index.

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Section: Introductionmentioning

confidence: 99%

Distributed feedback control of a fractional diffusion process

Maidi

Corriou

2018

Int. J. Dynam. Control

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“…Thus, results on the control of membranes [15], wings [12], beams [16,17], and plates [1,18] became available in the literature. A survey article [22] provides a review of the recent advances in the field of distributed parameter systems. A recent book by Meirovitch [11] provides an up-to-date treatment of the structural control field.…”

Section: Introductionmentioning

confidence: 99%

Active control of flexible systems by a mathematical programming approach

Nouri-Moghadam

Sadek

1993

Dynamics and Control

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Abstract.A class of control problems for a damped distributed parameter system governed by a system of partial differential equations with side constraints (equality and/or inequality) is considered. The proposed approach approximates each control force of the system by a Fourier-type series. In contrast to standard linear optimal control approaches, the method used here is based on the mathematical programming approach, in which the necessary condition of optimality is derived as a system of linear algebraic equations. The proposed approach is easy to apply to a large class of control problems. A vibrating beam excited by an initial disturbance is studied numerically in which the effectiveness of the control and the amount of force spent in the process are investigated in relation to the reduction to the dynamic response.

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“…= A( T ) T + B"( T)tl' + ge( T)U' (16) Any temperature measurement can be described in terms of the nodal temperature as…”

Section: = A( T)t + B( T)umentioning

confidence: 99%

“…The state-space model of the system is given by (16) and (17). The state-space matrices are temperature dependent and hence the system is non-linear.…”

Section: ~=C(t)t+d'(t)~'+d'(t)u' (17)mentioning

confidence: 99%

Solid-liquid interface shape control during crystal growth

Srinivasan

Batur

Rosenthal³

et al.

Proceedings of 1995 American Control Conference - ACC'95

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This paper deals with the problem of controlling the solid-liquid interface shape during solidification of molten material inside a Bridgman-Stockbarger furnace. The boundary conditions that would achieve the desired interface shape are found using feedback controls A state-space model of the solidification process is determined by employing the finite element method on the goveming conduction equation obtained through the apparent heat capacity formulation. This model is used to design a dynamic controller that would set up a desired interface shape by making use of all available temperature measurements.

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Recent advances in the study of distributed parameter systems

Cited by 25 publications

References 139 publications

Distributed feedback control of a fractional diffusion process

Distributed feedback control of a fractional diffusion process

Active control of flexible systems by a mathematical programming approach

Solid-liquid interface shape control during crystal growth

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