Dynamic optimization of processes with time varying hydraulic delays

Clerget, Charles-Henri; Petit, Nicolas

doi:10.1016/j.jprocont.2019.04.013

Cited by 11 publications

(2 citation statements)

References 31 publications

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“…25,26 In addition to constant input delay, integral type delay has also been the object of further study because of its application in temperature dynamics, spark-ignited models, 27 and fluid-transport phenomena. 28 A specific example is hydraulic delays, 29,30 which depend on the past input value via a specific integration approach; such systems with integral delays can be stabilized through an iterative algorithm 29,30 or the backstepping method. 31 More recently, the control design for PDEs with spatially distributed delays has attracted new attention.…”

Section: Introductionmentioning

confidence: 99%

Radially varying delay‐compensated distributed control of reaction‐diffusion PDEs on n‐ball under revolution symmetry conditions

Guan

2022

Intl J Robust & Nonlinear

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In this article, a distributed control design is developed via partial differential equation (PDE) backstepping for a class of reaction-diffusion PDEs on n-ball under revolution symmetry conditions in the presence of radial spatially varying actuator delay. The actuator delay is modeled by a two-dimensional (2D) first-order hyperbolic PDE with spatially varying boundary, resulting in a cascaded transport-diffusion PDE system. Two-step backstepping transformation is introduced for the control design. First, a new Volterra transformation for the n-ball under revolution symmetry is proposed that allows the kernel function to be solvable. Different from the kernel in the 1D domain, which is expressed by the classical Fourier series, the kernel of the n-ball under revolution symmetry conditions is based on the Fourier-Bessel series. The resulting Volterra transformation is an implicit one that contains the state of the target system on both sides of the definition. Based on the implicit transformation, we employ the successive approximations approach to derive the second-step transformation, namely, an explicit transformation, and arrive at a stable target system. The inverse transformation is also derived, to prove L 2 exponential stability of the closed-loop system.The stability analysis requires more technical skills that are not needed in solving the spatially varying delay compensation problem when the domain is 1D.Numerical simulation examples of 3D and 4D revolution-symmetrical systems illustrate the effectiveness of the controller.

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Section: Introductionmentioning

confidence: 99%

Radially varying delay‐compensated distributed control of reaction‐diffusion PDEs on n‐ball under revolution symmetry conditions

Guan

2022

Intl J Robust & Nonlinear

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“…However, up to our knowledge, only a few theoretical studies have investigated control related issues. Notable exceptions are [7] which proposes an heuristic control design in the case of a state delay and [12], [13] which investigate optimal control for a general class of nonlinear systems with both input and state transport delays.…”

Section: Introductionmentioning

confidence: 99%

Constant time-horizon prediction-based stabilization for linear systems with input-dependent input delay

Falcon

Bresch‐Pietri

2021

2021 60th IEEE Conference on Decision and Control (CDC)

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This paper investigates prediction-based stabilization for a class of linear systems subject to input-dependent input delay. The delay under consideration is implicitly defined by an integral relation depending on past values of the input. This situation is frequent in the process industry. We propose here to use a prediction on an horizon equal to the equilibrium value of the delay. By relying on a novel transport Partial Differential Equation (PDE) representation of the delay, encapsulating the input-dependency, we prove local exponential stabilization of the closed-loop system.

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Constrained explicit GPC formulation analysis for multivariable, underactuated and time-delay systems

Fonseca

Dantas

Dantas³

et al. 2021

Int. J. Dynam. Control

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Dynamic optimization of processes with time varying hydraulic delays

Cited by 11 publications

References 31 publications

Radially varying delay‐compensated distributed control of reaction‐diffusion PDEs on n‐ball under revolution symmetry conditions

Radially varying delay‐compensated distributed control of reaction‐diffusion PDEs on n‐ball under revolution symmetry conditions

Constant time-horizon prediction-based stabilization for linear systems with input-dependent input delay

Constrained explicit GPC formulation analysis for multivariable, underactuated and time-delay systems

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