LQ control design of a class of hyperbolic PDE systems: Application to fixed-bed reactor

Aksikas, Ilyasse; Fuxman, Adrian; Forbes, J. Fraser; Winkin, Joseph J.

doi:10.1016/j.automatica.2009.02.017

Cited by 107 publications

(46 citation statements)

References 10 publications

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“…Aksikas et al 8 presented a model-based approach, which needs the full knowledge of the PDE model. Thus, it cannot be used for the case that internal system dynamics is unknown.…”

Section: Problem Descriptionmentioning

confidence: 99%

Heuristic Dynamic Programming Algorithm for Optimal Control Design of Linear Continuous-Time Hyperbolic PDE Systems

Luo

2012

Ind. Eng. Chem. Res.

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This work considers the optimal control problem of linear continuous-time hyperbolic partial differential equation (PDE) systems with partially unknown system dynamics. To respect the infinite-dimensional nature of the hyperbolic PDE system, the problem can be reduced to finding a solution of the space-dependent Riccati differential equation (SDRDE), which requires the full system model. Therefore, a heuristic dynamic programming (HDP) algorithm is proposed to achieve online optimal control of the hyperbolic PDE system, which online collects data accrued along system trajectories and learns the solution of the SDRDE without requiring the internal system dynamics. The convergence of HDP algorithm is established by showing that the HDP algorithm generates a nondecreasing sequence which uniformly converges to the solution of the SDRDE. For implementation purposes, the HDP algorithm is realized by developing an approximate approach based on the method of weighted residuals. Finally, the application on a steam-jacketed tubular heat exchanger demonstrates the effectiveness of the developed control approach.

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“…Aksikas et al 8 presented a model-based approach, which needs the full knowledge of the PDE model. Thus, it cannot be used for the case that internal system dynamics is unknown.…”

Section: Problem Descriptionmentioning

confidence: 99%

Heuristic Dynamic Programming Algorithm for Optimal Control Design of Linear Continuous-Time Hyperbolic PDE Systems

Luo

2012

Ind. Eng. Chem. Res.

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“…For example, in biomechanics when modeling the phenomena of electrical activity in the heart, the resulting equations are coupled systems of PDEs (see, e.g., [21][22][23]). Coupled systems of PDEs also occur in modeling of some chemical and material engineering processes such as system containing a continuous stirred tank reactor (CSTR) and a plug flow reactor (PFR) in series (see [24,25]). Various applications of coupled systems can be found in solid state physics and mechanics; for example, dynamics of multideformable bodies coupled by standard light fractional order discrete continuum layers is described by coupled systems of fractional order partial differential equations [7,[26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solutions of Coupled Systems of Fractional Order Partial Differential Equations

Shah

2017

Advances in Mathematical Physics

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We develop a numerical method by using operational matrices of fractional order integrations and differentiations to obtain approximate solutions to a class of coupled systems of fractional order partial differential equations (FPDEs). We use shifted Legendre polynomials in two variables. With the help of the aforesaid matrices, we convert the system under consideration to a system of easily solvable algebraic equation of Sylvester type. During this process, we need no discretization of the data. We also provide error analysis and some test problems to demonstrate the established technique.

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“…This method is widely applied for heat exchangers, fixed-bed reactors, plug-flow reactors, etc ( [13] and references therein). An LQ-controller for a class of hyperbolic PDEs can be found in [14] and references therein. In this work, inspired from [5], we aim at developing a new control technique which takes into considerations the practical constraints on the volumetric flow rate while ensuring the tracking of the reference setpoint.…”

Section: Introductionmentioning

confidence: 99%

Observer-based bilinear control of first-order hyperbolic PDEs: Application to the solar collector

Mechhoud

Laleg‐Kirati

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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Abstract-In this paper, we investigate the problem of bilinear control of a solar collector plant using the available boundary and solar irradiance measurements. The solar collector is described by a first-order 1D hyperbolic partial differential equation where the pump volumetric flow rate acts as the plant control input. By combining a boundary state observer and an internal energy-based control law, a nonlinear observer based feedback controller is proposed. With a feed-forward control term, the effect of the solar radiation is cancelled. Using the Lyapunov approach we prove that the proposed control guarantees the global exponential stability of both the plant and the tracking error. Simulation results are provided to illustrate the performance of the proposed method.

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LQ control design of a class of hyperbolic PDE systems: Application to fixed-bed reactor

Cited by 107 publications

References 10 publications

Heuristic Dynamic Programming Algorithm for Optimal Control Design of Linear Continuous-Time Hyperbolic PDE Systems

Heuristic Dynamic Programming Algorithm for Optimal Control Design of Linear Continuous-Time Hyperbolic PDE Systems

Numerical Solutions of Coupled Systems of Fractional Order Partial Differential Equations

Observer-based bilinear control of first-order hyperbolic PDEs: Application to the solar collector

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