Optimal Boundary Control for Selective Catalytic Reduction Distributed Parameter Model

This paper is devoted to design a model-based boundary optimal controller for selective catalytic reduction system. The mathematical model consists of coupled parabolic-hyperbolic PDEs with an ODE. The main objective is to manipulate the ammonia gas at the inlet of the SCR in order to reduce the amount of NOx and ammonia slip as much as possible. The augmented infinite-dimensional state space representation has been used in order to solve the corresponding linear-quadratic control problem. The dynamical properties of both the linearized system and its augmented version have been studied. Under some technical conditions, it has been shown that the augmented system generates an exponentially stabilizable and detectable C0-semigroups. The linear-quadratic control problem has been solved for the augmented system. A decoupling technique has been implemented to decouple and solve the corresponding Riccati equation. An algorithm has been developed to describe the steps of solving the Riccati equation. Numerical simulations for the closed-loop system have been implemented to show the controller performances. - 2018Scopu

Model-based optimal boundary control of selective catalytic reduction in diesel-powered vehicles

This paper is devoted to design a model-based boundary optimal controller for selective catalytic reduction system. The mathematical model consists of coupled parabolic-hyperbolic PDEs with an ODE. The main objective is to manipulate the ammonia gas at the inlet of the SCR in order to reduce the amount of NOx and ammonia slip as much as possible. The augmented infinite-dimensional state space representation has been used in order to solve the corresponding linear-quadratic control problem. The dynamical properties of both the linearized system and its augmented version have been studied. Under some technical conditions, it has been shown that the augmented system generates an exponentially stabilizable and detectable C0-semigroups. The linear-quadratic control problem has been solved for the augmented system. A decoupling technique has been implemented to decouple and solve the corresponding Riccati equation. An algorithm has been developed to describe the steps of solving the Riccati equation. Numerical simulations for the closed-loop system have been implemented to show the controller performances.Scopu

Boundary linear-quadratic control for a system of coupled parabolic-hyperbolic PDEs and ODE

The paper deals with the design of a boundary optimal controller for a general model of parabolic-hyperbolic PDEs coupled with an ODE. The augmented infinite-dimensional state space representation has been used in order to solve the control problem. It has been shown that the system generates a C0-semigroup by using the perturbation theorem and then the dynamical properties of the system have been studied. Lyapunov equation has been used to show the exponential stabilizability and detectability of the system. The linear-quadratic control problem has been solved and an algorithm has been developed to solve the corresponding operator Riccati equation. Monolithic catalyst reactor model has been used to test the performances of the developed controller through numerical simulations. 2017 IEEE.Scopu

Optimal control of coupled parabolic–hyperbolic non-autonomous PDEs: infinite-dimensional state-space approach

This paper deals with the design of an optimal state-feedback linear-quadratic (LQ) controller for a system of coupled parabolic–hypebolic non-autonomous partial differential equations (PDEs). The infinite-dimensional state space representation and the corresponding operator Riccati differential equation are used to solve the control problem. Dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the LQ-optimal control problem and also to guarantee the exponential stability of the closed-loop system. Thanks to the eigenvalues and eigenfunctions of the parabolic operator and also the fact that the hyperbolic-associated operator Riccati differential equation can be converted to a scalar Riccati PDE, an algorithm to solve the LQ control problem has been presented. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ optimal controller designed in the early portion of the paper is implemented for the original non-linear model. Numerical simulations are performed to show the controller performances

Optimal linear–quadratic control of coupled parabolic–hyperbolic PDEs

This paper focuses on the optimal control design for a system of coupled parabolic-hypebolic partial differential equations by using the infinite-dimensional state-space description and the corresponding operator Riccati equation. Some dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the linear-quadratic (LQ)-optimal control problem. A state LQ-feedback operator is computed by solving the operator Riccati equation, which is converted into a set of algebraic and differential Riccati equations, thanks to the eigenvalues and the eigenvectors of the parabolic operator. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ-optimal controller designed in the early portion of the paper is implemented for the original nonlinear model. Numerical simulations are performed to show the controller performances. 1 2016 Informa UK Limited, trading as Taylor & Francis Group.Dr Ilyasse Aksikas acknowledges financial support of Qatar University under the internal grant [grant number QUUG-CAS-DMSP-15-16-10].Scopu

LQ (optimal) control of hyperbolic PDAEs

The linear quadratic control synthesis for a set of coupled first-order hyperbolic partial differential and algebraic equations is presented by using the infinite-dimensional Hilbert state-space representation of the system and the well-known operator Riccati equation (ORE) method. Solving the algebraic equations and substituting them into the partial differential equations (PDEs) results in a model consisting of a set of pure hyperbolic PDEs. The resulting PDE system involves a hyperbolic operator in which the velocity matrix is spatially varying, non-symmetric, and its eigenvalues are not necessarily negative through of the domain. The C0-semigroup generation property of such an operator is proven and it is shown that the generated C 0-semigroup is exponentially stable and, consequently, the ORE has a unique and non-negative solution. Conversion of the ORE into a matrix Riccati differential equation allows the use of a numerical scheme to solve the control problem.Scopu