Extended State-Dependent Differential Riccati Equation (ESDDRE) Controller Design for a Chemical Plug-Flow Reactor via Time-Delay Partial Differential Equation

Abstract

Numerous processes in chemical and biological engineering make use of tubular reactors. A particular kind of tubular reactor was known as a chemical plug-flow reactor (PFR) when there is no diffusion term. This paper offers a nonlinear controller for a non-isothermal PFR governed by time-delay first-order partial differential equation (PDE). Due to, an Extended state-dependent differential Riccati equation (ESDDRE) of the PFR system, a sub-optimal nonlinear controller is suggested. At the first step, an Extended pseudo-linearization (EPL) presentation of the PFR with State-dependent coefficients (SDC) is designed. All of the time-delay terms in this representation are situated in the input vectors as well as the system matrices. Then, a control signal regard on the ESDDRE controller is generated by introducing a Hamiltonian equation and performance index according to the PDE systems. Moreover, the asymptotic stability regarded on ESDDRE controller is guaranteed by applying a suitable Lyapunov theory. Simulation results verify the efficiency of the recommended ESDDRE controller method for two EPL form presentations with different time delays.