Optimal periodic forcing of nonlinear chemical processes for performance improvements

Abstract

Unsteady‐state periodic operations can improve the optimal steady‐state performance of nonlinear chemical processes. To examine if the optimal periodic operation is proper and to obtain the optimal forcing functions subject to various control and state constraints it is suggested in this paper to convert the problems into a form which is suitable for constrained nonlinear programming. The adopted numerical optimization method is based on employing the control parametrization technique and is thus capable of dealing with the problem of multiple input forcings and obtaining optimal forcing functions and/or parameters while subject to general constraints. Besides, it provides information about to what extent the process performance can be improved by adopting the optimal periodic control.

Application of iterative learning control to an exothermic semibatch chemical reactor

“…where represents (8) then is given by (9) where represents the th column of the matrix, that can be shaped as follows: (10) By getting the difference of the predicted tracking error sequences at and (7), (9) the recurrent temporal expression can be derived where (11) where is the incremental control value [ , details about the computation will be given later in the following sections], is the predicted tracking error sequence ( ) of the th batch. Computation of (11) is initialized as follows [8], [14]: (12) It was noticed that such initializations were the key idea to include previous data in the current computations of the predicted tracking error sequence [8].…”

Numerical Solution of the Optimal Periodic Control Problem Using Differential Flatness

“…Other techniques for the solution of the OPC problem are direct optimization methods which work directly with the problem in (1)-(5) without recourse to the necessary conditions. The input is either parametrized in terms of suitable basis functions or discretized over a time grid to convert the problem into a standard nonlinear programming (NLP) form (see [14] and [15]). However, the unknown and periodic state boundary conditions of the OPC problem pose a significant challenge to any of these methods.…”

“…Typical shooting algorithms for solving such systems have been discussed in [13] in the context of optimal control problems but the situation is more complicated in OPC by the fact that the time interval for integration, T is unknown and the state boundary conditions are periodic. Other techniques proposed include direct solution of the OPC problem by either discretizing u over a time grid (control vector discretization) or parametrizing it using a known basis set (control vector parametrization) [14], [15]. The aim of this note is to present an approach based on the notion of differential flatness to solve the OPC problem efficiently.…”

Nonlinear frequency response analysis of forced periodic operation of non-isothermal CSTR with simultaneous modulation of inlet concentration and inlet temperature

“…Forced periodic operations of non-isothermal CSTRs have been investigated in the past fifty years both for single and two-input modulation (Ritter and Douglas, 1970;Sinčić and Bailey, 1977;Sterman and Ydstie 1990a, 1990b, 1991Rigopoulos et al, 1988;Chen et al, 1994;Sidhu et al, 2007). The theoretical and experimental investigations have shown that, in some cases, significant enhancement in the reactor performance can be obtained by forced periodic operation.…”