Multistability Control in Periodically Forced Catalytic Reac

stabilization of reactor behavior A novel approach of the chemical reactor stabilization is proposed by using a multistability control. A creation of an additional stable steady state by changing the reactor multiplicity features is a main idea of the mult

Multistability Control in Periodically Forced Catalytic ReactorDepartment of Mathematics and Computer Sciences, Ben Gurion University of the Negev, P.O.B 653, 84105, Beer Sheva, Israel e-mails: vladimir@bgumail.bgu.ac.il; pan lov@indigo.cs.bgu.ac.il Keywords: multiscale system, steady-state multiplicity, catalytic CSTR, forced periodic operation, stabilization of reactor behavior A novel approach of the chemical reactor stabilization is proposed by using a multistability control. A creation of an additional stable steady state by changing the reactor multiplicity features is a main idea of the multistability control. Proposed approach employs a special type of periodic forced operation, called mediating operation. Mediating operation is able to change a qualitative character of the reactor dynamic behavior, particularly, to produce additional stable steady states in an intermediate temperature area. Feed ow rate is considered as a manipulated variable. Changing of CSTR multiplicity is investigated for two{step control inputs. It is shown that CSTR under two{step control can exhibit at most ve steady states having stable intermediate steady state. Two constructive procedures are proposed for nding out control parameters which provide a creation of the stable steady state in selected intermediate area.

Vladimir Gol'dshtein and Vadim Pan lov

ABSTRACT

1. INTRODUCTIONChemically reacting systems are an example of dynamical systems which may exhibit complicated dynamic features with multiple steady states. The study addresses multiplicity phenomenon in a catalytic Continuous Stirred Tank Reactor (CSTR) driven by a special type of the forced periodic operation. Stabilization of reactor behavior is viewed, traditionally, as potential bene t of a general periodic operation approach. The proposed forced periodic operation, called mediating operation, is able to control steady-state multiplicity which entails new application elds of general forced periodic operation approach for the stabilization purpose. The method assumes a creation of a new stable steady state by changing multiplicity features of the chemical reactor. It should be noted that direct applications of a such complicated phenomena as steady-state multiplicity are still problematic because usually complicated situations should be avoided in real systems. So a proposed control of the multi-stability can be viewed also as one of the rst attempts to use a complexity of dynamic behavior in a positive sense, i.e. as a control purpose. A wide spectrum of multivariable dynamical systems can be characterized by di erent time scales. A periodic operation of intermediate mode with respect to slow and fast system time scales is rather interesting to study from the control point of view. The type of periodic operation that is mediating operation has been proposed in application to catalytic chemical reactor engineering 1,2]. The main goal of mediating operation is a control of the multivariable system

by manipulating control variables of a minimal number. Feed ow is a single input for CSTR, so feed ow rate is considered as a single manipulated variable. Two signi cantly di erent dynamic scales, slow for temperature processes and fast for concentration processes, can be singled out for catalytic gas{solid reactor (section 2). Thus, the simplest two-scale model of multiscale systems with widely separated time scales is studied under periodic operation in intermediate mode. Multiple steady states and corresponded phenomena are considered brie y in the section 3 from a point view of the catastrophe theory. Multistability control supposes a creation of a stable steady state in the selected area. So it is of a practical interest to nd control parameters which provide desired e ect. Particularly the e ect can be obtained by an achievement of the ve multiplicity with three stable steady states. A procedure for a description of the convenient control parameter region is presented in the section 4.

2. REACTOR MODEL UNDER MEDIATING OPERATIONA subject of modeling is a two{phase well{stirred tank reactor (brie y CSTR) with a gas mixture reacting on the surface of a solid catalyst. A thermal equilibrium between di erent phases in the reactor at any time is assumed . For a single rst{order reaction the heat and

stabilization of reactor behavior A novel approach of the chemical reactor stabilization is proposed by using a multistability control. A creation of an additional stable steady state by changing the reactor multiplicity features is a main idea of the mult

mass balance equations of the gas{solid CSTR can be reduced to the following dimensionless form 1]d dt d dt

=?u? (? c )+ B (1? )k( )=?u+ (1? )k( )0

(1)

where| dimensionless temperature;| reactor productivity, conversion (dimensionless concentration); u| dimensionless feed ow rate (control variable), u= 1=Da for unforced reactor; Da| Damkohler number;| dimensionless heat-transfer coe cient; B| dimensionless reaction heat (adiabatic temperature rise); k( )= exp=(1+ )]| exponential function, de ned by Arrhenius law. The ratio of a gas heat capacity to the total reactor heat capacity, is considered as a small parameter, because the solid catalyst density is 10 times greater than the gas mixture density. Thus system (1) is a singularly perturbed system with a small parameter 1. Further following asymptotic analysis scheme 3] a zero{approximation,= 0, of system (1) is considered, d=?u? (? )+ B (1? )k ( ) c dt (2) k 0=?u+ (1? )k( )=)=k u3 ( ) ( )+

In 1] has been shown that heat processes are approximately 1= times slower than concentration processes in gas{solid CSTR, i.e …… 此处隐藏：7550字，全部文档内容请下载后查看。喜欢就下载吧 ……