Forced periodic control of an exothermic CSTR with multiple input oscillations

Abstract

Interaction among various oscillating inputs may result in significant modifications in the behavior of a system under forced periodic control.Forced oscillations in the input flow rate and input concentrations of an exothermic continuous stirred tank reactor enable the stabilized operation of the CSTR in the unstable steady state region. Reactor temperature oscillations under forced periodic control are similar to the oscillations resulting from proportional-integral feedback or nonlinear (push-pull) feedback control, and under some operating conditions the oscillation amplitude is significantly lower. Theoretical and experimental studies illustrate the effects of forcing frequency and phase shift on reactor behavior. Konstantinos Rigopoulos Xianshu Shu Ali CinarDepartments of Chemical and Electrical Engineering Illinois Institute of Technology Chicago, IL 60616 IntroductionForced periodic operation of chemical reactors has been used effectively for conversion improvement, selectivity, and yield enhancement in complex reactions and the stabilization of reactor operation. References to various review papers, different analysis techniques developed, and applications reported are given by Cinar et al. (1987a). Recently there has been a revival of interest in periodically forced systems. Promising experimental results on yield improvement in catalytic reactions have been reported (Cutlip, 1979, Jain et al., 1982Wilson and Rinker, 1982;Barshad and Gulari, 1985,1986;Silveston et al., 1986). A technique based on the Carleman linearization of nonlinear plant equations and the maximization of a time-averaged performance measure has been proposed (Lyberatos and Svoronos, 1987) for determining the optimal periodic operation and has been applied to an isothermal reactor model for the selection of the best forcing frequency, amplitude, and waveform. Common features of periodically forced reacting systems, particularly properties of spontaneously oscillating systems that are forced periodically, have been considered (Kevrekidis et al., 1986) and an algorithm using stroboscopic representation has been presented for the numerical computation and stability analysis of invariant tori. In stabilizing reactor operation by periodic forcing, the vibrational control approach has provided successful theoretical and experimental results (Cinar et al., 1987a, b).Vibrational control (Meerkov, 1982) is a method for modification of the dynamic properties of a system by introducing fast,

Mediating operation of heterogeneous CSTR

“…9. Note that the selected forcing function gives the same average output as a nonsymmetric rectangular waveform (see, for example, Rigopoulos et al, 1988). Thus by using relation Da = l/u, the second equation of the system (Eq.…”

“…That is an open-loop control method using fast oscillations of system parameters. Applications of vibrational control by multiple oscillations of feed flow rate and concentrations have been studied by Cinar and coworkers (Cinar et al, 1987b;Rigopoulos et al, 1988;Shu et al, 1989). In vibrational control approach CSTR has been considered as a one-scale system with respect to fast operation mode.…”

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.…”

Nonlinear predictive control of periodically forced chemical reactors

“…Numerous theoretical and experimental investigations have shown that forced periodic operation of chemical reactors can lead to increased conversion, enhanced yield, reduced parametric sensitivity, reduced hot-spot problems, and stabilized reactor operation in the unstable steady-state region (Bailey, 1977;Cutlip, 1979;Gulari, 1985, 1986;Char et al, 1987a,b;Rigopoulos et al, 1988;Sterman and Ydstie, 1990a,b;Silveston, 1991;Ozgulaen et al, 1992a,b). The control of periodically forced reactors, however, is an important and interesting issue which has not received the attention it deserves.…”

“…Later, Rigopoulos et al (1988) used the same CSTR system with forced periodic, proportional-integral (PI) feedback, and nonlinear feedback (push-pull) control laws for stabilized operation. In the case of PI control, the controller settings are tuned such that high-frequency, small-amplitude sustained oscillations in reactor temperature are generated via feedback.…”