Vibrational Control of Chemical Reactors: Stabilization and Conversion Improvement in an Exothermic CSTR

Geometric methods for nonlinear process control. 1. Background

“…One way to verify the above proposition is a brute force calculation of the transfer function of the closed-loop system (13) for cAr lb and k = -!-(cAr + djcA"-1 + ... + dr-lCA + ß ) cA^b In carrying out this calculation, one can see that the closed-loop characteristic polynomial is det(s7 -A + bk) = -¿-cAdj(s7 -A)b(sr + dis""1 + ... + ß -lS + ß ) cA^lb 1. e., that the state feedback (24) places the closed-loop poles at the zeros of the process and at the roots of sr + ß^1 + ... + /3r-i« + ß Consequently, the closed-loop system will be internally stable (and therefore this control approach will "work") if and only if all zeros are in the left-half plane; i.e., (II) is minimum phase. For minimum phase systems, the closed-loop response will be ISE-optimal in the limit as the roots of sr + diSM + ... + /3r-is + ß tend to negative infinity (55).…”

Nonlinear control of chemical processes: a review

“…They note an extension that combines feedback control with vibrational control and mention that work is in progress in this area. Cinar et al (1987c), Rigopoulos et al (1988), and Shu et al (1989) show that forcing the input flow and concentration leads to improved conversion. Indeed, a higher reactor productivity can be achieved at a given average temperature.…”

Vibrational control of chemical reactors: Selectivity enhancement, stabilization and improvement of transient behavior

“…lt does not suffer from the restrictive assumptions such as small amplitude perturbation assumption of the _-criterion approach. In a previous DOE Grant [6], it has been applied to increase the stabilized operation region of a OSTR [7]and has been useful in assessing the effects of multiple input forcings [8,9]. The vibrational control method generates averaged system equations for a system subject to periodic forcing around a stable equilibrium point.…”