Vibrational control of systems with arrhenius dynamics

A nonlinear system with S-shape steady state characteristic is referred to as a system with Arrhenius dynamics. The negative slope part of the S-shape curve represents a set of unstable steady states. Using two examples of Arrhenius systems (catalytic reactor and continuous stirred tank reactor), it is shown that introduction of sufficiently fast oscillations in system's parameters generates a new Arrhenius system, the steady state characteristic of which has a smaller negative slope part. Results of analytical investigation as well as numerical simulation are presented. It is shown that vibrational stabilization of Arrhenius systems gives an increase in productivity of the plants.

[1]  S. M. Meerkov.  Condition of vibrational stabilizability for a class of nonlinear systems , 1982 .

[2]  Semyon Meerkov,et al.  Principle of vibrational control: Theory and applications , 1979, 1979 18th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[3]  Bernard J. Matkowsky,et al.  ON INHIBITING RUNAWAY IN CATALYTIC REACTORS , 1978 .

[4]  James E. Bailey,et al.  Pat-hological dynamic behavior of forced periodic chemical processes , 1977 .

[5]  J. E. Bailey,et al.  Nonlinear feedback control for operating a nonisothermal CSTR near an unstable steady state , 1977 .

[6]  Elmer Gilbert,et al.  Optimal periodic control: A general theory of necessary conditions , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[7]  Aubrey B. Poore,et al.  The classification of the dynamic behavior of continuous stirred tank reactors—influence of reactor residence time , 1976 .

[8]  D. D. Bruns,et al.  Process operation near an unstable steady state using nonlinear feedback control , 1975 .

[9]  S. Rinaldi,et al.  Status of periodic optimization of dynamical systems , 1974 .

[10]  Magne Fjeld,et al.  Relaxed controls in asynchronous quenching and dynamical optimization , 1974 .

[11]  A. B. Poore,et al.  On the dynamic behavior of continuous stirred tank reactors , 1974 .

[12]  James E. Bailey,et al.  PERIODIC OPERATION OF CHEMICAL REACTORS: A REVIEW , 1974 .

[13]  Optimal periodic control of lumped parameter systems , 1974 .

[14]  J. E. Bailey,et al.  Comparison between two sufficient conditions for improvement of an optimal steady-state process by periodic operation , 1971 .

[15]  High-frequency optimal periodic processes , 1970 .

[16]  C. Mcgreavy,et al.  Generalised criteria for the stability of catalytic reactors , 1970 .

[17]  C. McGreavy,et al.  Stability studies of single catalyst particles , 1970 .

[18]  R. Bellman.  Dynamic Programming , 1957, Science.

[19]  N. Bogolyubov,et al.  Asymptotic Methods in the Theory of Nonlinear Oscillations , 1961 .

[20]  Rutherford Aris,et al.  An analysis of chemical reactor stability and control—II: The evolution of proportional control☆ , 1958 .

[21]  Rutherford Aris,et al.  An analysis of chemical reactor stability and control—I: The possibility of local control, with perfect or imperfect control mechanisms , 1958 .

[22]  Rutherford Aris,et al.  An analysis of chemical reactor stability and control—III: The principles of programming reactor calculations. Some extensions☆ , 1958 .

[23]  O. Bilous,et al.  Chemical reactor stability and sensitivity , 1955 .