Fast Estimation of Quasi-Steady States of Cyclic Nonlinear Processes Based on Higher-Order Frequency Response Functions. Case Study: Cyclic Operation of an Adsorption Column

A new method for fast approximate calculation of quasi-steady states of cyclic processes is presented. The method is based on the concept of higher-order frequency response functions. The system input is represented in the form of Fourier series, whereas the output is presented in the form of Volterra series. For practical applications, both the input and the output series are approximated by finitelength sums. In this way, the approximate periodic quasi-steady state of the system output is calculated directly, without long numerical integrations. Cyclic operation of an adsorption column with periodic fluctuations of the inlet concentration or/and adsorbent temperature is used as a case study for testing the new method. The necessary frequency response functions (FRFs), up to the third order, are derived, based on the equilibrium dispersion model. The method is tested for sinusoidal and rectangular input changes. The approximate solutions based on the FRFs, up to the third order, and a finite number of input harmonics, are calculated for different input frequencies and amplitudes and compared with the numerical solutions. Very good agreement is obtained.