Design and application of state variable feedback controllers for a packed trickle bed column with carbon dioxide absorption

Abstract

State variable feedback controllers using two or more process variables often yield a substantial improvement in control loop performance over that achieved with conventional feedback controllers. To date, no systematic procedure has been set forth in the literature for choosing the best process variables for state variable controllers. The problem of selecting the best variable for such a controller is particularly acute for distributed parameter system, since there is such a large number of state variables to choose from. A new, systematic design scheme for selecting the best of available process variables is proposed and demonstrated in this work. This scheme is applied to the backflow cell model of a packed bed absorption column available in the laboratory. It is of interest to manipulate water flow rate to the absorber so as to minimize the variation of the carbon dioxide gas concentration near the top of the column (controlled variable) for a step increase in the inlet gas concentration. The design scheme first performs a dynamic optimization to determine the state and control time trajectories which minimize an integral-time-square-error performance index. This index was chosen to describe the control objective noted above. Next, the statistical Step Up procedure uses the optimal state and control trajectories to determine the order of Importance of available states in terms of their abilities to reduce the performance index.