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This paper describes the application of nonlinear model-predictive control (NMPC) to two distributed-parameter processes. The first system is a packed distillation column. The process gain varies in sign with the reboiler heat duty due to mass transfer effects. As a result, only a linear controller with gain scheduling can successfully control the process, but this prevents the outputs from settling to a steady state. The change in the sign of the gain also implies that there is a maximum achievable separation. NMPC recognizes this limit on the achievable separation, and does not continuously alter the manipulated variables in an attempt to reach an unrealizable set point. The second example is a fixed-bed catalytic reactor. Like the packed column, the fixed-bed reactor may require that the control algorithm deal with equilibrium effects that cause the sign of the reactor gain to vary. In addition, the time constants as well as the delay time of the system vary significantly with the gas flow rate. Inverse response may also be exhibited by the system. Because of the wide range of nonlinear effects that these systems exhibit, NMPC is an intuitively appealing approach that appears to be especially well-suited for such processes. In each case NMPC performance is superior to that of traditional linear controllers. |
