Dynamics and Control of the Cumulative Mass Fraction of a Particle Size Distribution

A transfer function for the dynamics of the cumulative mass fraction (CMF) of a particle size distribution (PSD) is developed. It fits the general form Gp=P1(s)-P2(s)e^-Tds/Q(s) frequently encountered in systems modeled by hyperbolic partial differential equations. Systems of this type are given the name quasi rational distributed systems (QRDS). QRDS can have an infinity of right half-plane zeros but do not exhibit delayed or inverse response. A procedure for designing predictive controllers for QRDS using a Smith predictor structure is presented. It uses pole placement to obtain a controller parameterization with the adjustable parameters being selected to satisfy robustness specifications. A controller for CMF, designed using this procedure, performs better than a PID controller.