Optimal dispensing strategy for a two component xerographic development process

Inconsistent color reproduction is a major performance and quality issue for high volume digital press. Literature has shown that loss of developability of the toner particles in the development stage of xerography is a main contributing factor for inconsistent color reproduction. Previous works have shown that a second order system model is able to predict and characterize the inevitable loss of developability. In this paper, a nonlinear constrained optimal control problem is formulated to find the optimal dispensing strategy that maximizes the time for which acceptable developability is maintained. An analytical solution to the constrained optimal control problem is derived based on the Maximum Principle without explicitly solving for the costate dynamics. Results show that the state feedback based optimal dispensing strategy starts with the minimal allowable dispensing rate while increasing the development voltage to maintain the desired development quality until the maximal development voltage is reached. Then, the optimal dispense rate switches to maintain the developability at maximal development voltage. Numerical examples support the analytical solution.