Control analysis of a hybrid two-component development process

In this paper, we will illustrate the utility of a control oriented model for a hybrid two component development process. The model used for control extracts relevant characteristics from an experimentally validated numerical model based on toner age distribution and development probability. Equilibrium analysis of the model shows, that developability loss associated with low area coverage, low humidity operating conditions can be attributed to the fact that the development process is not operating around an equilibrium point. Velocity field analysis indicates the process has limited controllability under these operating conditions. Based on these observations, a constrained optimal control problem is formulated to develop a control strategy to maximize the operating time while maintaining acceptable developability. The numerical solution shows that for a given operating condition, with bounded toner concentration and development voltage, the optimal dispense strategy is a concatenation of a zero-dispense profile and a controlled dispense rate associated with operating the development voltage at its maximum value.