Internal Process Controls - Control of Color Imaging Systems: Analysis and Design - page 514

9.11 TC CONTROL LOOP
In a typical two-component development housing, toners and carriers are mixed in
the sump at a speci

ed ratio known as the TC (Section 10.2.3). The toner particles
consist of dyed or colored thermoplastic powder that is mixed with coarser carrier
granules, such as ferromagnetic granules. The toner particles and carrier granules are
selected such that the toner particles acquire the appropriate charge during mixing.
This mixture is transported to the development zone where the toner particles are
presented to the latent image on the photoconductor. When they are brought into
contact with the charged photoconductive surface, the greater attractive force
between the electrostatic latent image and the toner particles causes the toner
particles to transfer from the carrier granules and adhere to the electrostatic latent
image. In some of the multicolor electrophotographic print engines, the mixture is
picked up by a developer roll, metered using a trim bar to achieve a uniform
thickness with toner particles alone and transported to the development zone.
The concentration of toner in the development housing has an effect on the amount
of toner attracted to charged portions of the photoconductor. For instance, the higher
the concentration of toner in the housing, the more toner is attracted to the photocon-
ductor (Equations 10.30 and 10.31). TC can be controlled by controlling the rate at
which toner from the toner supply is delivered to the developer housing. TC sensors
[29

36] are used to sense, for example, the magnetic reluctance associated with
magnetic carrier particles in the developer housing. As the TC grows higher, the
average spacing between the carrier beads gets larger and the reluctance becomes
lower. The magnetic reluctance signal is used to measure the TC in the developer.
Developer granule size, developer age, tribo, and, possibly, the temperature and RH
affect the TC measurements. These factors are referred to as sensor noise, and some of
them can be carefully measured, estimated (e.g., toner age [31,32]), and isolated from
the actual signal depending on the complexity and cost associated with the system.
Changing the TC in the developer housing can affect the lightness or darkness of
a rendered image. Hence, the TC can be used as one of the xerographic process
actuators [16] in addition to those used in level 2 controls as described in Section 9.6.
The design of such a feedback system could be inherently simple if we didn

-

t have
the complexity of the transport delay in dispensing the toner to the developer
housing, that is, the rate limitation in dispense and consumption of toner as images
are rendered at production speed. In Section 9.13, we show a systematic way to
realize a feedback system with a transport delay using state feedback control
approaches. In this section, by maintaining TC constant at a set point, we minimize
the number of factors affecting the developability, and the toner dispense rate is used
as the actuator [35].

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9.11.1 O PEN -L OOP TC M ODEL
TC is the ratio of toner mass to the carrier mass. In simple terms, the toner mass (t m )
at cycle k can be modeled by the following difference equation

t m ( k þ 1 ) ¼ t m ( k ) þ m d ( k m) m i ( k ) ( 9 : 59 )