Toner maintenance subsystem for a printing machine

An apparatus for controlling the concentration of toner within a developer material of carrier and toner. The apparatus having a control means for generating a toner addition signal indicative of the amount of toner to be added to the developer material. The control means including the ability to measure the concentration of toner within the developer material during at least a first period and a second period subsequent to the first period. The control means also determining a first concentration error as a function of the deviation between the toner concentration measured during the first period and a reference toner concentration and a second concentration error as a function of the deviation between the toner concentration measured during the second period and the reference toner concentration. Subsequently, the control means generates the toner addition signal as a function of the first and second concentration error values. The apparatus also includes means, responsive to the toner addition signal, for regulating the addition of toner to said developer material.

This invention relates generally to a printing machine, and more 
particularly concerns an apparatus for controlling the concentration of 
toner in the development system of an electrophotographic printing 
machine. 
In a typical electrophotographic printing process, a photoconductive member 
is charged to a substantially uniform potential so as to sensitize the 
surface thereof. The charged portion of the photoconductive member is 
exposed to a light image of an original document being reproduced. 
Exposure of the charged photoconductive member selectively dissipates the 
charge thereon in the irradiated areas. This records an electrostatic 
latent image on the photoconductive member corresponding to the 
informational areas contained within the original document. After the 
electrostatic latent image is recorded on the photoconductive member, the 
latent image is developed by bringing a developer material into contact 
therewith. Generally, the developer material comprises toner particles 
adhering triboelectrically to carrier granules. The toner particles are 
attracted from the carrier granules to the latent image forming a toner 
powder image on the photoconductive member. The toner powder image is then 
transferred from the photoconductive member to a copy sheet. Subsequently, 
the toner particles are heated to permanently affix the powder image to 
the copy sheet. 
In a machine of the foregoing type, it is desirable to regulate the 
addition of toner particles to the developer material in order to 
ultimately control the triboelectric characteristics (tribo) of the 
developer material. However, control of the triboelectric characteristics 
of the developer material are generally considered to be a function of the 
toner concentration within the material. Therefore, for practical 
purposes, machines of the foreoing type usually attempt to control the 
concentration of toner in the developer material. 
Various approaches have been devised for controlling the concentration of 
toner in the development system. The following disclosures appear to be 
relevant: 
U.S. Pat. No. 3,873,002 
Patentee: Davidson et al. 
Issued: Mar. 25, 1975. 
U.S. Pat. No. 4,318,610 
Patentee: Grace. 
Issued: Mar. 9, 1982. 
U.S. Pat. No. 4,326,646 
Patentee: Lavery et al. 
Issued: Apr. 27, 1982. 
U.S. Pat. No. 4,348,099 
Patentee: Fantozzi. 
Issued: Sept. 7, 1982. 
U.S. Pat. No. 4,956,669 
Patentee: Nakamura et al. 
Issued: Sept. 11, 1990. 
The relevant portions of the foregoing patents may be summarized as 
follows: 
Davidson et al. describes a control device which regulates the dispensing 
of predetermined quantities of particles from a storage container to a mix 
for maintaining the concentration thereof substantially at a preselected 
level. Specifically, a detecting means is used to determine the toner 
concentration and to signal a count detector. Subsequently, control logic 
analyzes the value contained in the count detector to determine whether a 
half or full toner dispense cycle is required. 
Grace describes an apparatus in which toner particle concentration within a 
developer mixture and charging of the photoconductive surface are 
controlled. More specifically, an infrared densitometer generates 
electrical signals proportional to the developed toner mass of test areas 
on the photoconductive surface. The signals are fed through a conversion 
circuit and subsequently interpreted by a controller. The controller 
energizes a toner dispense motor, via a logic interface, whenever the 
detected density of the toner concentration test patch is below a nominal 
level. In addition, successive energizing of the toner dispense motor 
without an increase in detected density results in the generation of a 
"toner container empty" signal by the controller. 
Lavery et al. discloses an automatic development control system utilizing a 
control loop to vary the time period of activation of a toner dispenser. 
The toner dispenser is activated for a predetermined fraction of the copy 
cycle depending upon the relative density of a test patch versus a desired 
density. For example, when the detected test patch toner density is first 
indicated as low, the toner dispenser is activated for a period of 0.5 
seconds. For successive indications of a low toner density the toner 
dispenser is activated in increments of 0.5 seconds up to a maximum period 
of 1.5 seconds. 
Fantozzi teaches a sample data control system for controlling charge, 
illumination, toner dispensing, and developer bias. The system disclosed 
utilizes a toner dispensing control loop for regulating toner, wherein the 
control loop responds to a signal from an infrared sensor which detects 
the density of a developed test patch. Specifically, the voltage level 
from the sensor is compared against a reference voltage. If the voltage 
from the sensor is indicative of a toner density less than the desired 
density, the dispense motor is activated at a low or high rate. Once the 
toner density is determined to be sufficiently greater than the desired 
density, the dispense motor is turned off. This control process continues 
with the dispense motor being activated as required and the adjustment or 
activation of the toner dispenser being made if required preferably after 
each even copy cycle. 
Finally, Nakamura et al. describes a control apparatus for controlling the 
concentration of toner incorporated in developing material by means of 
controlling toner replenishment. Specifically, a toner concentration 
detecting sensor signal is analyzed to detect an abnormal sensor 
condition. When such a situation occurs, toner is dispensed at a constant 
volume. If the sensor is operating normally, an average signal level is 
used to determine the toner volume to be dispensed. 
In accordance with one aspect of the present invention, there is provided 
an apparatus for controlling the concentration of toner within a developer 
material of carrier and toner having a control means for generating a 
toner addition signal indicative of the amount of toner to be added to the 
developer material. The control means including the ability to measure the 
concentration of toner within the developer material during at least a 
first period and a second period subsequent to the first period. The 
control means also determining a first concentration error value as a 
function of the deviation between the toner concentration measured during 
the first period and a first reference toner concentration and a second 
concentration error value as a function of the deviation between the toner 
concentration measured during the second period and a second reference 
toner concentration. Subsequently, the control means generates the toner 
addition signal as a function of the first and second concentration error 
values. The apparatus also includes means, responsive to the toner 
addition signal, for regulating the addition of toner to said developer 
material. 
Pursuant to another aspect of the features of the present invention, there 
is provided an electrophotographic printing machine having a development 
subsystem arranged to supply a developer mixture, with a controlled toner 
concentration, for the development of a latent electrostatic image, and 
means for periodically measuring the toner concentration within the 
developer mixture. The machine also includes means, operative at a first 
time, for calculating a first error value which is indicative of the 
deviation of the measured toner concentration from a first desired toner 
concentration, and means, operative at a second time subsequent to the 
first time, for calculating a second error value which is indicative of 
the deviation of the measured toner concentration from a second desired 
toner concentration. In addition, means for determining the amount of 
toner that was added to the development mixture are operative between the 
first and second times to determine the amount of toner added to the 
developer mixture. Moreover, the machine includes means for generating a 
toner dispense level in response to the first error value, the second 
error value and the amount of toner added, and regulating means to 
regulate the addition of toner to the development mixture in response to 
the toner dispense level.

While the present invention will hereinafter be described in connection 
with a preferred embodiment thereof, it will be understood that it is not 
intended to limit the invention to that embodiment. On the contrary, it is 
intended to cover all alternatives, modifications, and equivalents, as may 
be included within the spirit and scope of the invention as defined by the 
appended claims. 
For a general understanding of the features of the present invention, 
reference is made to the drawings. In the drawings, like reference 
numerals have been used throughout to identify identical elements. FIG. 1 
schematically depicts an electrophotographic printing machine 
incorporating the features of the present invention therein. It will 
become evident from the following discussion that the apparatus of the 
present invention may be employed in a wide variety of devices and is not 
specifically limited in its application to the particular embodiment 
depicted herein. 
Referring to FIG. 1 of the drawings, the electrophotographic printing 
machine employs a photoconductive belt 10. Preferably, the photoconductive 
belt 10 is made from a photoconductive material coated on a ground layer, 
which, in turn, is coated on an anti-curl backing layer. The 
photoconductive material is made from a transport layer coated on a 
generator layer. The transport layer transports positive charges from the 
generator layer. The interface layer is coated on the ground layer. The 
transport layer contains small molecules of 
di-m-tolydiphenylbiphenyldiamine dispersed in a polycarbonate. The 
generation layer is made from trigonal selenium. The grounding layer is 
made from a titanium coated Mylar. The ground layer is very thin and 
allows light to pass therethrough. Other suitable photoconductive 
materials, ground layers, and anti-curl backing layers may also be 
employed. Belt 10 moves in the direction of arrow 12 to advance successive 
portions of the photoconductive surface sequentially through the various 
processing stations disposed about the path of movement thereof. Belt 10 
is entrained about stripping roller 14, tensioning roller 16, idler 
rollers 18, and drive roller 20. Stripping roller 14 and idler rollers 18 
are mounted rotatably so as to rotate with belt 10. Tensioning roller 16 
is resiliently urged against belt 10 to maintain belt 10 under the desired 
tension. Drive roller 20 is rotated by a motor coupled thereto by suitable 
means such as a belt drive. As roller 20 rotates, it advances belt 10 in 
the direction of arrow 12. 
Initially, a portion of the photoconductive surface passes through charging 
station A. At charging station A, two corona generating devices, indicated 
generally by the reference numerals 22 and 24, charge photoconductive belt 
10 to a relatively high, substantially uniform potential. Corona 
generating device 22 places all of the required charge on photoconductive 
belt 10. Corona generating device 24 acts as a leveling device, and fills 
in any areas missed by corona generating device 22. 
Next, the charged portion of the photoconductive surface is advanced 
through imaging station B. At imaging station B, a document handling unit, 
indicated generally by the reference numeral 26, is positioned over platen 
28 of the printing machine. Document handling unit 26 sequentially feeds 
original documents from a stack of documents placed by the operator face 
up in a normal forward collated order in the document stacking and holding 
tray. A document feeder located below the tray forwards the bottom 
document in the stack to a pair of take-away rollers. The bottom sheet is 
then fed by the rollers through a document guide to a feed roll pair and 
belt. The belt advances the document to platen 28. After imaging, the 
original document is fed from platen 28 by the belt into a guide and feed 
roll pair. The document then advances into an inverter mechanism and back 
to the top of the stack of original documents through the feed roll pair. 
A position gate is provided to divert the document to the inverter or to 
the feed roll pair. Imaging of a document is achieved by lamps 30 which 
illuminate the document on platen 28. Light rays reflected from the 
document are transmitted through lens 32. Lens 32 focuses light images of 
the original document onto the charged portion of photoconductive belt 10 
to selectively dissipate the charge thereon. This records an electrostatic 
latent image on the photoconductive belt which corresponds to the 
informational areas contained within the original document. In this way, a 
plurality of original documents may be sequentially exposed. 
Alternatively, document handling unit 26 may be pivoted away from platen 
28 and an original document positioned manually thereon. One or more 
copies of the original document may be reproduced by the printing machine. 
The original document is exposed and a latent image recorded on the 
photoconductive belt. Thereafter, belt 10 advances the electrostatic 
latent image recorded thereon to development station C. 
Development station C has three magnetic brush developer rolls, indicated 
generally by the reference numerals 34, 36 and 38. Paddle wheel 35 picks 
up developer material from developer sump 114 and delivers it to the 
developer rolls. When developer material reaches rolls 34 and 36, it is 
magnetically split between the rolls with half the developer material 
being delivered to each roll. Photoconductive belt 10 is partially wrapped 
about rolls 34 and 36 to form extended development zones. Developer roll 
38 is a cleanup roll. A magnetic roll, positioned after developer roll 38, 
in the direction of arrow 12, is a carrier granule removal device adapted 
to remove any carrier granules adhering to belt 10. Thus, rolls 34 and 36 
advance developer material into contact with the electrostatic latent 
image. The latent image attracts toner particles from the carrier granules 
of the developer material to form a developed toner powder image on the 
photoconductive surface of belt 10. Belt 10 then advances the developed 
toner powder image to transfer station D. 
At transfer station D, a copy sheet is moved into contact with the toner 
powder image. First, photoconductive belt 10 is exposed to a pre-transfer 
light from a lamp (not shown) to reduce the attraction between 
photoconductive belt 10 and the toner powder image. Next, a corona 
generating device 40 charges the copy sheet to the proper magnitude and 
polarity so that the copy sheet is tacked to photoconductive belt 10 and 
the toner powder image attracted from the photoconductive belt to the copy 
sheet. After transfer, corona generator 42 charges the copy sheet to the 
opposite polarity to detack the copy sheet from belt 10. Conveyor 44 
advances the copy sheet to fusing station E. 
Fusing station E includes a fuser assembly, indicated generally by the 
reference numeral 46 which permanently affixes the transferred toner 
powder image to the copy sheet. Preferably, fuser assembly 46 includes a 
heated fuser roller 48 and a pressure roller 50 with the powder image on 
the copy sheet contacting fuser roller 48. The pressure roller is cammed 
against the fuser roller to provide the necessary pressure to fix the 
toner powder image to the copy sheet. The fuser roll is internally heated 
by a quartz lamp. Release agent, stored in a reservoir, is pumped to a 
metering roll. A trim blade trims off the excess release agent. The 
release agent transfers to a donor roll and then to the fuser roll. 
After fusing, the copy sheets are fed through a decurler 52. Decurler 52 
bends the copy sheet in one direction to put a known curl in the copy 
sheet and then bends it in the opposite direction to remove the curl. 
Forwarding rollers 54 then advance the sheet to duplex turn roll 56. Duplex 
solenoid gate 58 guides the sheet to the finishing station F or to duplex 
tray 60. At finishing station F, copy sheets are stacked in compiler trays 
to form sets of copy sheets. The sheets of each set are optionally stapled 
to one another. The sets of copy sheets are then delivered to a stacking 
tray. In the stacking tray, each set of copy sheets may be offset from an 
adjacent set of copy sheets. Further details of finishing station F will 
be described hereinafter with reference to FIG. 2. 
With continued reference to FIG. 1, when duplex solenoid gate 58 diverts 
the sheet into duplex tray 60. Duplex tray 60 provides an intermediate or 
buffer storage for those sheets that have been printed on one side and on 
which an image will be subsequently printed on the second, opposed side 
thereof, i.e. the sheets being duplexed. The sheets are stacked in duplex 
tray 60 face down on top of one another in the order in which they are 
copied. 
In order to complete duplex copying, the simplex sheets in tray 60 are fed, 
in seriatim, by bottom feeder 62 from tray 60 back to transfer station D 
via conveyor 64 and rollers 66 for transfer of the toner powder image to 
the opposed sides of the copy sheets. Inasmuch as successive bottom sheets 
are fed from duplex tray 60, the proper or clean side of the copy sheet is 
positioned in contact with belt 10 at transfer station D so that the toner 
powder image is transferred thereto. The duplex sheet is then fed through 
the same path as the simplex sheet to be advanced to finishing station F. 
Copy sheets are fed to transfer station D from the secondary tray 68. The 
secondary tray 68 includes an elevator driven by a bidirectional AC motor. 
Its controller has the ability to drive the tray up or down. When the tray 
is in the down position, stacks of copy sheets are loaded thereon or 
unloaded therefrom. In the up position, successive copy sheets may be fed 
therefrom by sheet feeder 70. Sheet feeder 70 is a friction retard feeder 
utilizing a feed belt and take-away rolls to advance successive copy 
sheets to transport 64 which advances the sheets to rolls 66 and then to 
transfer station D. 
Copy sheets may also be fed to transfer station D from the auxiliary tray 
72. The auxiliary tray 72 includes an elevator driven by a bidirectional 
AC motor. Its controller has the ability to drive the tray up or down. 
When the tray is in the down position, stacks of copy sheets are loaded 
thereon or unloaded therefrom. In the up position, successive copy sheets 
may be fed therefrom by sheet feeder 74. Sheet feeder 74 is a friction 
retard feeder utilizing a feed belt and take-away rolls to advance 
successive copy sheets to transport 64 which advances the sheets to rolls 
66 and then to transfer station D. 
Secondary tray 68 and auxiliary tray 72 are secondary sources of copy 
sheets. A high capacity feeder, indicated generally by the reference 
numeral 76, is the primary source of copy sheets. High capacity feeder 76 
includes a tray 78 supported on an elevator 80. The elevator is driven by 
a bidirectional AC motor to move the tray up or down. In the up position, 
the copy sheets are advanced from the tray to transfer station D. A 
fluffer and air knife 83 direct air onto the stack of copy sheets on tray 
78 to separate the uppermost sheet from the stack of copy sheets. A vacuum 
pulls the uppermost sheet against feed belt 81. Feed belt 81 feeds 
successive uppermost sheets from the stack to an take-away drive roll 82 
and idler rolls 84. The drive roll and idler rolls guide the sheet onto 
transport 86. Transport 86 advances the sheet to rolls 66 which, in turn, 
move the sheet to transfer station station D. 
Invariably, after the copy sheet is separated from the photoconductive belt 
10, some residual particles remain adhering thereto. After transfer, 
photoconductive belt 10 passes beneath corona generating device 94 which 
charges the residual toner particles to the proper polarity. Thereafter, 
the pre-charge erase lamp (not shown), located inside photoconductive belt 
10, discharges the photoconductive belt in preparation for the next 
charging cycle. Residual particles are removed from the photoconductive 
surface at cleaning station G. Cleaning station G includes an electrically 
biased cleaner brush 88 and two de-toning rolls 90 and 92, i.e. waste and 
reclaim de-toning rolls. The reclaim roll is electrically biased 
negatively relative to the cleaner roll so as to remove toner particles 
therefrom. The waste roll is electrically biased positively relative to 
the reclaim roll so as to remove paper debris and wrong sign toner 
particles. The toner particles on the reclaim roll are scraped off and 
deposited in a reclaim auger (not shown), where it is transported out of 
the rear of cleaning station G. 
The various machine functions are regulated by a controller. The controller 
is preferably a programmable microprocessor which controls all of the 
machine functions hereinbefore described. The controller provides a 
comparison count of the copy sheets, the number of documents being 
recirculated, the number of copy sheets selected by the operator, time 
delays, jam corrections, etc. The control of all of the exemplary systems 
heretofore described may be accomplished by conventional control switch 
inputs from the printing machine consoles selected by the operator. 
Conventional sheet path sensors or switches may be utilized to keep track 
of the position of the documents and the copy sheets. In addition, the 
controller regulates the various positions of the gates depending upon the 
mode of operation selected. 
Referring now to FIG. 2, the general operation of the toner maintenance 
subsystem within development station C will now be described. Exposure 
station B includes a test area generator (not shown) to discharge a 
portion of belt 10 to produce a latent test area. Generally, the 
discharged or latent test area will occupy an inter-document zone so as to 
avoid any deleterious effects to latent images exposed from the platen. 
After discharging the test area, belt 10 is advanced to development 
station C where the toner is deposited upon the latent test area. The 
amount or mass of toner deposited upon the test area is indicative of the 
toner concentration within the developer material at the time the area is 
developed. Specifically, the toner maintenance subsystem is designed to 
improve copy quality by controlling the amount or mass of toner developed 
on the copy sheet, for a given document area coverage, by regulating the 
concentration of toner within the developer material. 
Subsequent to development of the test area, belt 10 is advanced thereby 
causing the developed test area to pass infrared lamp/detector module 120. 
More specifically, an infrared (I/R) lamp within module 120 directs a 
light beam onto the developed test area of belt 10. Concurrently, an I/R 
detector within module 120 detects the intensity of the reflected beam. 
The intensity is a measure of the reflectivity of the developed test area. 
Module 120 sends a signal representative of the intensity to conversion 
circuitry 122 which in turn integrates and converts the signal to provide 
a measurement of the developed toner mass residing on the developed test 
area. The detected toner mass is referred to as ird in FIG. 3. 
Development station C receives toner from a toner dispenser indicated 
generally by reference numeral 110. The supply of toner is maintained in 
container 112 and is introduced to development sump 114 via mixing auger 
116 which is driven at a constant rate whenever AC motor 118 is energized. 
Energizing AC motor 118 not only drives auger 116 but also drives a 
metering roll (not shown) that regulates the flow of toner into the auger. 
For example, auger 116 may comprise a helical spring mounted in a tube, 
whereby rotation of the spring causes toner to advance through the tube 
and to be mixed with developer material recycled from the the developer 
sump 114. The energizing of motor 118 is directly controlled by dispense 
motor control 126 which in turn is signaled by the toner dispense control 
loop of the present invention. Introduction of the toner in this way would 
assure that uncharged toner is never introduced directly into the 
development station C. 
To enable a better understanding of the toner maintenance system, a 
mathematical model was derived to represent the feedback control system 
illustrated in FIG. 3. The five part model specifically relates the toner 
triboelectric charge or tribo (tr(t)) and toner concentration in the 
developer material (tc(t)) using an ordinary differential equation. 
Referring now to FIG. 3, the toner concentration is modeled by the 
following equation: 
##EQU1## 
where u(t) is the rate at which toner is added to developer material in 
developer sump 114, control signal 150, v(t) is the rate at which toner is 
removed from the developer material due to developement of latent 
electrostatic images, and M.sub.c is the mass of the carrier in the 
developer material. In general, the developer material acts as an 
integrator for the net toner input flow. 
Second, the amount of toner developed on the photoconductive belt is a 
function of the tribo, the toner concentration and the voltage on belt 10. 
A simplified model of the tribo, defined hereinafter as the ratio of the 
total charge on a batch of toner particles to the total mass of the 
particles, is represented by a first order differential equation as 
follows: 
##EQU2## 
where .beta. is the charging rate of the toner particles, tr.infin. is a 
constant representing the maximum attainable tribo charge, M.sub.T is the 
mass of the toner within the developer material, and tr.sub.i is the 
initial charge of the toner after dispense from container 112 of FIG. 2. 
Next, the toner development model was established with the following 
empirical relationship: 
##EQU3## 
where dma(t) represents the developed mass of toner, signal 152, V.sub.dev 
the bias development voltage, tr(t) the tribo of the toner in the 
developer material, signal 154, and tc(t) the toner concentration in the 
developer material, signal 156. Furthermore, parameters a, b, and c are 
system dependent constants. 
Fourth, the toner dispenser, consisting of the aforementioned mixing auger 
116 and AC motor 118, was studied to characterize the time required for a 
toner particle to travel the length of the auger tube. There is an 
inherent lag time between the actual addition of the toner particle to the 
auger and the time when the particle exits the auger having been mixed 
with the recycled developer material. This transportation lag is modeled 
by: 
EQU u(t)=u'(t-.mu.) (4) 
where .mu. is a constant delay, block 158, representative of a lag time of 
about 25 seconds, u'(t) is the rate at which the motor dispenses toner, 
signal 150, and u(t) is, again, the rate at which toner is available in 
the developer housing (i.e. when it reaches the end of auger 116), shown 
as signal 160. Generally, the dispense control strategy is to toggle AC 
motor 118 "on" and "off" each sampling period. Furthermore, if T is the 
sampling period, dc(k) the duty cycle of AC motor 118 in the k.sup.th 
sampling period, and u.sub.max the rate at which toner is dispensed to 
auger 116 when AC motor 118 is "on", then the amount of toner dispensed in 
the k.sup.th sampling period is equal to Tdc(k)u.sub.max. 
Finally, the infrared sensor, module 120, which converts reflectance to a 
digital representation (ird(t)) can be used to approximate the developed 
mass of toner on the test area. A typical relationship between module 120 
output, ird(t) as shown by signal 162, and the developed mass, dma(t) or 
signal 152, is expressed in a linear fashion as follows: 
EQU ird(t)=m.sub.1 dma(t)+m.sub.2 (5) 
where m.sub.1 and m.sub.2 are constants. It is important to note that the 
reflectance of the developed test area is measured after the test area has 
passed development station C, thereby introducing a time lag into the 
control loop. Such a delay could be incorporated into the ird measurement, 
however, due to the delay incorporated in the toner dispense model 
(Equation 4) and the speed of belt 10, no delay was factored into the 
sensor equation. It was further determined that a dma setpoint of 0.52 
mg/cm.sup.2 corresponds to an ird setpoint, illustrated as input signal 
166, of about 85 ird bits. While the dma setpoint indicated is typical of 
the present embodiment, the value is variable depending upon the 
mechanical configuration of the machine, as well as, the type of toner 
used in the developer material. 
The toner maintenance subsystem is controlled by the linear feedback 
control system illustrated in FIG. 3. After modeling the individual 
components of the toner maintenance system, it was necessary to design a 
control law to reduce the steady state error in developed mass that occurs 
through toner removal as a result of latent image development. Initially, 
the nonlinear state and output equations, Equations 1, 2, and 3, were 
linearized. Subsequently, the linearized model equations were discretized 
under the assumption that toner dispensing is accomplished in a 
pulse-width modulated fashion. Pulse-width modulation (PWM) of the control 
signal is an alternative to amplitude modulation and arises since the 
actuator is an AC motor which is either "on" or "off". Due to PWM, the 
resulting differential equations were once again nonlinear and another 
linearization step was required. Finally, a discrete time feedback system 
was synthesized to achieve zero steady state error regulation, including 
the selection of a discrete time proportional-integral (PI) compensator to 
meet the requirements. The resulting control law, expressed as a 
difference equation, is as follows: 
EQU .delta.(k)=.alpha..sub.1 e(k)-.alpha..sub.2 e(k-1)+.delta.(k-1)(6) 
where .alpha..sub.1 and .alpha..sub.2 are constants and .delta.(k) 
represents the present difference, signal 168, .delta.(k-1) represents the 
previous difference. Error e(k), where e(k)=dma(k)-0.52, reflects the 
deviation between the actual developed mass and the desired developed 
toner mass of 0.52 mg/cm.sup.2. In addition, the previous error term 
e(k-1) is representative of the previous deviation between the previously 
measured toner mass dma(k-1) and the desired mass of 0.52 mg/cm.sup.2. 
Practically speaking, the error terms e(k) and e(k-1) were determined by 
calculating the deviation between the incoming ird signal and the ird 
setpoint of 85 as previously mentioned. Alternatively, the desired toner 
mass may be a variable value that is changed in accordance with a specific 
document type or in response to other system factors. Furthermore, the 
duty cycle of AC motor 118, dc(k) and signal 164, is related to .delta.(k) 
by the normalized equation: 
EQU dc(k)=.delta.(k)+0.5 (7) 
The control law is also constrained by the limits dc(k).epsilon.[0.2 0.8] 
in a preferred embodiment, where the lower limit is established by 
quantifying the amount of time required to overcome the inertia within the 
development subsystem. The upper limit is based upon the portion of the 
duty cycle required to obtain a predetermined maximum amount of toner 
dispense. The upper limit is a function of the rate at which AC motor 118 
is driven, thereby requiring a limit of 0.8 when the motor is driven by 60 
Hz AC power and a limit of 1.0 when the motor is driven by 50 Hz AC power. 
Furthermore, the control limits may be set in memory which is coupled to 
controller 124, preferably non-volatile memory (NVM). The control law and 
the associated constraints are implemented as follows: 
______________________________________ 
if .delta.(k) + 0.5 .ltoreq. 0.1 
**Excess - No Duty Cycle** 
then dc(k) = 0; 
elseif .delta.(k) + 0.5 .ltoreq. 0.2 
**Low Duty Cycle** 
then dc(k) = 0.2; 
elseif .delta.(k) + 0.5 .ltoreq. 0.8 
**Normal Duty Cycle** 
then dc(k) = .delta.(k) + 0.5; 
elseif .delta.(k) + 0.5 &gt; 0.8 
**High Duty Cycle** 
then dc(k) = 0.8; 
______________________________________ 
In the implementation of the above control law, certain modifications were 
made to make the implementation more efficient from a software and 
arithmetic processing standpoint. Specifically, the control law was 
restated as follows: 
EQU CD(n)=CD(n-1)+.alpha..sub.1 E(n)-.alpha..sub.2 E(n-1)-MD(n-1)(8) 
where CD(n) represents the toner dispense level currently required 
.delta.(n), CD(n-1) represents the previous toner dispense level 
.delta.(n-1), E(n) the current error term e(n), and E(n-1) the previous 
error term e(n-1). The MD(n-1) term is introduced to track negative values 
for .delta.(n) in order to eliminate the need for sign checking of the 
control variables. For example, when .delta.(n) is a positive value, CD(n) 
is equal to .delta.(n) and MD(n) is reset to zero. Moreover, when 
.delta.(n) is negative, MD(n) is set equal to -.delta.(n) and CD(n) is 
reset to zero. In this manner, the sign of the resultant difference is 
tracked via two separate variables. 
Referring now to FIGS. 4A and 4B, the toner concentration control process 
begins at step 210. The control process implemented in the preferred 
embodiment hereafter described is based upon Equation 8 above, which 
includes the minor modifications indicated to enable the process to be 
controlled by a microcontroller or microprocessor (e.g., an Intel.RTM. 
8085). At step 212, controller 124 of FIG. 2 determines the current toner 
concentration error term E(n) by calculating the difference between the 
ird signal from the infrared detector, via conversion circuit 122 of FIG. 
2, and the ird setpoint. Next, in step 214 the previous toner 
concentration error term E(n-1) is retrieved from memory having been 
calculated and stored during a previous control period. Steps 216 and 218 
retrieve the previous dispense (CD(n-1)) and excess (MD(n-1)) values from 
memory, the values having been generated during the preceding control 
period. Subsequently, step 220 calculates current toner dispense level 
CD(n) in accordance with Equation 8, substituting the appropriate 
constants or weighting factors, .alpha..sub.1 and .alpha..sub.2. 
Having calculated current dispense level CD(n) in step 220, the controller 
then tests the sign of CD(n) at step 222. If the sign of CD(n) is 
negative, CD(n) is indicative of an excess toner concentration. 
Consequently, additional toner will not be added to the developer 
material. However, in order to track the excess toner concentration, 
excess concentration value MD(n) is set equal to the magnitude of CD(n), 
neglecting the sign of CD(n), at step 224. Subsequently, at step 226, 
CD(n) is reset to zero as described previously to prevent addition of 
toner to the developer material. If CD(n) was determined to be a positive 
value, as the result of decision step 222, the excess concentration value 
MD(n) is reset to zero at step 228 to prevent further propagation of the 
excess toner error. 
Once all the current values are established, step 230 saves them for use 
during the following control period. More specifically, step 230 stores 
the values as follows: 
EQU CD(n-1).rarw.CD(n), 
EQU E(n-1).rarw.E(n), 
and 
EQU MD(n-1).rarw.MD(n). 
In addition, this step may include the ability to limit the values of both 
CD(n) and/or MD(n) in order to limit the propagation of large amounts of 
error that occur due to system limitations. For example, if CD(n) were 
unbounded, the error could accumulate over many periods and when the 
system was able to respond accordingly, an excessive amount of toner may 
be added to the developer material. 
In the succeeding steps, the duty cycle of the AC motor is determined in 
accordance with the aforementioned control law. Generally, the control law 
is implemented as a software programmed CASE or SELECT statement but for 
clarity it has been illustrated in FIG. 4B as a series of decision steps. 
Step 232 first tests CD(n) to determine if it is less than the minimum 
level required to initiate the dispensing of toner. Decision step 232 
illustrates the comparison of CD(n) against a value (MIN-100). The value 
(MIN-100) is indicative of a threshold level below which no toner is to be 
added to the system (i.e. the system is within reasonable error of the 
desired toner concentration). If CD(n) is below (MIN-100), the duty cycle 
is set at 0 at step 234 and no toner will be dispensed from container 112 
of FIG. 2 to developer sump 114. 
Step 236 tests CD(n) to determine if it is greater than the maximum 
dispense level (MAX), where MAX is a normalized representation of the 0.8 
limit imposed on the control law. If CD(n) meets or exceeds MAX, the duty 
cycle of the AC motor is set to a predetermined HIGH duty cycle at step 
238. Generally, the duty cycle associated with HIGH is determined at the 
time the machine is installed in order to compensate for the differences 
in performance of AC motor 118 when utilizing 50 or 60 Hertz AC power. If 
CD(n) was less than MAX, testing continues at step 240 where CD(n) is 
compared to MIN, where MIN is the normalized representation of the 0.2 
limit of the control law. If CD(n) is less than MIN, it falls into the 
lower fixed duty cycle range and the duty cycle is set to NORMAL at step 
244, the NORMAL duty cycle being determined in a similar manner as the 
HIGH duty cycle. Otherwise, the duty cycle is established in proportion to 
the value of CD(n) in step 242. Specifically, the duty cycle is determined 
as a function of the value of CD(n). 
Subsequent to determining a non-zero duty cycle for the AC dispense motor 
118, the motor is energized at step 246 via a signal passed from 
controller 124 to dispense motor control 126, both of FIG. 2. Wait step 
248 delays further processing until the duty cycle time has been reached, 
at which time processing continues with step 250. Step 250 stops AC motor 
118, also via dispense motor control 126, thereby preventing further toner 
addition from occurring. The control process is completed at step 250 and 
the control process is exited until a subsequent control cycle is 
initiated once again at step 210. 
In recapitulation, the apparatus of the present invention includes an 
apparatus for controlling the concentration of toner within a developer 
material of carrier and toner having a control means for generating a 
toner addition signal indicative of the amount of toner to be added to the 
developer material. The control means including the ability to measure the 
concentration of toner within the developer material during at least a 
first period and a second period subsequent to the first period. The 
control means also determining a first concentration error value as a 
function of the deviation between the toner concentration measured during 
the first period and a first reference toner concentration and a second 
concentration error value as a function of the deviation between the toner 
concentration measured during the second period and a second reference 
toner concentration. Subsequently, the control means generates the toner 
addition signal as a function of the first and second concentration error 
values. The apparatus also includes means, responsive to the toner 
addition signal, for regulating the addition of toner to said developer 
material. 
It is, therefore, evident that there has been provided, in accordance with 
the present invention, an apparatus that fully satisfies the aims and 
advantages hereinbefore set forth. While this invention has been described 
in conjunction with a preferred embodiment thereof, it is evident that 
many alternatives, modifications, and variations will be apparent to those 
skilled in the art. Accordingly, it is intended to embrace all such 
alternatives, modifications and variations as fall within the spirit and 
broad scope of the appended claims.