Optimal Design andMultiple-Input Multiple-Output Control Strate-gies for Media Handling in Copier and Printer Machines.

Media handling systems such as copier and printing machines are optimized for a narrow range of sheetproperties. As a result, they often perform poorly when using media with non-standard characteristics, suchas recycled paper. This is due to the fact that copier machines are predominantly controlled in an openloop fashion, i.e. there is little or no error correction during media transport. Recent research activities bythe PI and his collaborators have addressed the aforementioned robustness problem by successfully using amechatronics design paradigm. A distributed hybrid hierarchical control strategy, which controls in closedloop fashion the spacings between media, was formulated and implemented on an experimental setup. Bymodifying a copier paperpath layout, adding extra sensors and actuators under computer control, exper-imental results have shown that the modified paperpath performs with high robustness and precision fora wide variety of media at state-of-the-art throughputs. Research results obtained only pertain to mediacontrol in the longitudinal direction. However, most modern media and packaging handling systems alsorequire precise lateral and skew control of the media.

The goals of the proposed research are: 1) To formulate and implement a mechatronics solution for mediahandling systems that will allow accurate steering of the media along three in-plane degrees of freedom, whilemaintaining high throughput and robust performance to a wide variety of media characteristics. 2) Formulateand implement a new extended hybrid control architecture, for media handling systems that can effectivelycontrol switching media dynamics with coupled degrees of freedom and nonholonomic dynamics. 3) Todevelop a new optimal mechatronic design methodology for media handling systems and other distributedmechatronic systems. 4) To develop a fully functional rapid-prototyping research and instructional platform,which will be re-configurable and capable of testing in real-time, and with electro-mechanical hardware, avariety of multivariable, nonlinear and hybrid control methodologies.

The intellectual merits of the proposed research reside in the analysis of fundamental issues associatedwith controlling the continuous flow of discrete objects, whose motion must be accurately controlled andsynchronized with each other and with other events, but can only be actuated at discrete spatial locations,and are subjected to nonholonomic motion constraints. As part of this problem, it is necessary to formulatenew extended hybrid hierarchical models for these systems and to develop new methodologies for abstractingthe nonholonomic-constrained motion of a large group of objects into a distributed model that can describethe global behavior of system. We also propose to formulate a new optimal design methodology for simulta-neously synthesizing the control system and component layout of distributed mechatronic systems. This willbe achieved by abstracting the influence of critical design parameters on the system’s close loop performanceand determining, using optimal control and game theory, optimal layout configurations and a set of minimumperformance specifications for several of the system’s components.

Broader impacts: The outcomes of this project will introduce and demonstrate new mechatronicsapproaches for solving fundamental problems in the control and design of media handling devices, whichare currently of critical importance to the American copier industry, and are common to a large class ofassembly, manufacturing, robotics and transportation systems. The project also provides a unique way topromote teaching and learning. This project will provide our institution, UCB, with an instructionalplatform of a mechatronic system. This mechatronics solution will be ideal for implementing and testinga large class of control methodologies with varying degrees of sophistication. These include multivariablecontrol of nonlinear systems with adaptive control schemes, as well as control of hybrid systems. Ourcurrent longitudinal paperpath experimental setup has been repeatedly used as a case study in hybrid systemcourses. Moreover, it has become an extremely effective instructional tool for demonstrating the advantagesof utilizing feedback versus open loop control in mechatronic devices. The improvements obtained withfeedback control are dramatic both visually and audibly. We intend to expand the use of this paperpathfixture for instructional experimental setups for graduate and undergraduate control courses. Also, the PIsupervises the research of students of diverse background, ethnicity and genders, in fact some thestudents that will be involved in this project belong to underrepresented groups.

The new control and design developments in this project will be carried out in close cooperation withthe Xerox Corporation, the industrial partner in the project. As in our previous GOALI project, we plan tocontinue disseminating our research findings at leading conferences such as the American Control Conference,the ASME IMECE and the IFAC Conference on Mechatronic Systems.

1

1 Introduction

Most customer dissatisfaction with current printers and copiers is due to the poor performance of theirmedia handling systems. Typical malfunctions include paper jams, high shutdown frequencies, unreliablefeeder behavior, image smearing or damage to documents.

An ideal media handling system has the following desirable characteristics:

1. It is able to accommodate different papers and non-traditional media, such as transparencies, envelopes,labels and cardboard, having a large variety of materials, sizes, thickness, weight and surface properties.

2. It does not shut down and is nearly jam free, except due to extreme malfunctions.

3. It is capable of a registration accuracy (i.e. the alignment accuracy of the media with the toner imageon the photoreceptor) within 0.1 mm.

4. It is able to accommodate an almost arbitrary copy job description.

5. It can have an arbitrarily complex layout of the paperpath, which guides the medias, without compro-mising performance.

6. It is durable and does not require frequent operator intervention or servicing.

Achieving these characteristics requires a fundamentally new approach to the design of media handlingsystems. One key deficiency in current media handling systems is the fact that they operate in a predomi-nantly open loop fashion and, as a consequence, rely on the inherent robustness of the underlying mechanicalsystem. The use of sensors is typically limited to the detection of failures and the triggering of machineshutdowns.

A primary task of the media handling system is to accurately deliver medias to the image transfer station(ITS). Images consist of toner particles on a rotating photoreceptor drum or moving photoreceptor belt.For correct image transfer, also referred to as registration, medias must be delivered with zero longitudinal,lateral and skew position errors. This is not unique to a media handling system, but to all types of transportsystems that move objects for inspection, assembly and packaging. The current trend in these industries isto enlarge the operational envelope, in particular at high speeds.

In the recently completed NSF GOALI Project, “Mechatronics Design and Control of Media HandlingMechanisms for Printing Engines”, we made significant achievements in accurately and reliably deliveringmedia to the ITS. This was accomplished by modifying the copier paperpath layout by adding extra actuators,sensors and computer control in several sections in the media handling layout. The research successfullydemonstrated closed loop control of paper positions and spacings. A distributed, hybrid hierarchical controlstrategy, which controls the spacings between papers, was implemented on the experimental setup, developedand built at University of California at Berkeley (UCB). Parts of conventional copiers were supplied by Xeroxand used to built this experimental system. Experimental results show robust performance and precisionfor a wide variety of media at the paper transport speed as high as 180 pages/min. Further details of theachievements of this project will be given in §3.

In this proposal we seek to continue the very effective collaboration that was established in our previousGOALI project between the Xerox Corporation and UC Berkeley. The goal of this project is to developand demonstrate a fundamentally new approach to the design, control and optimal design of media handlingsystems, and to extend and generalize this appraoch to a wide variety of other distributed mechatronicsystems. We have concluded that the mechatronics approach to the design of media handling systems, whichwas initiated in our previous GOALI project, is promising to achieve this goal. However, there are stillfundamental problems that must be studied before the mechatronics approach can be fully incorporated intothe actual design of media handling systems. In particular, it has been noted that further research effortshould be devoted in the following topics:

1. The previous project addressed the control of spacings and positions of papers in the longitudinal di-rection only. For correct image transfer to papers, however, it is also important to position each paperaccurately in terms of skew and lateral directions. Thus, a mechatronics solution should be sought toregister the paper in all directions (longitudinal, lateral and skew), before the media lead edge reachesthe ITS.

1

FinisherFuser rolls

vd

vx f

v

Photo-receptor

Original document

beltExposure

Image(toner particles)Sensors

Conventional Copier

Motor

Image transfersection (ITS)Paperpath redesign

Multiple Independentsections

Feeder trays

Feeder unit

Figure 1: Schematic overview of the conventional and redesigned paperpath and other copier subsystems.

2. The advantages of modifying the paperpath layout, by introducing sensors and actuators for closed loopcontrol of the positions and spacings of medias, were also demonstrated in our previous project. Thiswas achieved by dividing the paperpath into sections, which were independently controlled. However,there still remains to be developed a comprehensive methodology for carrying out the optimally designof the paperpath layout, including the number of sections in which the paperpath should be dividedinto, and how each section should be sized. A preliminary study has shown that the paperpath layoutdesign and control problems can be simultaneously casted in an optimal control formalism and thatdynamic programming can be used to solve such classes of problems.

The remainder of this proposal is organized as follows. In the next section, we will briefly review thebackground for our proposed research, including current practice in the copier industry. The accomplishmentsof our previous NSF GOALI project, which set the foundation of our proposed research will be reviewed in§3. The methodology of our proposed research will be presented in §4. The expected scientific contributionsand the broader impact of the proposed research will be discussed in §5. Finally, §6 containes the researchplan and timelines for this project.

2 Background

2.1 Basic Copier Machine Layout

Figure 1 shows a schematic representation of the typical components inside a cut media copier. The paperpathtransports medias from one or more feeder units to the ITS, where images are transferred onto medias. Notethat typical paperpaths have a more complex layout configuration. An image consists of charged tonerparticles on a rotating photoreceptor belt or drum. After having passed through the ITS, a fuser “bakes”the toner image onto the media which then proceeds to the finisher where it is sorted and stapled.

Current paperpath designs usually consist of a collection of roller pairs, further referred to as nips. A nipconsists of a driving roller and a spring loaded backup roller, with medias passing in between the two rollers.Baffles guide the medias from one nip to the next. As shown in Figure 1, a single motor drives most of thenips. Timing belts are used to connect the individual nips.

There exists a wide variety of paperpath designs in the patent literature. Examples can be foundin [1][2][3][4][5]. Most designs bring medias to a halt before delivering them to the ITS, mainly to eliminateskew errors. Many designs also use solenoids to lift rollers and thereby avoid roller velocity synchronizationconstraints during media transfer between two rollers.

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2.2 Open Loop Operating Principle

The purpose of the paperpath is to deliver medias in time to the ITS in order to transfer an image correctlyonto the media, which will be subsequently referred to as the registration process. Current copiers set upcopy jobs in an open loop fashion. When a user initiates a copyjob, a preprogrammed sequence of operations,driven by a clock, feeds and transports medias, engages and disengages clutches, generates and transfersimages. Nip velocities are controlled such that medias follow nominal trajectories in open loop. Since mostnips are driven by the same motor, open loop trajectories typically specify the same velocity for all mediasin the copyjob. Clutches are used to temporarily halt medias.

Open loop control provides little tolerance for media position errors, i.e. deviations from the nominaltrajectory, as there is no opportunity for error correction. Current copiers can only detect, but not correctdeviations from nominal media behavior. Sensors along the paperpath detect when medias pass by, relativeto the start of the copyjob. When a media is late or early, i.e. it passes a sensor outside a given time window,the machine shuts down and the user is requested to remove all medias from the paperpath and start overagain. The job therefore requires user intervention. This malfunction is referred to as a soft jam, since themedias are still intact, in contrast to a hard jam where a media is torn or crumpled.

For acceptable performance, open loop control requires predictable behavior of the underlying mechanicalsystem, which includes both the copier hardware and the medias. Today’s copier machines minimize theoccurrence of soft jams by limiting throughput and adhering to severe design restrictions:

1. The allowable media choice for use in copier machines is restricted [6]. Nominal open loop trajectoriesare set up for medias with specific weight and stiffness properties.

2. Robust control is achieved by conservative design of the paperpath hardware. Rigid steel parts andtight manufacturing tolerances ensure that the same control code works for each individual machine.Large nip pressures minimize media slippage.

3. Machines are required to operate in specific environmental conditions. There exist restrictions on bothroom humidity and temperature.

2.3 Media Handling Performance Limitations

Assuming that the design restrictions in § 2.2 are satisfied, the copier throughput is limited by a maximumbound on soft jam rates. The achievable throughput is typically found by extensive testing and fine-tuningof the paperpath architecture.

The main limitation of control is its sensitivity to varying media properties. Using different types ofmedias or identical medias under different environmental conditions not only affects feeding characteristics,but also travel times along the paperpath. Component wear presents an additional problem for control.

In general, it is very hard to obtain reliable and repeatable feed characteristics. Most feeder units usefriction to separate medias and feed a single media into the paperpath. Media type, surface finish, feedertype, environmental conditions, component wear and manufacturing tolerances all influence the frictioncharacteristics and therefore feeder errors.

In addition to variations in feeder times, varying media properties also affect media behavior along thepaperpath. Depending on the media stiffness, medias may travel differently in a bend of the paperpath. Thisis illustrated in Figure 2. A more flexible media is pressed by central forces against the outer baffle of the bend,while a stiffer media offers more resistance to bending and touches the inner baffle. As a result, the stiffermedia follows a shorter paperpath and reaches the next roller sooner. Since the control strategy assumes aspecific paperpath length, different media properties will introduce deviations from nominal behavior.

In order to be able to guarantee robust performance for a wide range of media, one must clearly switchfrom the open loop control principle to the closed loop control principle.

3 Research Achievements

This section summarizes the achievements from the previous NSF GOALI project (project number 9632828),“Mechatronics Design and Control of Media Handling Mechanisms for Printing Engines”.

3

PSfrag replacements∆∆

Stiff mediaFlexible media

Figure 2: Different paths taken by thin and thick medias as they go through a bend in the paperpath.

3.1 Development of a Mechatronics Solution Approach

As argued in § 2.3, the main performance limitation factor in current copier machines is the open loopoperating principle. Our previous research has shown that large performance gains can be obtained byintroducing closed loop control. This approach however also requires adequate actuation and instrumentationfor controlling and measuring media positions, both of which are not present in the current architecture.Robust media handling therefore introduces the need for a major paperpath redesign. The close connectionbetween hardware design and control is typical for many mechatronics applications.

Our research has also shown that to improve in media handling performance, a copier paperpath’s hard-ware design has to be modified to allow for closed loop control. The changes to make are determined by lettingcontrol considerations, such as improved controllability, guide the design at an early stage. More specifically,the single motor system is replaced by a collection of independently driven subsystems by splitting up thepaperpath into multiple sections, as shown in Figure 1. In each section, a set of rollers connected by timingbelts, is driven by its own motor. The new degrees of freedom enable independent position control of mediasin different sections by running the sections at different velocities. Additional optical sensors and encodersare used to improve the media position estimates, or observability of the system. Note that the number ofsections in Figure 1 is exaggerated to illustrate the principle.

The increased level of flexibility of the redesigned paperpath allows for independent media position correc-tions, but naturally also leads to a more complicated machine and a need for intelligent control to coordinatethe motions of the different sections. A real-time control system must interface with the machine and controlall degrees of freedom. This is an integral part of the mechatronics approach [7][8] achieved in our previousproject. The control goal of synchronizing the position and velocity of every media with those of its image onthe photoreceptor belt were accomplished despite variations in media properties, feeding errors and variousdisturbances along the paperpath.

3.2 Modelling of Hybrid Paperpath Dynamics

The mathematical model of the paperpath was important in the development and implementation of controlstrategies used to achieve the control goal. The paperpath dynamics consist of two parts: the section dynamicsand the media dynamics. An overview of the paperpath dynamics is shown in Figure 3.

As a first approximation, to simplify analysis and control design, the section dynamics can be ignored. Inthis case, the system inputs are the section velocities sj . The paperpath dynamics in this case are referred toas the “1/s-model”, since the resulting dynamics are essentially single integrators. Alternatively, the sectiondynamics can be modelled by single integrators. The paperpath dynamics in this case are referred to as the“1/s2-model”, since the resulting dynamics are essentially double integrators.

When modelling section dynamics, medias are assumed not to influence sections in any way. Since mediasare very light compared to section and motor inertias, this assumption is valid most of the time. Oneexception is when a media is being transferred from one section to another. If at this time the receivingsection runs at a higher velocity than the delivering section, forces may be transmitted between the two

4

Section

DC-motor

1) Section dynamics

2) Sheet Dynamics

PSfrag replacements

s = K i s

s

i i

x

1

s

1

s 1/s-model

1/s2-model

Figure 3: Simplified dynamics of a copier paperpath

PSfrag replacements

x =

s1

s1

000

x =

0000s3

Figure 4: The media dynamics are governed by a finitestate machine.

High LevelControl 1

Low LevelControl 1

High LevelControl 2

Supervisory LevelControl

Low LevelControl 2

High LevelControl 3

Low LevelControl 3

Section 1

Sheet Dynamics

Section 2 Section 3

Reference Velocity +Feedforward Acceleration

ControlSignal

SectionVelocity

SheetPositions

On

Off Default

Jam recovery

Figure 5: Overview of the Controller Structure.

sections through the media. In order to avoid this complication and in order to not damage medias, sectionvelocities are synchronized during media transfer.

The media dynamics can be described by a set of hybrid integrators. In any given configuration of mediasalong the paperpath, the velocities of medias in a section are given by that section’s velocity. When a medialeaves a section, the media velocity is suddenly dictated by the velocity of the next downstream section. Themap from section velocities to media velocities is therefore governed by a finite state machine with statescorresponding to all the different configurations of medias in the paperpath, see Figure 4 for a 5-media copyjob and a paperpath consisting of 3 sections. The map from media velocities to positions consists of regularintegrators. The combined discrete dynamics of the state machine together with the continuous integratordynamics result in the hybrid dynamics exhibited by the paperpath. The term hybrid refers to the fact thatthe dynamics exhibit both discrete and continuous time behavior, by switching discretely between differentcontinuous time models. This characteristic of the media dynamics considerably complicates control systemdesign.

3.3 Hybrid Hierarchical Control

The paperpath dynamics contain a map from section velocities to media velocities with hybrid characteristics.One possible approach to hybrid systems control which was used in this project is to use a hybrid hierarchicalcontrol architecture. The hierarchical structure reduces the design complexity by using different levels ofabstraction. The hybrid characteristics of the controller can profit from the richer plant model structure ifadopted to the hybrid model. Typical examples can be found in the area of automated highway systems [9]

5

Figure 6: Overview of the experimental setup.

and air traffic control [10].Research accomplishments by the PI and his collaborators have equally resulted in a hybrid hierarchical

control solution [11, 12] for this system. The control strategy matches the most downstream media with itscorresponding image and makes the spacings between upstream medias track the spacing between imageson the photoreceptor belt. The matching of the most downstream media with its corresponding image isreferred to as Absolute Reference Tracking Control (ARTC), and the control of spacings between pages isreferred to as Inter-Sheet Spacing Control (ISSC).

An overview of the different layers in the combined plant and controller system is given in Figure 5 forthree sections in the paperpath. The physical system is represented by the two bottom layers, which containthe hybrid media dynamics and continuous section dynamics. Next, the controller is represented by the threetop layers. The Low Level Control layer contains a velocity feedback loop for each section. This layer isdiscrete time. Reference velocity signals for the low level controller are generated by the High Level Controllayer. Note that all velocity commands must satisfy the system constraints. Depending on the mode of thesystem, the high level controller switches discretely between different control laws. Its dynamics are thereforehybrid. Finally, the overall mode of operation is determined by the Supervisory Level Control layer. Thislayer is purely discrete. Note that there is one single supervisory control layer for the paperpath, but eachsection has its own low and high level controllers.

3.4 Rapid Prototyping and Experimental Setup

Apart from the successful development and implementation of a hybrid hierarchical control architecture, acomplete rapid prototyping system was built in the PI’s laboratory to test and verify different control schemes.This system consists of the experimental setup, shown in Figure 6, and the control system consists of astandard PC and a dSPACE DS1103 controller board [13]. This experimental setup was used to demonstratethe performance improvements of the new control approach [14]. This experimental setup will also be used forthe proposed extensions of the research project. Controller design, simulation and real-time implementationare performed in the same rapid prototyping environment. This approach speeds up the development processas it allows a smooth transition from simulation to experiment.

Matlab and Simulink are the primary software tools used for the development and simulation of the pa-perpath control algorithm. Stateflow, an additional toolbox for the Simulink environment, enables graphicalcoding of discrete state machines and proved useful for coding the high level control modes.

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0 0.5 1 1.50.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

x [m]

d [m

]

Figure 7: Evolution of the intermedia spacings(simulation)

0 0.5 1 1.50.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

x [m]

d [m

]

Figure 8: Evolution of the inter-sheet spacings(experimental)

The developed simulation model provides an arbitrary choice of complexity, from simplified dynamics,identified section models, hardware in the loop to full control of the experimental setup. The different levelsof complexity allow the gradual development of control strategies. This was the case of the implementationof the overall hybrid hierarchical control strategy. Each section control was first design and implemented,then it was follow by the overall hybrid control implementation.

This rapid prototype system has already proved its usefulness and flexibility in the implementation ofother hybrid control strategies. It was used in the implementation of other hybrid control strategies taught inone of the courses at UCB, EE291E. The overall system is a hybrid system with each section independentlycontrolled. Such a complete system is currently absent in other educational settings for students to gaininsights into this type of control implementation.

3.5 Experimental Results

Figures 7 and 8 show simulation and experimental results for a 10-media copyjob [15]. The initial spacingerrors in the simulation are such that they match the actual initial spacing errors observed during theexperimental run. Both runs are identical except that the simulation uses identified section models and onlycontains the modelled friction disturbances, which are cancelled by feedforward.

Figures 7 and 8 show the evolution of the inter-media spacings versus the position along the paperpath fora simulation and an experimental run respectively. Note the close correspondence. The grey areas representsections, the darker area is the image transfer section (ITS). The vertical dashed lines in Fig. 8 correspondto sensor locations on the experimental setup.

The final positioning accuracy for an experimental run is within 0.5 mm. This value could possibly bereduced by using an analog position sensor [16] at the end of the paperpath in combination with higherbandwidth control. This may require another separate section or roller. Note the discrete changes in mediaspacing when a media crosses a sensor. This follows from the media position estimate updates by theobserver [17].

4 Proposed Research

The goal of the proposed research is to address all of the aforementioned deficiencies in distributed mediahandling systems by developing new control and mechatronics design methodologies for these systems, aswell as new rapid-prototyping laboratory research and instructional equipment, where these methodologiescan be effectively tested. Specifically, we intend to achieve the following four objectives. We will develop amechatronics solution for media handling systems that will allow accurate steering of the media along three

7

degrees of freedom, while maintaining high throughput and robust performance to a wide variety of mediacharacteristics. We will formulate a new extended hybrid control architecture, which can effectively controlswitching media dynamics with coupled degrees of freedom and nonholonomic dynamics. We will develop anew mechatronics optimal design methodology for the simultaneous synthesis of the control system and pathlayout of media handling devices. Finally, we will develop a fully functional rapid-prototyping research andinstructional platform, which will be re-configurable and capable of testing in real-time, and with electro-mechanical hardware, a variety of multivariable, nonlinear and hybrid system design and verification controlmethodologies. In what follows, we discuss each objective in some detail.

4.1 Enhanced Mechatronic Design of Media Handling Systems

For proper operation of a photocopier or printer, it is required that the media (paper) be delivered to theImage Transfer Station (ITS) at the pre-specified time and that it be properly aligned (i.e. registered), so thatthe image is placed on the paper at the right location and orientation. This is particularly important in colorprinting, where each color may be transferred at different times and by different stations. As stated in §2.3,current state-of-the art registration mechanisms, which are normally placed before the ITS, operate in openloop fashion. The paper is sensed once and then tracking errors are corrected with no continuous feedback,resulting in large registration errors. Moreover, the current devices that are used to correct registrationerrors do so either by bringing the media to a complete stop or by moving it at low longitudinal speeds.Consequently, most of these devices end up damaging the edges of the media and/or producing visibletraction marks on the media.

To decrease registration errors, while maintaining high throughputs and robustness to various media, itis necessary to design a new class of registration mechanisms, which can steer the media under continuousfeedback. We propose to design and evaluate two mechatronics solutions for such devices. The first incorpo-rates nips that are allowed to steer. In this case, the coupled actuation of the two nips allows the paper to beinstantaneously steered along its three independent in-plane degrees of freedom (i.e the coupled nip actuation

allows the decoupled control of the paper’s longitudinal, lateral and out-of-plane k-axis angular velocities),as shown in Figure 10. In the second approach, the registration mechanism will incorporate nips that cannotsteer, but can be driven independently. In this case the media steering problems becomes nonholonomic, aswill be discussed subsequently.

4.1.1 Hardware Design

We proposed the design, fabrication and testing of a registration station, which will continuously sense themedia trajectory and can be used as a test bed for evaluating media registration control schemes for bothsteerable and non-steerable nips. The key innovative feature of this new device are two steerable nips, whichare independently actuated, as schematically depicted in Fig. 9. Each nip is able to rotate in two directions,one perpendicular and one parallel to the paper plane. This coupled actuation allows decoupled control ofthe paper’s in-plane linear velocity and k-axis angular velocity, as shown in Figure 10.

The proposed mechanism will be equipped with sensors, actuators and an embedded computer to allowthe control algorithm for proper media registration.

As shown in Figure 9, the device will be equipped with four optical sensors that will be used to detectthe longitudinal position of the media. Three of those sensors will be optical transmissive sensors (e.g. photoeyes), which are capable of detecting the passing of the lead and trailing edges of the media. The fourthlongitudinal optical sensor will be analog and will be placed closest to the ITS for accuracy. Measuring theportion of the sensor that is obscured by the media, allows accurate sensing of the media’s front and trailingedges’ position. Two other optical analog sensors will be placed in the lateral edge region of the media asshown in Figure 9. Measuring the portion of each sensor that is obscured by the media, allows accuratesensing of the media’s lateral edge position and skew.

The two-nip setup discussed above can also be used to evaluate control strategies that employ non-steerablenips, by constraining the out-of-plane nip angular velocities to be zero.

8

Process Motor1

Process Motor 2

Analog Sensor

On/Off Position Sensors

Edge Sensors

Backer Ball

Paper

RotatingTable

Steering Motor

Timing Belt

Top View

Side View

PSfrag replacements

On/OffPositionSensors

Figure 9: Steerable Nips Shematic

PSfrag replacementsA

B

VA

VB

γA

γB

θı

x

y

Figure 10: Velocities at point A and B of the media

4.1.2 Media Registration Control

The control strategy during media registration will depend on whether steerable or non-steerable nips areutilized in that station. Steerable nips permit a more swift correction of lateral and skew errors, but increaseboth the fabrication and maintenance cost of the unit. In contrast, non-steerable nips can only indirectlycorrect lateral errors through steering of the media, requiring more complex trajectory feedforward andfeedback control algorithms. However, the mechanical design of a non-steerable nip is simpler, and is probablycheaper to fabricate and maintain than its steerable counterpart.

Registration Control Using Steerable Nips

As discussed in §4.1.1, a registration station that uses steerable nips can, in principle, independently controlthe instantaneous point velocity of the media at the two contact points, as shown in Fig. 10, where thecontact velocities are respectively labeled ~vA and ~vB . However, because the media can neither be stretchednor compressed, a constraint must be imposed at the control level, requiring the component of both vectorsbe equal along the line that connects both contact points, i.e. ~vA · −~vB · = 0, where is in the direction ofthe vector connecting the nip contact points A and B. This constraint reduces the available control degreesof freedom to three. In this system, the dominant dynamics are the inertia of the motors and stiffness oftiming belts. Moreover, the kinematic map between the angular rotations of the actuators and the motion ofmedia is nonlinear. We plan to design, implement and test several multivariable nonlinear control schemesfor this system.

Registration Control Using Non-Steerable Nips

It is also possible to correct media registration errors using independently actuated non-steerable nips. Inthis case, the media steering control problem becomes nonholonomic. A system is said to be nonholonomicif it is subjected to a set of non-integrable Pfaffian constraints

A(q)q = 0, A(q) ∈ Rk×n, (1)

9

i.e., there does not exist a vector-valued function h : Q → Rk such that

A(q)q = 0 ⇔∂h

∂qq = 0. (2)

where Q is the configuration space, n is the dimension of system configuration q, k is the number of constraints.If the constraints do not restrict the researchable configurations, which is the case in this problem, then thesystem is considered to be completely nonholonomic. Nonholonomic constraints arise in a wide class ofmechatronic control problems involving mechanical systems with rolling or sliding contacts, such as wheeledvehicles and mobile robots, underactuated mechanical systems such as multi-fingered robot hands and spacerobots, etc. The control of nonholonomic mechanical systems has attracted significant recent attention [18].

We have conducted a preliminary analysis of our media steering control problem and believe that it hassimilar properties to the two-wheeled mobile cart steering problem; with the obvious difference that, in ourcase, the media moves while the driving nips rotate about a fix axle. Letting xc, yc and θc denote the positionand skew coordinates of the media relative to a fixed coordinate frame, and vc the translational velocity ofthe media, we can write following media kinematic equations

xc

yc

θc

=

cos θc 0sin θc 0

0 1

[

vc

ωc

]

(3)

with the nonholonomic constraintsin θc xc − cos θc yc = 0 . (4)

The control objective is to track a reference media position and orientation. This problem appears tobelong to a class of nonholonomic trajectory tracking problems, for which some results have been derived, c.f.[19][20][21] and [22]. In the case of media registration control, we can assume that the reference trajectory isa straight line: vr = vn and ωr = 0, where vn is the nominal longitudinal velocity of the media. Therefore,xr = vrt and yr = θr = 0. Defining the tracking errors in the mobile media coordinates, we obtain thefollowing tracking error kinematics:

e =

xe

ye

θe

=

cos θc sin θc 0− sin θc cos θc 0

0 0 1

xr − xc

yr − yc

θr − θc

(5)

We have also conducted a preliminary study on the feasibility of using nonholonomic tracking controllersfor the media registration problem and the results appear promising. Fig. 12 shows the response of thetracking errors in (5) under the action of the tracking controller proposed by [23]:

vd =

[

vd

ωd

]

=

[

vr cos θe + kxxe

ωr + vr(kyye + kθ sin θe)

]

(6)

where vd and ωd are the desired translational and angular velocities expressed in the sheet frame. kx, ky andkθ are positive constants, which are selected using Lyapunov’s direct method. The desired velocity vd andactual velocity vc are related by the actuator dynamics.

The results in Figs. 11 and 12 where obtained under the simplifying assumption that the actuatorsdynamics are modeled as pure single integrators. In the simulation, a letter-sized media, moving at anominal longitudinal velocity vr = 0.5 m/s, has to be registered from an initial error state of xe0 = −4 mm,

ye0 = 6 mm, θe0 = 2◦, with an input saturation of ±15 m/s2

for both nips. The results in Figs. 11 and 12reveal that simplified tracking error dynamics can be effectively stabilized. Notice that, in order to correctfor the lateral errors, the control system has to first increase skew errors, before driving all errors to zero.This type of response is typical of nonholonomic systems.

4.1.3 Modification of the Experimental Test Bed

Currently, the experimental fixture shown in Fig. 6, has three sections, non of which is capable of mediaregistration. These sections however, are fully instrumented and have allowed us to test a variety of hybrid

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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5−8

−6

−4

−2

0

2

4

6

8Evolutions of tracking errors

Time [s]

xe [mm]

ye [mm]

θe [deg]

Figure 11: Evolution of tracking errors

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Velocities of two drive rollers

[m/s

]

v1

v2

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5−20

−10

0

10

20Control inputs

Time [s]

[m/s

2 ]

u1

u2

Figure 12: Velocities of drive rollers and control inputs

longitudinal control strategies such as ARTC and ISSC [11, 12], as described in §3.3. We plan to first replacethe last section with a registration fixture with steerable nips, as described in §4.1. The fixture will also beused to implement and test nonholonomic control systems for non-steerable nips.

We plan to eventually replace all three sections with fixtures capable of partially correcting registrationerrors, in order to implement and test hybrid control schemes incorporating the coupled longitudinal andnonholonomic lateral and skew dynamics, as described in §4.2.

4.2 Extended Hybrid Hierarchical Control

Instead of utilizing a single registration fixture at the end of the media path, it may be more cost effective touse several registration fixtures, with limited registration capabilities, along the media path. In this manner,the initial lateral and skew errors, created at the feeding station, can be gradually corrected, as the mediamoves from one fixture to the next, in a similar fashion as longitudinal spacing errors are corrected in ourcurrent experimental setup, described in §3. In order to control such media handling systems, it is necessaryto design a new class of extended hybrid hierarchical control architecture that can effectively control switchingmedia dynamics, which will now include coupling between the longitudinal, lateral and skew media dynamics,as well as nonholonomic behavior in several of its switching modes.

We proposed to derived a set of hierarchical modeling layers for such a system and formulate, implementand eventually test hybrid control laws, which can synchronize sections with coupled nonholonomic hybriddynamics. We will initially follow a similar controller synthesis to the one that was successfully used in theformulation of hybrid hierarchical architecture of our current system (cf. §3.3), but we will also incorporatein our synthesis methodology modern hybrid system synthesis and verification tools, such as Hi-tech [24, 25].

4.3 Optimal Design of Distributed Mechatronic Systems

There exists a strong coupling between machine design, controller design and the resulting overall performanceof a mechatronics system. In media handling devices, several layout design parameters critically influence theultimate achievable performance of the system. For example, the number of sections in the media handlingpath directly affects the extend to which media can be independently controlled, as well as the magnitude ofthe initial registration errors that can be removed. Additionally, mechanical dimensions, such as the distancebetween sections, and electro-mechanical component limitations, such as actuator velocity and accelerationbounds and sensor placement and signal to noise ratio (SNR), directly influence the achievable performanceof the system.

We propose to formulate a new optimal design methodology for simultaneously synthesizing the controlsystem and component layout of distributed mechatronic systems. This will be achieved by abstracting the

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influence of critical design parameters on the system’s close loop performance and determining, using optimalcontrol and game theory, optimal layout configurations and a set of minimum performance specifications forseveral of the system’s components.

4.4 Illustrative Example: Optimal Paper Handling Layout Design Using Dy-

namic Programming

We describe here, for illustrative purposes, the design of a longitudinal paperpath control system and itscomponent layout for the paper-handling system that was described in §3.1. The primary goal of the systemis to move papers from the paper feeder to the photoreceptor unit, so that, by the time that papers reachthe photoreceptor, their location is matched with its corresponding image in the photoreceptor belt. Thiscan be achieved by several control strateges. A secondary goal of the control system pertains on how themedia moves along the paperpath. In this example this secondary goal consists in keeping the inter-paperspacing as close as possible to the spacing between images on the photoreceptor belt. This is illustrated inFigure 13. The advantage of specifying this secondary goal is that, if the first media matches up with itsimage, the subsequent medias are in a good position for zero error arrival also. In addition, by focusing ona desired relative spacing, the problem of overlapping medias is indirectly avoided.

PSfrag replacements

ds

ds ds

ds

Figure 13: Desired Sheet Spacing corresponding to Interimage Spacing

In order to simultaneously design both a feedback control system and a paper-path layout, we definea control reward function, J , which assigns the highest reward to control strategies that best satisfy boththe primary and secondary control goals. Subsequently, we find an optimal feedback control solution whichoptimizes this reward function using dynamic programming (DP). By a proper formulation of the problemand choice of state variables, DP can handle the hybrid dynamics, multiple constraints and non-linear rewardfunction encountered in copier paperpath control. Its optimal control solution offers both:

• A feedback control law in the form of a table look-up.

• The reachable set of all allowable initial states that can be handled by the controller, at each stationin the paperpath.

The reachable set for each station is computed in a recursive manner, starting from the station closest tothe ITS. It contains all initial states for which every media can be transferred to the ITS with zero positionand velocity errors.

The size of the reachable set indicates to what extent constraints imposed by the design of the downstreamstations limit the control freedom of that station. A small reachable set indicates many constraints and fewopportunities to control, while a large reachable set indicates a significant control freedom. Enhancing theperformance of the downstream stations and/or modifying the downstream paperpath layout increases thereachable set of a station.

By studying the effect of different machine configurations and component specifications on the resultingreachable set for all stations, it is possible to determine how to distribute sections along a paperpath andwhat should be the minimum achievable performance of each section. This information can be extremelyvaluable for designing paperpath lay-out in future products.

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A paperpath layout and its corresponding optimal control system were designed using the DP approachoutlined above [26], with promising results. In this study, only the longitudinal media control problem wasconsidered and pure integrator sections models, as described in §3.2, were utilized.

The following optimal control reward function J was used in design

J(x(0)) =

T∑

k=0

{

−P (d(k) − ds)T W (d(k) − ds) + Q

N∑

media i=1

δ(xi(k) − xITS)δ(k − tf,i)

}

(7)

where N is the number of medias in copyjob, k is the sample time, T is the duration of copyjob (in numberof samples), d is N × 1 media spacings, ds is N × 1 desired media spacings, P,Q > 0 are weighting factors,W > 0 is a N ×N weighting matrix, xi is the position of media i, xITS is the entrance to the ITS, δ(.) is thedelta function, tf,i is the (sampled) image arrival time at the ITS for media i, and x(0) is the initial state.

A table-lookup feedback control strategy and a corresponding reachable set for each section in the paper-path were calculated using DP. By examining the reachable sets at each design outcome, and iterating thedesign procedure, an improved paperpath layout, was determined, which required fewer sections with relaxedperformance requirements in the upstream sections.

There are however potential drawbacks of the DP approach, such as Bellman’s curse of dimensionality,which may limit the feasibility of this approach in a general system, and this requires further study. For ageneral paperpath system, the DP approach may still be able to successfully handle most actuator and paperpath layout constraints. However, the resulting optimal control action lookup table may be large, whichmay limit the sample frequency of the optimal control action. Practical use of this control strategy mayrequire the use of a Neural Network for example to store and efficiently retrieve the lookup table [27], or ahierarchical control strategy may be implemented where the optimal lookup table is used to generate a highlevel, slowly sampled reference trajectory and fast sampled low level controllers are used to make the paperstrack the optimal reference trajectories.

4.5 Rapid-prototyping research and instructional platform

We propose to develop a fully functional rapid-prototyping research and instructional platform. This platformwill be reconfigurable and capable of testing in real-time, and with electro-mechanical hardware, a variety ofmultivariable, nonlinear, adaptive and hybrid control methodologies.

The longitudinal paperpath experimental setup that was developed in our previous GOALI project hasbeen used as a case study in our college-wide hybrid system graduate course, and several of our studentshave used this setup in their final project, to implement and test hybrid systems controllers. We plan tofurther develop this platform, so that it can be used as an effective instructional tool in such courses. To doso, we plan to 1) collaborate with the instructors teaching the hybrid systems course, by formulating hybridautomata models of our paperpath platform, which can be seamlessly used with the hybrid modeling andverification tools that are being developed and used at UC Berkeley, such as SHIFT and Hi-Tech and 2)develop a real-time environment, where the resulting hybrid control systems can be experimentally verifiedand tested using the paperpath platform.

Our current experimental setup has also become an extremely effective instructional tool for demonstratingthe advantages of utilizing feedback versus open loop control in mechatronic devices, since the performanceimprovements gained in our setup by the use of feedback control are dramatic both visually and audibly.We plan to continue showcasing this paltform to undegraduate and graduate students, as well as high schoolvisitors. In addition, we plan to design smaller experimental setups, using a variety of paper-path fixtures,which will be used in both undergraduate and graduate courses to implement and test a variety of controlalgorithms for use in media handling and distributed mechatronic systems.

5 Contribution and Impact of the Proposed Research

5.1 Broader Impacts

As emphasized in the attached letter of support from Xerox, we expect that the outcomes of this projectwill introduce and demonstrate fresh approaches to solving fundamental problems in the control and design

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of media handling devices. For example, the research detailed in §4.1 and §4.2 will solve the problem ofachieving high precision, high throughput media handling with three degrees of freedom, which is currentlyof critical importance to the American copier industry. The added flexibility, which is obtained with theintroduction of closed loop control to media handling devices, also provides additional benefits beyond theoriginal goals. For example, a new functionality in the area of paperpath control could be automatic jamclearance. With this feature, a machine under closed loop media control can remove jammed medias andresume normal operation without operator intervention. The basic principle is illustrated in Fig. 14. When amedia jams, its trailing edge usually remains intact. Because of the added degrees of freedom, it now becomespossible to drive a section backwards, to remove the damaged media and speed up the next upstream media toreplace the removed media. If successfully executed, the end-result would make the jam recovery completelytransparent to the user. Some ideas in this context are detailed in [28] and [5].

Figure 14: Illustration of a jam recovery sequence

The proposed research covers fundamentals aspects in multivariable, nonlinear and hybrid systems controltheories, as well as the integration of sensors, actuators and embedded control systems in the design, analysis,simulation and experimental testing of a compact, yet realistic distributed mechatronic system, which requiresa relatively complex hierarchical control architecture for its operation. Thus, much of the project outcomewill become ideal material for inclusion in control and mechatronic courses.

Our goal is to eventually transform our paperpath testbed into a fully functional rapid-prototyping plat-form, where a variety of control methodologies can be readily simulated, implemented and tested at severaldifferent layers of a control hierarchy, in an instructional setting. In particular, we believe that this platformwill be an invaluable educational tool for the laboratory instruction of hybrid systems, and other controlmethodologies for distributed and complex systems.

Finally, the PI supervises the research of a large group of graduate students, with diverse background,ethnicity, and mix of genders (both the PI and one of graduate student researchers (GSR) assigned to workon this project are Hispanic). The proposed project will become a catalyst for interaction among several ofthe PI’s graduate students, as well as many other undergraduate and graduate students in the control andmechatronics programs at Berkeley.

5.2 Intellectual Merits

The control problems described in §4.1 and §4.2 are of fundamental nature and appear in many engineeringsystems that deal with the continuous flow of discrete objects, whose motion must be accurately controlledand synchronized with each other and other events. Such problems are frequently encountered in manyassembly, manufacturing and transportation systems. As the discrete components become smaller and theproduction volumes increase, performance requirements in terms of positioning accuracy and speed becomeincreasing stringent, and the mechatronics approach proposed in this project becomes ideally suited to addressthese problems. The problem of steering discrete objects in a plane using media handling devices with eitherfully actuated or under-actuated mechanisms, as described in §4.1, has received surprisingly little attention.Moreover, the coordinated motion of a large number of objects, where each object is under nonholonomicconstraints, described in §4.2, is an extremely important and frequently encountered problem, which hasnot yet been adequately solved. Similar problems are encountered in the traffic flow control of automatedhighway systems. To date, only traffic flow and coordinated motion control problems, which deal with

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holonomic systems, have been successfully solved [9]. One of the key problems that will be investigated ishow to efficiently determined a reachable set in each of the discrete stations of a media handling system,when the moving objects are subjected to nonholonomic constraints. Another important problem that willbe investigated in this research, consists in finding a good methodology for abstracting the nonholonomic-constrained motion of a large group of objects into some form of distributed parameter model that candescribe the global behavior of system [29].

The methodology proposed in §4.3 for designing media handling systems represents an innovative designapproach, which may yield similar design methodologies for other distributed mechatronics systems. It isimportant to note that, although the proposed methodology relies on the use of optimal control and gametheory, and produces an optimal feedback control law, its main innovation lies in its use as a design tool fordetermining the performance specifications of the mechanical components that integrate the media handlingsystem and the overall layout of the paperpath.

The results of our previous GOALI project were presented at leading conferences such as American ControlConference, ASME IMECE, and the IFAC Conference on Mechatronic Systems, and we plan to continue toparticipate in and disseminate our research findings at these leading conferences.

6 Research Plan and Timelines

The proposed project is planned to be carried out within a period of three years with the following schedule:

1. 2003/9 ∼ 2003/12: Literature review. Steerable nip design (§4.1.1). Formulation of media regis-tration control systems (§4.1.2). Begin formulation of the optimal design methodology for distributedmechatronic systems (§4.3).

2. 2004/1 ∼ 2004/5: Fabrication of a registration station with steerable nips. (§4.1.1). Further researchin sheet registration control using steerable and non-steerable nips (§4.1.2). Model formulation of theextended hierarchical hybrid architecture for the media handling system. (§4.2).

3. 2004/6 ∼ 2004/12: Installation of the first media registration station on the paperpath experimentalsetup (§4.1.3). Control software development. Hardware-in-the-loop (HIL) simulation and experimentalevaluations of media registration control systems (§4.1.2). Optimal design formulation of paperpathsystems (§4.3).

4. 2005/1 ∼ 2005/6: Formulation and verification using hybrid systems verification tools of the extendedhierarchical hybrid architecture for the media handling system. (§4.2). Optimal design of paperpathlayout (§4.3). Fabrication of additional registration stations.

5. 2005/7 ∼ 2005/12: Installation of additional registration stations (§4.1.3). Implementation of theextended hierarchical hybrid architecture for the media handling system. (§4.2). Development of anintegrated software tool for testing in real-time control methodologies. Development of hybrid automatamodels for incorporation in hybrid systems modeling and verification instructional software. (§4.5).

6. 2006/1 ∼ 2006/8: Continuation of the activities in 5. Final report presentation and project conclu-sion.

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