FEEDBACK-BASED DOCUMENT HANDLING CONTROL SYSTEM

Abstract

A method and system for performing sheet registration are disclosed. Output values for a sheet may be identified within a reference frame. A difference between each output value and a corresponding desired output value may be determined. Input values may be determined based on at least the differences. State feedback values may be determined based on information received from one or more sensors. Acceleration values may be determined for multiple drive rolls based on the input values and the state feedback values. A desired angular velocity for each drive roll may be determined based on the corresponding acceleration value. A motor voltage may be determined for each drive roll that tracks an observed angular velocity value to the desired angular velocity value. The acceleration values may create a linear relationship between the input values and the second derivatives of the output values. The steps may be performed multiple times.

Description

DETAILED DESCRIPTION

A closed-loop feedback control process may have numerous advantages over open-loop control processes, such as the one described above. For example, the closed-loop control process may improve accuracy and robustness. The inboard and outboard nips 105, 110 may be the two actuators for a sheet registration system. However, error between desired and actual sheet velocities may occur. Error may be caused by, for example, a discrepancy between the actual sheet velocity and an assumed sheet velocity. Current systems assume that the rotational motion of parts within the device, specifically the drive rolls that contact and impart motion on a sheet being registered, exactly determine the sheet motion. Manufacturing tolerances, nip strain and slip may create errors in the assumed linear relationship between roller rotation and sheet velocity. Also, finite servo bandwidth may lead to other errors. Even if the sheet velocity is perfectly and precisely measured, tracking error may exist in the presence of noise and disturbances. Error may also result as the desired velocity changes for a sheet.

The proposed closed-loop algorithm may take advantage of position feedback during every sample period to increase the accuracy and robustness of registration. Open-loop motion planning cannot take advantage of position feedback. As such, the open-loop approach may be subject to inescapable sheet velocity errors that lead directly to registration error. In contrast, the closed-loop approach described herein may use feedback to ensure that the sheet velocities automatically adjust in real-time based on the actual sheet position measured during registration. As such, the closed-loop approach may be less sensitive to velocity error and servo bandwidth and may be more robust as a result.

In addition, current open-loop algorithms may rely on learning based on performance assessment to satisfy performance specifications. Additional sensors may be required to perform the learning process increasing the cost of the registration system. When a novel sheet is introduced, such as, for example, during initialization of a printing machine, when feed trays are changed, and/or when switching between two sheet types, “out of specification” performance may occur for a plurality of sheets while the algorithm converges. In some systems, the out of specification performance may exist for 20 sheets or more.

FIG. 3 depicts an exemplary closed-loop feedback motion planning control process according to an embodiment. The closed-loop control process 300 may use information retrieved from a sheet registration system, such as the system shown in FIGS. 1A and 1B, to register a sheet. Information retrieved from the sensors, such as CCD1, CCD2, CCDL, PE2, PEL and encoders on the roll shafts, may be used to determine a position and rotation of a sheet during the registration process. Other sheet registration systems, having more or fewer sensors that are placed in a variety of locations, may be used within the scope of the present disclosure, which is not limited to use with the system shown in FIGS. 1A and 1B.

Referring back to FIG. 3, a reference frame may initially he selected (for example, as described below in reference to FIGS. 4A and 4B), and two outputs y may be selected based on the reference frame. A coordinate system is constructed within a reference frame (i.e., a perspective from which a system is observed) to analyze the operation of the sheet registration system. For example, the reference frame in FIG. 4A is selected based upon the orientation of the drive rolls (nips). In contrast, the reference frame in FIG. 4B is selected based upon the orientation of the sheet.

To be effective, the input-output linearization module 310 may require the selection of an appropriate reference frame. FIG. 4A depicts an exemplary reference frame based on the drive rolls, where the process direction (i.e., the direction that the sheet is intended to be directed) is defined to be the x-axis, and the y-axis is perpendicular to the x-axis in, for example, an inboard direction. A five dimensional state vector x may be defined in the basis of this reference frame:

x=[x y θ ω₁ ω₂]^T,

where: {x,y} denote the coordinates of the center of mass of the sheet (P_s);

• • θ denotes the angle of the sheet relative to the x-axis, and
  • {ω₁, ω₂} denote the angular velocities of the outboard and inboard drive rolls, respectively.

The sheet states q=[x y θ]^T are a subset of state vector x. If no slip exists between the drive rolls and the sheet, three kinematic equations may relate the sheet states to the angular velocities:

$\stackrel{.}{\theta }=\frac{c\left({\omega }_1-{\omega }_2\right)}{2a},\stackrel{.}{x}=\frac{c\left({\omega }_1+{\omega }_2\right)}{2}-y\stackrel{.}{\theta },\mathrm{and}\stackrel{.}{y}=x\stackrel{.}{\theta },$

where: c denotes the radius of the drive rolls: and

• • 2a denotes the distance between the rolls as shown in FIG. 4A.
  • The fundamental goal of a sheet registration device may be to make a point on the sheet track a desired straight line path with zero skew at the process velocity. In the basis of the reference frame, this desired trajectory is described by:

x _d(t)=v_dt+x_di, y_d(t)=y_di, and θ_d(t)=0,

where: v_d denotes the process velocity; and

• • {x_di, y_d1} describes the desired initial position of the center of mass of the sheet.

One problem with the reference frame shown in FIG. 4A is that input-output linearization cannot be applied because no two outputs y can be readily found in the basis of the frame that guarantee the convergence of the three sheet states q to the desired sheet trajectory. Accordingly, a different reference frame must be determined that can satisfy this requirement in order to provide closed-loop feedback linearization.

FIG. 4B depicts an exemplary reference frame based on the orientation of the sheet in the process according to an embodiment. The reference frame in FIG. 4B may incorporate a virtual body fixed to the drive rolls. The drive rolls and the virtual body may form a “cart” riding along the underside of the sheet to describe an XY reference frame. A five dimensional state vector may be defined with respect to the XY reference frame:

x_c[X Y Θ ω₁ ω₂]^T,

where: {X, Y} denote the coordinates of the center of the cart (P_c);

• • Θ denotes the angle between the cart and the XY coordinate system; and
  • {ω₁, ω₂} denote the angular velocities of the outboard and inboard drive rolls, respectively. These angular velocities are common to state vector x within the xy frame.

The cart states may be defined as a subset of x_c, q_c=[X Y Θ]^T. The transformations between the sheet and the cart states may be defined as:

X=−(x cos θ+y sin θ), Y=−(−x sin θ+y cos θ), Θ=−θ.

The cart and sheet orientations, Θ and θ, may differ in sense because the cart “moves” in the opposite direction of the sheet. In other words, if the sheet were a surface on which the drive wheels propelled the virtual cart, the drive wheels would propel the cart in a direction substantially opposite from the process direction. By substituting these transformations into the desired sheet trajectory determined above, the desired cart trajectory that achieves sheet registration may be determined:

X _d(t)=−v_dt−x_di, Y_d(t)=−y_di, and Θ_d(t)=0.

The outputs y may correspond to the position of a center of the virtual cart, which may be determined by using information retrieved from the one or more sensors. A set of desired outputs y_d may also be determined. In an embodiment, the desired output values may correspond to the position of a point that is on a line bisecting the nips (wheels of the cart) 105, 110. In operation, the convergence of the outputs y to the desired outputs y_d may guarantee convergence of the three sheet states (i.e., the two-dimensional position of the sheet and the rotation of the sheet with respect to a process direction) to the desired (registered) trajectory. The differences between the values of the desired outputs and the corresponding current output values may be used as inputs to a gain-scheduled error dynamics controller 305 that accounts for error dynamics. This controller 305 may have output values v.

Due to the limited amount of time available to perform registration, employing gain-scheduling or a variable set of gains within the error dynamics controller 305 may be a vital component in a sheet registration system employing closed-loop feedback control. Gain scheduling may be used, for example, by sheet registration systems in the presence of otherwise insurmountable constraints with, for example, a static set of gains. A gain schedule effectively minimizes the forces placed on a sheet while still achieving sheet registration. The gain-scheduled error dynamics controller 305 may perform this by, for example, starting with low gains to minimize the high accelerations characteristic of the early portion of registration and then increasing the gain values as the sheet progresses through the sheet registration system to guarantee convergence in the available time.

An input-output linearization module 310 may receive the outputs of the error dynamics controller 305 (v) and state feedback values x_c to produce acceleration values u for the nips 105, 110. The state feedback values x_c may include, for example, the position and rotation of the sheet and the angular velocities of each drive roll associated with a nip 105, 110. The sheet position and rotation may be determined based on sensor information from, for example, the sensors described above with respect to FIG. 1B or any other sensor configuration that can detect the orientation of a sheet. The angular velocity of each drive roll may be determined by, for example, encoders and/or sensors on the drive roll. The acceleration values u may be used to create a linear relationship between the inputs v and the second derivatives of the outputs y of the closed-loop feedback control process.

Kinematic equations (based on an assumption of no slip) for the cart may include:

{dot over (X)} cos Θ+{dot over (Y)} sin Θ+a{dot over (Θ)}−cω₁=0, {dot over (X)} cos Θ+{dot over (Y)} sin Θ−a{dot over (Θ)}−cω₂=0, and {dot over (Y)} cos Θ−{dot over (X)} sin Θ=0,

which can be written in matrix form as:

${\stackrel{.}{q}}_c=S\left(q_c\right)\omega \left(t\right)$ $\begin{array}{ccc}\mathrm{where}\text{:}& & S\left(q_c\right)={\left[\begin{array}{ccc}\frac{1}{2}c\cos \Theta & \frac{1}{2}c\sin \Theta & \frac{c}{2a}\\ \frac{1}{2}c\cos \Theta & \frac{1}{2}c\sin \Theta & -\frac{c}{2a}\end{array}\right]}^T;\mathrm{and}\\ & & \omega \left(t\right)={\left[\begin{array}{cc}{\omega }_1& {\omega }_2\end{array}\right]}^T.\end{array}$

Assuming a set of accelerations u=[u₁ u₂]^T, the resulting cart state equations may be written in companion form:

{dot over (x)} _c =f(x_c)+G(x_c)u,

where:

$\begin{array}{cc}f\left(x_c\right)={\left[\begin{array}{cc}\underset{1\times 3}{{\left(S\omega \right)}^T}& \underset{1\times 2}{0}\end{array}\right]}^T,& G\left(x_c\right)={\lfloor \begin{array}{cc}\underset{2\times 3}{0}& \underset{2\times 2}{I}\end{array}\rfloor }^T.\end{array}$

As with the angular velocities of the drive rolls ω, the accelerations of the drive tolls u may be common to the equations of both reference frames.

The position of a point P_b (an exemplary P_b is shown in FIG. 4B) may be selected to define the outputs y. P_b may be used to assist in achieving linearization between the inputs and the outputs to the sheet registration system. The position of P_b may be described in equation form as: y=h(q_c)=[X_bY_b]^T=[X+b cos Θ Y+b sin Θ]^T. Substituting the desired trajectory of the cart into these equations may result in the corresponding desired output equations: y_d=[y_d—1 y_d—2]^T=[−v_dt−x_di+b−y_di ]^T. Convergence of outputs y to desired values y_d may guarantee convergence of cart states q_c to the desired cart trajectory, which in turn may guarantee the convergence of the sheet states q to the desired (registered) sheet trajectory.

In order to perform linearization between the inputs and the outputs, the output must be recursively differentiated until a direct relationship exists between the inputs and the outputs. Differentiating the outputs once provides the following:

$\stackrel{.}{y}=\frac{}{t}h\left(x_c\right)=\nabla h\left(x_c\right){\stackrel{.}{x}}_c=\nabla h\left(x_c\right)\left(f+\mathrm{Gu}\right)=L_fh+L_g\mathrm{hu}$ $\begin{array}{ccc}\mathrm{where}\text{:}& & L_fh=\left[\begin{array}{c}{L}_fh_1\\ L_fh_2\end{array}\right]\mathrm{and}L_gh=\left[\begin{array}{cc}{L}_{g_1}h_1& L_{g_2}h_2\\ L_{g_1}h_2& L_{g_2}h_2\end{array}\right].\end{array}$

Here, ∇h(x_c) denotes the Jacobian of h(x_c). The Lie derivative of any scalar h with respect to any vector f is a scalar function defined by L_fh=∇hf (essentially the directional derivative of h in an f space: f·∇h). Evaluating the second term of the right hand side of the equation above results in

$L_gh=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right],$

which establishes that the first differentiation does not introduce the output. Differentiating a second time may provide the following equation:

$\ddot{y}=\frac{}{t}\stackrel{.}{y}=\nabla \left(L_f\right)h{\stackrel{.}{x}}_c=L_f^2h+L_gL_f\mathrm{hu}=H+\Psi u,\mathrm{where}\text{:}$ $H=L_f^2h=\left[\begin{array}{c}{L}_f^2h_1\\ L_f^2h_2\end{array}\right]$ $\mathrm{and}$ $\Psi =L_gL_fh=\left[\begin{array}{cc}{L}_{g_1}L_fh_1& L_{g_2}L_fh_2\\ L_{g_1}L_fh_2& L_{g_2}L_fh\end{array}\right].\mathrm{In}\mathrm{this}\mathrm{case},\Psi =-\frac{c}{2a}\left[\begin{array}{cc}a\cos \Theta -b\sin \Theta & a\cos \Theta +b\sin \Theta \\ b\cos \Theta +a\sin \Theta & -b\cos \Theta +a\sin \Theta \end{array}\right].$

Both rows of Ψ may be non-zero (i.e., each row contains at least one non-zero element). Accordingly, the value of at least one input may appear in both outputs after two differentiations. The determinant of Ψ may be seen to be nonzero if b is nonzero: i.e., the decoupling matrix is non-singular. The inverse of Ψ may be computed to be:

${\Psi }^{-1}=-\frac{1}{\mathrm{bc}}\left[\begin{array}{cc}-a\sin \Theta +b\cos \Theta & a\cos \Theta +b\sin \Theta \\ a\sin \Theta +b\cos \Theta & -a\cos \Theta +b\sin \Theta \end{array}\right].$

An input v may be introduced, and u may he defined in terms of v as u=Ψ^{31 1}(v−H). u may be solved in closed form as:

$\frac{1}{4a^2\mathrm{bc}}\left[\begin{array}{c}4a^2\left(-b\cos \Theta +a\sin \Theta \right)v_1-4a^2\left(a\cos \Theta +b\sin \Theta \right)v_2+\\ c^2\left({\omega }_1-{\omega }_2\right)\left(\left(a^2-b^2\right){\omega }_1+\left(a^2+b^2\right){\omega }_2\right)\\ -4a^2\left(b\cos \Theta +a\sin \Theta \right)v_1+4a^2\left(a\cos \Theta -b\sin \Theta \right)v_2-\\ c^2\left({\omega }_1-{\omega }_2\right)\left(\left(a^2+b^2\right){\omega }_1+\left(a^2-b^2\right){\omega }_2\right)\end{array}\right]$

Substituting u into the equation for ÿ, the problem is reduced to the second order vector equation: ÿ=v. This system is linear and uncoupled because each input v_i only affects a corresponding output y_i.

Having reduced the problem to a linear form, the error e may be defined as e=y_d−y. The error dynamics may now be constructed by expressing v as a function of e and y_d: v=ÿ_d+k_dė+k_pe, which may be rewritten as: ë+k_dė+k_pe=0. Because these equations are uncoupled, the values of k_d—i and k_p—i (differential and proportional gain values for each drive roll) directly place the poles: p_1,2—i=−k_d±√{square root over (k_d—i²−4k_p—i)}. Choosing k_dii=2√{square root over (k_p—i)}, for example, may create critically damped error dynamics.

As the output error e converges to zero, the cart state error also converges to zero, but with a phase lag. The amount of phase lag between the convergence of the output and cart state may be adjustable via b. Using a smaller b may result in a smaller lag. In all, five parameters may be used to adjust the rate of convergence: the four gain values (the two-dimensional gain vectors k_d and k_p) and the value of b.

If no system constraints existed, the gain parameters mentioned above (k_d, k_p and b) would suffice to determine the control of the sheet. However, the time period for sheet registration is limited based on the throughput of the device. In addition, violating maximum tail wag and or nip force requirements may create image quality defects. Tail wag and nip force refer to effects which may damage or degrade registration of the sheet. For example, excessive tail wag could cause a sheet to strike the side of the paper path. Likewise, if a tangential nip force used to accelerate the sheet exceeds the force of static friction, slipping between the sheet and drive roll will occur.

To satisfy the time constraints for a sheet registration system, high gain (k_d, k_p) values and a small value of b may be desirable. However, to limit the effects of tail wag and nip force below acceptable thresholds, small gain values and a large value of b may be required. Depending on the input error and machine specifications, a viable solution may not exist if the gain values are static.

In order to circumvent these constraints, gain scheduling may be employed to permit adjustment of the gain values during the sheet registration process. Relatively low gain values may be employed at the onset of the registration process in order to satisfy max nip force and tail wag constraints, and relatively higher gain values may be employed towards the end of the process to guarantee timely convergence. The gain values may be adjusted to maintain a consistent amount of damping. In an alternate embodiment, the damping may also be modified. Although the value of b is not technically a gain value, the value of b may also be scheduled to provide an additional degree of freedom.

Referring back to FIG. 3, for input-output linearization to be effective, accelerations u may be accurately tracked at the drive rolls 325. To achieve this, the accelerations u may be integrated 315 to produce the desired velocities ω_d. One or more motor controllers 320 may be used to control the desired velocities ω_d. The one or more motor controllers 320 may generate motor voltages u_m for the motors that drive the drive rolls 325. The motor voltages u_m may determine the angular velocities ω at which each corresponding drive roll 325 is rotated. For example, a DC brushless servo motor may be used to create a pulse width modulated voltage u_m1 to track a desired velocity ω₁. In an alternate embodiment, any of a stepper motor, an AC servo motor, a DC brush servo motor, and other motors known to those of ordinary skill in the art can be used. The sheet velocity at each nip 105, 110 is computed as the radius (c) of the nip multiplied by the angular velocity of the nip (ω₁ for 105 and ω₂ for 110). The sheet velocity at each drive roll 325 may be defined as the radius (c) of the nip multiplied by the angular velocity of the drive roll. As shown in FIG. 3, each motor controller 320 may comprise a velocity controller. In an alternate embodiment, a feed-forward torque-based motor controller (not shown) may be used to control the torque exerted by the corresponding motor to track accelerations u directly.

The sheet velocity at each drive roll 325 may be defined as the radius (c) of the nip multiplied by the angular velocity of the drive roll. As shown in FIG. 3, each motor controller 320 may comprise a velocity controller. In an alternate embodiment, a torque controller (not shown) may be used to control the torque exerted by the corresponding motor.

The input-output linearization module 310 may utilize position feedback x_c that is generated every sample period. An observer module 330 may employ the following kinematic equations for the cart to evolve the cart position x_c based on the measured drive roll velocities ω:

$\stackrel{.}{X}=\frac{-c\left({\omega }_1+{\omega }_2\right)}{2}\cos \Theta ,Y=\frac{-c\left({\omega }_1+{\omega }_2\right)}{2}\sin \Theta ,\stackrel{.}{\Theta }=\frac{-c\left({\omega }_1-{\omega }_2\right)}{2a}.$

The observer module 330 may be initialized by an input position snapshot provided by the sensors. Only the cart position may be needed because the reference frame for the linearization module 310 may be based on the cart state x_c. The cart state values x_c may be converted to the corresponding sheet state values q_c using, for example, a processor 335 to compute the equations defined above,

EXAMPLE

An exemplary sheet registration system designed according to an embodiment was installed in a Xerox iGen3® print engine. The input velocity of the sheets into the drive rolls was approximately 1.025 m/s. The registration was performed at a process velocity of approximately 1.024 m/s, which correlates to approximately 200 pages per minute. The process velocity reduces to a registration time of approximately 0.145 seconds, which is the time in which input-output linearization must converge in order to function properly in the system.

The sheet feeding mechanism was adjusted to produce approximately 5 mm of input lateral error. FIG. 5 depicts graphs of the gain values used to converge the sheet where a damping ratio of 0.7 is maintained in the exemplary embodiment. For the gain values show in FIG. 5, the value for b was maintained at −10 mm.

FIG. 6 depicts a graph of the nip velocities for each nip. As shown in FIG. 6, the desired angular velocities for each drive roll and the actual angular velocities for each drive roll produced by the sheet registration system may be substantially the same.

FIG. 7 depicts a graph of the nip accelerations for each nip. FIG. 8 depicts a graph of the nip forces for each nip. Each of the nip accelerations and the tangential nip forces were filtered via a moving average filter to reduce the noise in the plot. As shown in FIGS. 7 and 8, the desired accelerations and forces closely matched the actual accelerations and forces for the sheet registration system.

FIG. 9 depicts a graph of the output error for the virtual cart. As shown in FIG. 9, the cart outputs asymptotically converged to the desired values via the input-output linearization process. Moreover, this convergence occurred within 100 ms, which is substantially less than the 145 ms limit based on the system constraints. The convergence of the cart outputs may guarantee the convergence of the cart states as depicted in FIGS. 10A-C, which depict graphs of the error for the X, Y and Θ states for the cart, respectively. In the results depicted in FIGS. 10A-C, the Y and Θ states converged approximately 20 ms later than the X state. The delay for the Y and Θ states may be largely attributed to the time that it takes P_c to converge to the desired trajectory after P_b has converged.

FIGS. 11A-C depict graphs of the error for the x, y, and θ states for the sheet, respectively. FIGS. 11A-C were generated by transforming the cart states to the sheet states via the equations defined above. Again, the convergence of the sheet is depicted in FIGS. 11A-C in approximately 100 Ms.

FIG. 12 depicts a graph of the sheet position as it moved through the sheet registration system. As shown in FIG. 12, the sheet's corners were determined based on sensor information and plotted as the sheet passes through the sheet registration system (from left to right). FIG. 12 depicts the outline of the sheet for four sample periods during the registration process. The first sample period is the input position snapshot. The CCD sensors, the process edge (PE) sensors and the drive rolls are included in FIG. 12 to provide a frame of reference for the sheet position. The drive rolls are also included to show that the paper is registered before entering the pre-transfer nip.

FIGS. 13A-C depict the observed sheet states as compared with the input and output snapshots. The input position snapshot may initialize the observer. Accordingly, no error exists at the start. The position of the cart may then be estimated by the encoders on the drive rolls. The accumulation of error may be summarized by the difference between the observed states and the output snapshot at the end of registration.

FIG. 14 may show the CCD (lateral edge sensor) readings during the sheet registration process. A zero CCD reading indicates a desired (i.e., perfectly registered) location of the lateral edge of the sheet. Rising edges in FIG. 14 indicate sheet arrival, and falling edges indicate sheet departure. CCD1 and CCD2 are used for the input snapshot and CCD1 and CCDL are used for the output snapshot. Separation of CCD readings may result from sheet skew (i.e., Θ error).

The numerical results for the sheet state error are depicted in Table 1.

	x − xd	y − yd	θ − θd
Input state error	0.535013 mm	−5.626886 mm	−3.985442 mrad
Output state error	−0.006469 mm	0.000699 mm	0.054475 mrad
(observed)
Output state error	−0.312800 mm	−0.056000 mm	−0.169594 mrad
(actual)

It will be appreciated that various of the above-disclosed and other features and functions, or alternatives thereof may be desirably combined into many other different systems or applications. It will also be appreciated that various presently unforeseen or unanticipated alternatives, modifications, variations or improvements therein may be subsequently made by those skilled in the art which are also intended to be encompassed by the disclosed embodiments.

Claims

1. A method of performing sheet registration the method comprising: identifying output values for a sheet within a reference frame;determining a difference between each output value and a corresponding desired output value;determining input values for the sheet based on at least the differences;determining state feedback values based on information received from one or more sensors;for each of a plurality of drive rolls: determining an acceleration value based on the input values and the state feedback values,determining a desired angular velocity value based on the acceleration value, anddetermining a motor voltage for a motor for the drive roll that tracks an observed angular velocity value for the drive roll to the desired angular velocity value for the drive roll,wherein the acceleration values create a linear differential relationship between the input values and the output values,wherein the above-listed steps are performed a plurality of times.

2. The method of claim 1 wherein the output values correspond to a twos dimensional position within the reference frame.

3. The method of claim 1 wherein the reference frame is based on the location of the drive rolls.

4. The method of claim 3 wherein the desired output values correspond to a position of a point that is on a line bisecting the drive rolls.

5. The method of claim 1 wherein the input values are further determined based on one or more constraints.

6. The method of claim 5 wherein the one or more constraints comprise a maximum force to be applied to a sheet by a drive roll.

7. The method of claim 5 wherein the one or more constraints comprise a maximum amount of rotational velocity to apply to the sheet.

8. The method of claim 5 wherein the one or more constraints comprise a maximum sheet registration time.

9. The method of claim 5 wherein the one or more constraints comprise an output velocity for the sheet.

10. The method of claim 1 wherein the state feedback values comprise a two-dimensional position of the sheet within the reference frame and an angle at which the sheet is oriented with respect to a process direction.

11. A system for performing sheet registration, the system comprising: one or more sensors;a plurality of drive rolls;a plurality of motors wherein each motor is associated with at least one drive roll; anda processor,wherein the processor comprises: a state feedback determination module for determining state feedback values based on information received from the one or more sensors,an output value identification module for determining output values based on the state feedback values,a difference generation module for determining the difference between each output value and a desired value for each output value,an input value determination module for determining input values based on at least the differences,an acceleration value determination module for determining an acceleration value for each drive roll based on the input values and the state feedback values,an angular velocity determination module for determining a desired angular velocity value for each drive roll based on the acceleration value, anda motor voltage determination module for determining a motor voltage for each motor, wherein the motor voltage determination module tracks an observed angular velocity value for each drive roll to the desired angular velocity value for the drive roll,wherein the acceleration values create a linear differential relationship between the input values and the output values.

12. The system of claim 11 wherein the output values correspond to a two-dimensional position within the reference frame.

13. The system of claim 11 wherein the reference frame is based on the location of the drive rolls.

14. The system of claim 13 wherein the desired output values correspond to a position of a point that is on a line bisecting the drive rolls.

15. The system of claim 11 wherein the input value determination module further determines the input values based on one or more constraints.

16. The system of claim 15 wherein the one or more constraints comprise a maximum force to be applied to a sheet by a drive roll.

17. The system of claim 15 wherein the one or more constraints comprise a maximum amount of rotational velocity to apply to the sheet.

18. The system of claim 15 wherein the one or more constraints comprise a maximum sheet registration time.

19. The system of claim 15 wherein the one or more constraints comprise an output velocity for the sheet.

20. The system of claim 11 wherein the state feedback values comprise a two-dimensional position of the sheet within the reference frame and an angle at which the sheet is oriented with respect to a process direction.