Dynamic Roll Eccentricity Identification Using Extended Kalman Filter State Estimation and Control Upgrade for Cold Rolling Mills

Abstract

Control system for cold rolling mills to improve sheet metal thickness uniformity. Sensors monitor the state of the cold rolling mill by measuring (i) roll eccentricity, (ii) roll slips during mill operation, (iii) mill disturbances from roll speed or roll force manifestations, and (iv) unknown disturbances referred to as process noise. The controller analyzes data from sensors to compensate. Data collected during the mill operation by the sensors are delayed in reaching the controller. This communication delay is accounted for by using a filter. Since an objective of the controller software is dynamic identification of eccentricity of the back up rolls, which is non-linear by nature, an Extended Kalman Filter may be used.

Claims

1. A controller for controlling thickness of sheet metal in a mill exiting a roll stand comprising a first work roll and a second work roll respectively positioned between a first back up roll and a second back up roll, the controller comprising a processor and code stored on media readable by the processor to control the thickness of the sheet metal, the controller comprising: an input comprising the thickness of the sheet metal and dynamic eccentricities of the first back up roller and the second back up roller; a model of the roll stand; a filter based on the model; and a controller output coupled to control a gap between the first work roll and the second work roll to produce the sheet metal.

2. The controller of claim 1 wherein the controller input further comprises roll slip between the first work roll and the second work roll.

3. The controller of claim 1 wherein the filter comprises an Extended Kalman Filter.

4. The controller of claim 1 wherein the model comprises input roll force, average roll gap, and angular velocities of the first back up roll and the second back up roll.

5. The controller of claim 1 is coupled to proximity sensors configured to measure rotational positions of the first back up roll and the second back up roll.

6. A method of programming a controller for controlling thickness of sheet metal produced by a roll stand, the method comprising: obtaining a model of the roll stand; receiving input comprising thickness of the sheet metal and dynamic eccentricities of a first work roll and a second work roll in the roll stand; generating a filter based on the model; adjusting parameters of the filter based on the input; and improving control of the thickness of the sheet metal produced by the roll stand;

7. The method of claim 6 wherein the filter is an Extended Kalman Filter.

8. The method of claim 6 further comprising obtaining a model for roll slip between the first work roll and the second work roll.

9. A controller for controlling thickness of sheet metal exiting a roll stand having a first work roll and a second work roll comprising: a processor; means of measuring the thickness of the sheet metal exiting the roll stand; means of determining eccentricity of the first work roll and the second work roll; a memory device coupled to the processor and comprising a readable program for execution by the processor to: receive an input comprising the thickness of the sheet metal and dynamic eccentricities of the first work roll and the second work roll, process a model of the roll stand; execute a filter based on the model; and provide an output coupled to control a roll gap between the first work roll and the second work roll.

10. The controller of claim 9 further comprising means of calculating roll slip between the first and second work rolls.

11. The controller of claim 9 wherein the filter is an Extended Kalman Filter.

12. The controller of claim 9 wherein the input further includes roll force, the roll gap, and angular velocities of the first back up roll and the second back up roll.

13. The controller of claim 12 wherein the angular velocities are determined by proximity sensors configured to measure rotational positions of the first back up roll and the second back up roll.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0023] FIG. 1 illustrates a sheet metal cold rolling mill system;

[0024] FIG. 2 is a schematic representation of an ideal and actual roll superimposed to illustrate eccentricity;

[0025] FIG. 3 is a flowchart that depicts operation of a control technique for a cold rolling mill (plant model);

[0026] FIG. 4 is a flowchart that describes a state of identification method with respect to roll speeds, its synchronization, and roll eccentricity;

[0027] FIG. 5 is a flowchart describing a method of estimating state or condition of a mill with sensor feedback using Extended Kalman Filter for operation of a cold rolling mill (plant model) as shown in FIG. 1;

[0028] FIG. 6 illustrates a rolled sheet metal system for sensing and controlling sheet metal thickness; and

[0029] FIG. 7 illustrates a computer system to implement a controller.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0030] The methods of the present invention include various inventive combinations of the following components:

[0031] (1) Dynamic identification of roll eccentricity and compensation for roll eccentricity; (2) Roll slip identification and compensation; (3) Extended Kalman Filter (EKF) based state estimation using dynamic partial state feedback; and (4) Operator tunable parameters to improve estimation of the state of the mill.

[0032] As appropriate, mill operators may implement the tunable parameters. The control system of the present invention will be described in controlling the thickness of sheet metal produced in a 4-hi stand cold rolling mill that is taken as a base reference (4-hi-mill). However, it is understood the invention is applicable to various other cold rolling mill arrangements. The description herein assumes that frequency of controller computation and frequency of captured sensor or observer feedback data may be designed and implemented to occur at suitable periodic time intervals deemed effective on the mill operations.

Definitions

[0033] As used herein, the following terms have the following meanings.

[0034] The term Work Roll (W R) refers to a set of rollers that are in contact with the surface of the sheet metal produced.

[0035] The term Back Up Roll (BUR) refers to a pair of rollers which are used to apply higher pressure on the WRs. The two pairs of rollers, namely the WRs and BURs are part of the 4-hi stand rolling mill.

[0036] The term Strip/Work piece refers to the metal sheet being produced.

[0037] The term Roll Gap refers to the gap between the pair of WRs, through which, the sheet is being produced.

[0038] The term Material Properties (c.sub.m) refers to properties of the strip.

[0039] The term Hydraulic Gap Control (HGC) Time Constant (?.sub.hyd) refers to the time constant of the controller for the roll gap. With regard to the base reference 4 high mill, hydraulic actuation applies the force onto the rollers.

[0040] The term WR main drive constant (?.sub.roll) refers to the drive constant of the speed controller for the WRs.

[0041] The term Reference angular velocity (?.sub.WRa) refers to the reference angular velocity which is computed according to the set point WR speed.

[0042] The term Diameter of BUR (D.sub.BUR) refers to the diameter of the BUR.

[0043] The following parameters describe the sensors monitoring the state or condition of the mill.

[0044] The term Entry thickness (h_1) refers to the thickness/height profile of a strip while entering the roll gap.

[0045] The term Exit thickness (h_2) refers to the thickness/height profile of a strip exiting the roll gap.

[0046] The term WR angular velocity (?.sub.WRa) refers to the angular velocities of the WRs (top and bottom).

[0047] The term BUR angular velocity (?.sub.BUR) refers to the angular velocities of BURs, wherein the top and bottom speeds are measured as N1 and N2, respectively, and are used to determine (?.sub.BUR).

[0048] The term Roll Force (F_roll) refers to the force that is applied on the rolls.

[0049] The term Avg_gap refers to the average gap between the WRs across its length.

[0050] The following parameter describe the actively controlled action on the mill.

[0051] The term screw position (S) refers to the screw position which is actively controlled to adjust the roll gap.

[0052] The following parameters are preset/predetermined before mill operations:

[0053] The term Strip speed (?.sub.strip) refers to the speed of the strip exiting the roll gap.

[0054] The term Mill speed refers to the mill speed that is set by the mill operator and which is translated to the WR angular velocity.

[0055] The term Mill Stretch (c.sub.g) refers to stretch that the 4 high-mill stand undergoes during mill operations.

[0056] The term Material Modulus (c.sub.m) refers to the bulk modulus of the metal strip being produced.

[0057] The term Reference Screw Position (S.sub.ref) refers to the screw position set at the start of mill operations.

[0058] The term Reference WR angular velocity (?.sub.WRref) refers to the angular velocities of the WRs at the start of mill operations.

[0059] The following parameters are the system uncertainties that are estimated and compensated:

[0060] The term Eccentricity (e) refers to the eccentricity in the circumference of the large BURs that leads to errors/deviations in the strip thickness.

[0061] The term Amplitude of roll eccentricity (a.sub.ecc=[a.sub.t a.sub.b]) refers to the eccentricity over the BURs.

[0062] The term Roll Slip refers to the difference in the speeds between the top and bottom WR.

[0063] The term Roll Gap refers to the end effect roll gap achieved resulting from the controlled screw position change is uncertain due to variations in the strip properties, mill stretch, roll force, and eccentricities.

[0064] FIG. 1 illustrates a metal rolling mill system 2 with thickness control. An example is the METALSMASTER process from Honeywell International, Inc. which is modified to include the inventive embodiments. A rolling mill stand may include four or more rolls mounted vertically, such as, two smaller diameter work rolls, each in contact with separately mounted larger-diameter back-up rolls.

[0065] Incoming metal strip 18 of thickness H is provided by a roll 16 of material that is reduced to a thickness h through a multiplicity of rolls 4, 12, 14, 8 that consists of top back up roll 4, top work roll 12, bottom work roll 14, and bottom back up roll 8 (which are referred to collectively as a 4-hi stand 30). The metal strip 18 may be ferrous and/or non-ferrous. Strip 20 which exits from stand 30 is collected by a roll 22. Proximity sensor 6 measures the rotational position of top BUR 4 and proximity sensor 10 measures the rotational position of the bottom BUR 8. For load signal sampling, rotation around the roll circumference may be divided into a number of segments, such as 32 segments. These rotational positions are used to compute the angular velocities of the two BURs 4,8, which are part of the mill state parameters. A feature of the invention is to measure the angular velocity of the back up rolls Various conventional devices can be employed. Proximity sensors can be used. Representative proximity sensors include the series IGMF/INFW inductive proximity switches made by EGE-Electronik Spezial Sensoren GmbH (Gettorf, DE). BUR 4,8 angular velocity may be assumed to be the same as the work roll's 12, 14 angular velocity. Alternatively, the top and bottom work rolls 12, 14 may also be equipped with proximity sensors (not shown) to measure their actual angular velocities.

[0066] The stand 30 is equipped with a gap positioning system 26, which may be mechanical, hydraulic, or a combination of both, and is controlled by a feedback device 28. The gap positioning system 26, which can vary the work roll gap or opening, includes a pair of screwdown motors each equipped with a screwdown or screw which clamps against opposite ends of the two BURs 4, 8 and thereby apply pressure (roll force) to the work rolls 12, 14. The strip 20 leaves the stand 30 at thickness h, which is measured by sensor 24, which may be an x-ray gauge. L is the stand 30 centerline. The control objective is to regulate this outgoing thickness h, such as, at a centerline, as closely as appropriate to a specified target thickness.

[0067] FIG. 2 is a schematic of eccentricity on a roll as an actual roll shape shown by solid line 42 and an ideal roll shape as shown by broken line 40 which are effectively coaxial. The amount of eccentricity is shown at a maximum eccentricity, e, at 46 as a difference between the ideal and actual radius. A proximity sensor 44 is positioned within a bottom BUR 14 from FIG. 1. The effect of eccentricity on thickness in a rolling application may be described as follows: Normally, an increased force means the exit thickness has increased (thus pushing the rolls apart). However, if the rolls are eccentric then when the largest radius passes through the roll gap, the force increases, but the exit thickness actually decreases. Hence, a change in force is misinterpreted when eccentricity components are present.

[0068] Thickness variations not directly related to roll eccentricity may be compensated separately. Pressure distributions from top 12 and bottom 14 work rolls may vary at nominal neutral position due to other reasons, such as roll bending with roll torque.

[0069] Mill stretch coefficient may be compensated in a mill-stand model. An HGC (hydraulic gap control) model may account for mill stretch, which is a non-linear function of rolling force.

[0070] A main drive model, including a series of non-linear ordinary differential equations, may be used to model main drive dynamics.

[0071] Deformation resistance may be based on a Bland, Ford, and Ellis model for roll force in cold strip rolling with tensions.

[0072] Damping coefficients and spring constants may be tuned.

[0073] Compensation may be included for roll slips, including forward slips, such as, by using roll gap control. The upper and lower work rolls may be subject to roll slips, such as due to variability in friction, so they may rotate at different speeds. This complicates the task of reducing variation in gauge of the strip being cold rolled. A slip factor variable may include a change in velocity between the work rolls and backup rolls. The slip factor may be exposed as a user tunable option.

[0074] The inventive Roll Eccentricity Compensation (REC) model uses real time/dynamic feedback for dynamic generation of an eccentricity signal with the aid of EKF to account for communication delays in feedbacks and process noise of mill operations. This involves a correlation and learning of the existing thickness deviation, the effective force and the manifested roll gap, into the model that generates an initial estimate of the eccentricity signal over the circumference of the Back Up Rolls. This is refined for real time identification of an eccentricity compensation signal which is suitable for the current state of mill operations.

[0075] With the present invention, proximity sensors 6, 10 are employed to track the BURs' 4, 8 angular position. Direct control conceptThe method Eccentricity information is identified from the roll force and dynamic state identification and estimation. The theoretical model is described in the following Sections 1 through 9.

Section 1. Definitions

[0076] Work Roll (WR): Reference angular velocity from rotary encoder {?.sub.WR} [0077] Back Up Roll (BUR): Diameter for top & bottom BUR {Diameter.sub.BUR} [0078] Strip/Work Piece: Material Properties {c.sub.m} [0079] Roll Gap: Hydraulic Gap Control (HGC) time constant {?.sub.hyd} [0080] WR main drive constant {?.sub.roll}

Section 2. Measurements:

State Observers

Thickness/Height Profile of Strip

[0081] Entry thickness {h.sub.1}measures the thickness of the strip before entering the work roll gap. An x-ray gauge can be employed. [0082] Exit thickness {h.sub.2}measures the thickness of the strip after exiting the work roll gap.
Angular velocities/Rotational Speeds [0083] WR angular velocity {?.sub.WR}This velocity can be determined with a proximity sensor that measures the rotational position and, hence, derives the angular velocity. [0084] BUR angular velocity {?.sub.BUR}This velocity can be determined with a proximity sensor.

[0085] Roll Force {F.sub.roll}Pressure is applied by changing the screw position of the hydraulic press to the work rolls typically in response to feedback.

3. Active Control Variables

[0086] Screw Position to adjust roll gap {S}

4. System Presets/Constant Parameters

[0087] Strip speed {?.sub.strip}) [0088] Mill speed (or) WR angular velocity {?.sub.WR} [0089] Mill Stretch {c.sub.g} [0090] Material Modulus {c.sub.m} [0091] Reference Screw Position {S.sub.ref} [0092] Reference WR angular velocity {?.sub.WRref}

Section 5. System Uncertainties

[0093] Roll eccentricity [0094] Eccentricity {e} [0095] Amplitude of roll eccentricity {(a.sub.ecc=[a.sub.t a.sub.b]}

[0096] Each for top and bottom BUR

Section 6. Mathematical Models

[0097] The following assumptions may be made as appropriate:

6.1 HGC Dynamics

[0098] Assume a first order system

[00001]$\left\{\frac{1}{{?}_{\mathrm{hyd}}s+1}\right\}$

[0099] Let this be

[00002]$?S=S_{\mathrm{ref}}-S$

6.2 Main Drive Dynamics

[0100] Assume a first order system

[00003]$\left\{\frac{1}{{?}_{\mathrm{roll}}s+1}\right\}$

[0101] Let this be

[00004]${\mathrm{??}}_{\mathrm{WR}}={?}_{{\mathrm{WR}}_{\mathrm{ref}}}-{?}_{\mathrm{WR}}$

6.3 Estimate of Roll Force

[0102] [00005]$F_{\mathrm{roll}}=\mathrm{function}\left(h_2,S,e\right)\mathrm{or}\mathrm{function}\left(c_m,h_1\right)F_{\mathrm{roll}}=c_g\left(h_2-S+e\right)F_{\mathrm{roll}}=c_m\left(h_1-h_2\right)$

6.4 Estimate of Exit Thickness

[0103] h.sub.2=function (c.sub.g, c.sub.m, h.sub.1, S, e)

[0104] Assume

[00006]$c_g\left(h_2-S+e\right)=c_m\left(h_1-h_2\right)$

[0105] Then,

[00007]$h_2=\frac{c_m{h}_1}{c_m+c_g}+\frac{c_{g}S}{c_m+c_g}-\frac{c_{g}e}{c_m+\mathrm{cg}}$

[0106] Assume, that there is no effect of c.sub.m and c.sub.g on entry thickness, h.sub.1

[0107] Then,

[00008]$h_2=\frac{c_{g}S}{c_m+c_g}-\frac{c_{g}e}{c_m+\mathrm{cg}}$

6.5 Estimate Screw Compensation Signal

[0108] From,

[00009]$F_{\mathrm{roll}}=c_g\left(h_2-S+e\right)$

[0109] Partial derivative of roll force w.r.t. exit thickness:

[00010]$\frac{?F_{\mathrm{roll}}}{?h_2}=c_g-c_g\frac{?S}{?h_2}$

[0110] substituting, F.sub.roll=?c.sub.m

[00011]$\frac{?S}{?h_2}=1+\frac{c_m}{c_g}$

[0111] Screw Compensation is,

[00012]$?S=\frac{?S}{?h_2}{h}_2=\left(1+\frac{c_m}{c_g}\right)h_2$

6.6 Estimate of Eccentricity Signal

[0112] Roll eccentricity is a periodic function that captures deformations on the BUR circum-surface. This periodic signal will change its properties with new work piece, WR angular velocity, roll force, and mill stretch.

[0113] Assume,

[00013]$e\left(t\right)=\underset{j=1}{\overset{H}{.Math.}}\underset{i=1}{\overset{N}{.Math.}}{a}_{\mathrm{ij}}\sin \left(j{?}_{i}t\right)$

[0114] Where, [0115] e(t).fwdarw.eccentricity signal [0116] N.fwdarw.no. of sine components [0117] H.fwdarw.no. of harmonics of each sine component [0118] a.sub.ij.fwdarw.Amplitude of j.sup.th sine component i [0119] ?.sub.i.fwdarw.Frequency of sine component i [0120] t.fwdarw.absolute time

[0121] Here, a single sine component is

e(t)=a sin(?t)

[0122] Let [0123] ?=?t

[0124] Then, the derivatives are: [0125] {dot over (?)}=? [0126] {dot over (?)}=0 [0127] {dot over (a)}=0

[0128] Let there be two components of eccentricity, each for top and bottom BUR

[0129] Then, we have:

[00014]$e\left(t\right)=a_t\sin {?}_t+a_b\sin {?}_b$

[0130] Where, [0131] Top BUR.fwdarw.?.sub.t, ?.sub.t, a.sub.t [0132] Bottom BUR.fwdarw.?.sub.b, ?.sub.b, a.sub.b

[0133] Then, the derivatives are: [0134] {dot over (?)}.sub.t=?.sub.t [0135] {dot over (?)}.sub.t=0 [0136] {dot over (a)}.sub.t=0 [0137] {dot over (?)}.sub.b=?.sub.b [0138] {dot over (?)}.sub.b=0 [0139] {dot over (a)}.sub.b=0

[0140] Given the non-linear profile, an Extended Kalman Filter (EKF) is chosen for state estimation.

[0141] The Extended Kalman Filter may be based on statistical inference.

Section 7. State Space Representation of the Mathematical Model

7.1 State Space Representations

[0142] [00015]$\left[\begin{array}{c}{h}_2\\ F_{\mathrm{roll}}\end{array}\right]=\left[\begin{array}{cc}\frac{c_g}{c_m+c_g}& 0\\ -\frac{c_g{c}_m}{c_g+c_m}& 0\end{array}\right]\left[\begin{array}{c}S\\ {?}_{\mathrm{WR}}\end{array}\right]+\left[\begin{array}{c}-\frac{c_g}{c_m+c_g}\\ \frac{c_g{c}_m}{c_m+c_g}\end{array}\right]e\left(t\right)\left[\begin{array}{c}\stackrel{.}{S}\\ \stackrel{.}{{?}_{\mathrm{WR}}}\end{array}\right]=\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]\left[\begin{array}{c}S\\ {?}_{\mathrm{WR}}\end{array}\right]+\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]\left[\begin{array}{c}{S}_{\mathrm{ref}}\\ {?}_{{\mathrm{WR}}_{\mathrm{ref}}}\end{array}\right]\mathrm{where},e\left(t\right).fwdarw.\left[\begin{array}{c}\stackrel{.}{{?}_t}\\ \stackrel{.}{{?}_t}\\ \stackrel{.}{a_t}\\ \stackrel{.}{{?}_b}\\ \stackrel{.}{{?}_b}\\ \stackrel{.}{a_b}\end{array}\right]=\left[\begin{array}{cccccc}0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\end{array}\right]\left[\begin{array}{c}{?}_t\\ {?}_t\\ a_t\\ {?}_b\\ {?}_b\\ a_b\end{array}\right]$

[0143] From the above, we construct:

State Transition Model

[0144] [00016]$\left[\stackrel{.}{X}=\mathrm{AX}+\mathrm{BU}\right]-\mathrm{by}\mathrm{convention}$

[0145] Astate transition matrix

[00017]$\begin{array}{ccccccccccc}-1/{?}_{\mathrm{hvd}}& 1/{?}_{\mathrm{hvd}}& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& -1/{?}_{\mathrm{roll}}& 1/{?}_{\mathrm{roll}}& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& \frac{{?}_t}{2?}& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& {?}_t& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& \frac{{?}_b}{2?}& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& {?}_t& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\end{array}$

XStates

[0146]

TABLE-US-00001 S screw position S.sub.ref reference screw position ?.sub.WR angular velocity of WR ?.sub.WR.sub.ref reference angular velocity of WR F initial rotation at the start of coil roll ?.sub.t angular frequency of top BUR ?.sub.t angular velocity of top BUR ?.sub.t amplitude of top BUR ?.sub.b angular frequency of bottom BUR ?.sub.b angular velocity of bottom BUR ?.sub.b amplitude of bottom BUR

[0147] The profile of eccentricity is filtered out by a complementary method using feedback from roll gap and roll force. The amplitude is scaled to millimeters to meet the compensation value for thickness correction. This correction which is calculated will be added as a sum component to Average Gap Output.

[0148] FIG. 3 is a control schematic which describes the process of identifying of the roll eccentricity during a cold rolling mill run-time. The roll force, average gap, and angular velocities of the two BURs (N1 and N2) are measured in steps 100, 102 and 110. These contribute to the dynamic partial state feedback for the entire system. Step 124 determines if there is a difference between the measured average roll gap and the set roll gap and, if so, the calculation is used to estimate an effective gap that is noisy, called gap noise 130. This is used to identify the effective roll force in step 100 that is filtered using gap noise in step 122. Meanwhile, an instantaneous amplitude of eccentricity is extracted from the instant in the waveform of the eccentricity signal in steps 126, 108. As an option, instantaneous data depicting the waveform of the eccentricity signal may be extracted by the operator at any time for further exploration of the mill status such as for maintenance and efficiency. The estimated amplitude of eccentricity corresponds to the deviation in the roll gap that needs to be corrected. This amplitude of eccentricity may be scaled up, or scaled down, by the operator, to accommodate other uncertainties in the mill, as defined by a gain constant, which, by default, may equal to 1 in step 128.

Section 8. Operator Tunable Parameters

[0149] The inventive method also allows tunability of various parameters appropriate for the rolling mill site. These parameters are accessible any time by the operators and may be employed to scale the eccentricity amplitude for further improvement. The tuning may be required only to troubleshoot operational issues. These parameters include, for example: [0150] Radius of top and bottom, WR and BUR. [0151] Mill Stretch {c.sub.g}.

[0152] Material Modulus {c.sub.m}. [0153] Eccentricity amplitude scaling. [0154] Number of harmonics. [0155] Execution rate.

[0156] Power Spectral Density (PSD) constants for process noise (q) and measurement noise (r): q_s, q_v, q_h, q_a, q_f, r_s, r_v, r_h, r_f

[0157] PSD constants are generic mathematical concepts which support noise functions. They can be tuned by the mill operator.

Section 9. Description of Method

[0158] FIG. 4 lists the roll synchronization and eccentricity identification steps for the inventive sensor and EKF-based roll eccentricity and compensation technique.

[0159] Roll synchronization begins with process step 140 which includes marker pulse tracking.

[0160] After process step 140, the next process step 142 includes roll circumference segmentation.

[0161] After process step 142, the next process step 144 includes Sync BUR rotations with state/reference variables.

[0162] After process step 144, the next process step 146 includes track delta rotational position segment-wise.

[0163] Process step 146 completes roll synchronization which is then followed by eccentricity identification which begins with process step 150 which includes track segment-wise roll force sensor data for top and bottom BUR.

[0164] After process step 150, the next process step 152 includes construct delta roll force distribution segment-wise between top and bottom BUR.

[0165] After process step 152, the next process step 154 includes compute eccentric roll force signal.

[0166] Process step 154 completes eccentricity identification.

[0167] Process steps 144, 146, and 152 also identify roll slips/profile the eccentricity over each BUR surface using roll force.

[0168] FIG. 5 shows the organization of the overall method, such as, in a MATLAB/software/firmware implementation.

[0169] Process step 160 begins with initialize state variables.

[0170] After process step 160, the next process step 162 includes declare sampling time and initial rotational position.

[0171] After process step 162, the next process step 163 includes eccentricity identification for top BUR & bottom BUR.

[0172] After process step 163, the next process step 164 includes construct state transition matrix [11?11].

[0173] After process step 164, the next process step 166 includes assume a measurement noise effect matrix [11?11].

[0174] After process step 166, the next process step 168 includes assume white noise PSD constants for measurement noise using measured state variables.

[0175] After process state 168, the next process state 170 includes discretize LTI ODE with Gaussian noise.

[0176] After process step 170, the next process state 172 includes construct EKF model time stepping the state estimation and covariance estimation.

[0177] After process step 172, the next process step 174 includes estimate eccentricity set point that is computed with each time step of state and covariance estimations.

[0178] The inventive process may be incorporated into a plant, such as, a cold rolling mill system 200, including those with automatic gauge control (AGC) and hydraulic gap control (HGC) controllers to improve the thickness accuracy of sheets produced. As shown in FIG. 6, a mill 202 may include output 210 from a controller 20. The output 210 may include roll eccentricity compensation, such as, is described in US 2018/0161839 to McGahan, which is incorporated herein by reference. The controller 206 may include input 208 from sensors 204, such as, for top and bottom BURs. The controller 206 may include a filter 220. The filter 220 may include various models 222, 224 by integration of an inventive method, such as, in a MATLAB script or in another suitable program into the controller environment. The model 222 may include state estimation and covariance (noise effect) estimation. The model 224 may include a state transition model with dynamic partial state feedback.

[0179] The inventive method may be implemented and validated in HTS lab simulation environment, for various cases of preset conditions. In an embodiment of the present invention, it showed an improvement of up to 10%, over the existing range of 0.5-1.5% thickness deviation. In another embodiment of the present invention, the thickness accuracy improved by an additional 10% over that of an AGC controller's performance.

[0180] 1. The eccentricity estimation adapts to the actual eccentricity changes in the rolling mill over time.

[0181] 2. Allows the operator to scale the eccentricity amplitude for further improvement.

[0182] 3. The noise model assumed in the plant process and measurements are operator tunable for Power Spectral Density (PSD) constants for further improvement.

[0183] FIG. 7 is a block schematic diagram of computer system 240 to implement the controller and methods according to example embodiments. Not all components need to be used in various embodiments One example computing device in the form of a computer system 240, may include processing unit 242, memory 244, removable storage 252, and non-removable storage 256. Although the example computing device is illustrated and described as computer system 240, the computing device may be in different forms in different embodiments. For example, the computing device may instead be a smartphone, a tablet, a smartwatch, or other computing device including the same or similar elements as illustrated and described with regard to FIG. 7. Devices such as smartphones, tablets, and smartwatches are generally collectively referred to as mobile devices. Furthermore, although the various data storage elements are illustrated as part of computer system 240, the storage may also, or alternatively, include cloud-based storage accessible via a network, such as the Internet.

[0184] Memory 244 may include volatile memory 248 and non-volatile memory 259. Computer system 240 may includeor have access to a computing environment that includesa variety of computer-readable media, such as volatile memory 248 and non-volatile memory 259, removable storage 252 and non-removable storage 256. Computer storage includes random access memory (RAM), read only memory (ROM), erasable programmable read-only memory (EPROM) & electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CD ROM), Digital Versatile Disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage, or other magnetic storage devices capable of storing computer-readable instructions for execution to perform functions described herein.

[0185] Computer system 240 may include, or have access to, a computing environment that includes input 258, output 260, and a communication interface 254. The output 260 may include a display device, such as a touchscreen, that also may serve as an input device. The input 258 may include one or more of a touchscreen, touchpad, mouse, keyboard, camera, one or more device-specific buttons, one or more sensors integrated within, or coupled via, wired or wireless data connections to computer system 240, and other input devices. The computer may operate in a networked environment using a communication connection to connect to one or more remote computers, such as database servers, including cloud-based servers and storage. The remote computer may include a personal computer (PC), server, router, network PC, a peer device or other common network node, or the like. The communication connection may include a Local Area Network (LAN), a Wide Area Network (WAN), cellular, WiFi, Bluetooth, or other networks.

[0186] Computer-readable instructions stored on a computer-readable storage device are executable by the processing unit 242 of the computer system 240. A hard drive. CD-ROM, and RAM are some examples of articles including a non-transitory computer-readable medium such as a storage device. The terms computer-readable medium and storage device do not include carrier waves. For example, a computer program 246 may be used to cause processing unit 242 to perform one or more methods or algorithms described herein.

[0187] The foregoing has described the principles, preferred embodiments and modes of operation of the present invention. However, the invention should not be construed as being limited to the particular embodiments discussed. Thus, the above-described embodiments should be regarded as illustrative rather than restrictive, and it should be appreciated that variations may be made in those embodiments by workers skilled in the art without departing from the scope of the present invention as defined by the following claims.