Model-based multi-variable predictive control for metal rolling mill

Abstract

SOLUTION: A control system employs a model-based multi-variable predictive control for cold rolling mills to improve sheet thickness uniformity to meet or exceed specifications in flatness. The control system is particularly suited for control of 4-hi non-reversible single-stand metal rolling mills. The mill stand has a first work roll and a second work roll respectively positioned between a first back up roll and a second back up roll. A plurality of sensors measures and acquires property data of the sheet of material. A model predictive controller manipulates actuators to regulate thickness and flatness. The controller executes automatic gauge control and automatic flatness control as metal sheet is rolled.EFFECT: Sheet metal thickness and flatness deviations from standard requirements are significantly reduced with attendant improved control accuracy as compared to traditional control approaches that use PID based closed loop controls.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to the control of metal rolling mills, and in particular to model-based multivariable predictive control for automatic gauge control and automatic flatness control of 4-hi non-reversing single stand metal rolling mills and the like. [Background technology]

[0002] In cold rolling, a sheet of metal material is reduced in gauge or thickness by passing the metal strip between rolling cylinder surfaces under pressure. A typical single-stand rolling mill feeds the material from an unwinding reel to a rewinding reel. The metal strip is passed between work rolls which are acted upon by respective backup rolls. A force is applied to at least one of the backup rolls. The rolling mill then produces a coil of sheet at a thinner, constant gauge.

[0003] Centerline thickness (gauge) deviation is a key performance indicator (KPI) in metal rolling applications. Many challenges exist in the design of a robust yet high-performance thickness control strategy. Challenges range from the presence of varying time delays between the mill stands and the measurement devices to significant nonlinearities over the operating range. Additionally, the requirement for fast disturbance rejection of measured disturbances such as inlet thickness and inlet speed, or unmeasured internal disturbances such as roll eccentricity, thermal growth, and thermo-mechanical wear of the work rolls, presents an ongoing challenge.

[0004] Current gauge and flatness in aluminum rolling may employ proportional-integral-derivative (PID) based closed loop control. The product optimization time required to achieve acceptable results is relatively long. Gauge and flatness control during acceleration / deceleration conditions of rolling is also not the same as during steady-run conditions. Summary of the Invention

[0005] The present invention is based on the development of a control system utilizing model-based multivariate predictive control for cold rolling mills to improve sheet thickness uniformity to meet or exceed flatness specifications. Compared to conventional control approaches using PID-based closed-loop control, deviations of sheet metal thickness and flatness from standard requirements can be significantly reduced with corresponding improvement in control accuracy. The present invention is suitable for the control of a 4-hi non-reversing single-stand metal rolling mill.

[0006] In one embodiment, the present invention is directed to a system for controlling thickness and flatness of sheet metal in a mill exiting stand that includes a first work roll and a second work roll disposed between a first backup roll and a second backup roll, respectively. The sheet metal moves in a machine direction. A plurality of sensors measure and acquire property data of the material sheet. A model predictive controller (MPC) operates actuators to manage the thickness and flatness. The controller performs automatic gauge control (AGC) and automatic flatness control (AFC) as the metal sheet is rolled. AGC refers to machine direction metal sheet control and AFC refers to cross direction metal sheet control nominally perpendicular to the machine direction.

[0007] In one aspect, the present invention is directed to a controller for controlling thickness and flatness of sheet metal in a mill exiting a roll stand comprising a first work roll and a second work roll positioned between a first backup roll and a second backup roll, respectively, the controller comprising a processor and code stored on a medium readable by the processor for controlling thickness of the sheet metal, the controller comprising: inputs including sheet metal thickness and flatness; A roll stand model, A model-based filter; and a controller output coupled to control a roll gap between the first work roll and the second work roll, roll force, mill speed and / or strip tension to produce the sheet metal.

[0008] In another aspect, the present invention is directed to a method of programming a controller for automatically controlling thickness and flatness of sheet metal produced by a roll stand, the method comprising: generating a model of the roll stand, the model being multivariate and predictive; receiving input including thickness and flatness variations of the sheet metal; generating a filter based on the model; and automatically adjusting parameters of the filter based on the input to control thickness and flatness of the sheet metal produced by the roll stand.

[0009] In a further aspect, the present invention is directed to a controller for controlling thickness and flatness of sheet metal exiting a roll stand having a first work roll and a second work roll, the controller comprising: A processor; a means for measuring the thickness of the sheet metal exiting the roll stand; means for measuring the flatness of the sheet metal exiting the roll stand; a memory device coupled to a processor, receiving input including thickness and flatness variations of the sheet metal; generating a model of a roll stand; Executing a filter based on a model and providing an output coupled to control a roll gap between the first work roll and the second work roll, a roll force, a mill speed, and / or a strip tension. [Brief description of the drawings]

[0010] [Figure 1] 1 shows a sheet metal cold rolling mill system. [Diagram 2] FIG. 1 illustrates a sheet metal cold rolling mill with automatic gauge control. [Diagram 3] FIG. 1 illustrates a sheet metal cold rolling mill with automatic flatness control. [Figure 4] FIG. 1 is a perspective view of a sheet metal rolling mill system. [Diagram 5] FIG. [Figure 6] FIG. 2 is a block diagram showing the operation of a controller. [Figure 7] FIG. 1 is a block diagram of a closed-loop MPC system. [Figure 8] FIG. 1 illustrates a computer system for implementing a controller. [Figure 9] FIG. 1 is a flow diagram of the method of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] Various embodiments of the invention are described in the claims of an apparatus and method for controlling thickness and flatness of sheet metal as produced in a 4-hi stand cold rolling mill (4-hi-mill) taken as the base standard, however, it is understood that the invention is applicable to other cold rolling mill configurations.

[0012] FIG. 1 illustrates a metal rolling mill system 2 that provides thickness control. The mill stand may include four or more rolls stacked and mounted vertically, for example, two smaller diameter work rolls 8, 10, each in contact with a separately mounted larger diameter backup roll 4, 6. An incoming metal strip or workpiece 1 is provided by a payoff stand 12, where the material is reduced to a certain thickness through a plurality of rolls 4, 8, 10, and 6, including an upper backup roll 4, an upper work roll 8, a lower work roll 10, and a lower backup roll 6 (collectively referred to as a 4-hi stand 5). The metal strip 1 may be ferrous and / or non-ferrous, such as steel, aluminum, etc. The metal strip has an entrance tension that is controlled by managing the respective speeds of the uncoiler and coiler. The metal strip 1 passes through a roll gap between a pair of work rolls 8, 10 and exits the roll gap as strip 3 with a strip speed of 10. The average gauge is the average thickness of the strip 3 between the two work rolls 810. Roll slip refers to the difference in speed between the upper work roll 8 and the lower work roll 10. Mill speed is the speed of the main mill motor connected to the work rolls. A C-frame / X-ray thickness sensor 16 measures the thickness of the strip 3 exiting the 4-hi stand before it is collected by the unwind stand 14. An automatic gauge control (AGC) system 18 receives the thickness measurements (from the X-ray sensor 16) and thickness targets (from an operator or otherwise) and sends separate signals for a gap output, a speed output, and a payoff tension output.

[0013] FIG. 2 shows the metal rolling system 22 showing the gap positioning mechanism, where the incoming metal strip 11 fed from the left reel 32 passes through the roll gap of the 4-hi stand 15 including the upper backup roll 24, the upper work roll 28, the lower work roll 30, and the lower backup roll 26. The thickness gauge 40 and the thickness gauge 36 measure the thickness of the inlet strip 11 and the outlet strip 13, respectively, before the outlet strip 13 is collected on the right reel 34. The reel motor current control 44 and the reel motor current control 42 govern the left reel 32 and the right reel 34, respectively. The 4-hi stand includes a gap positioning system 46, which may be mechanical, hydraulic, or a combination of both. The gap positioning system 46 is a system that may vary the work roll gap and includes a pair of screw down motors or hydraulic cylinders, each with a screw down or screw that clamp against the opposing ends of the backup rolls 24, 26, respectively, to apply a roll force (pressure) to the work rolls 28, 30. The delivered thickness of the strip 13, such as at the centerline, is properly controlled to be as close as possible to the target thickness. An automatic gauge control system 38 receives thickness measurements from the strip thickness sensors 40, 36 and sends signals to a hydraulic screw-down cylinder 46.

[0014] The model-based multivariable predictive controller (MPC) of the claimed invention includes a multivariable controller that operates four actuators for automatic gauge control (AGC) that manages (1) roll gap, (2) roll force, (3) inlet tension, and (4) mill speed. The multivariable controller also operates three actuators to manage (5) coolant or oil spray, (6) tilt control (differential gap or differential load), and (7) bending control for automatic flatness control (AFC). Differential gap is the difference between the driven roll gap and the non-driven roll gap. Differential load / force is the difference between the driven roll force and the non-driven roll force. Bend control adjusts the flatness between the (e.g., three) actuators.

[0015] Automatic Gauge Control (AGC)The term "AGC" or "gauge control" refers to the control of thickness in the machine direction in metals. Feedback is provided by one or more fixed point sensors.

[0016] Positioning of the work rolls is effective in heavier passes where the ends of the rolls do not touch as in light foil rolling. Within the operating range of a particular coil, the exit strip thickness is directly related to the roll gap opening. In lighter passes, the ends of the rolls touch, so the roll gap opening cannot be easily changed.

[0017] Mill speed is effective for AGC operation for foil passes where foil film thickness (which decreases as speed increases) can substantially affect strip thickness. Mill speed is set by the mill operator and converted to work roll angular velocity. Payoff tension is most effective for foils and thin sheets. The control mode is selected (e.g. by the mill operator) before starting mill rolling.

[0018] Roll Gap and Force Control: Closed loop control of gauge or thickness via roll gap and force control set points, used in the heavier passes in mills that have a closed loop roll positioning system with roll position and pressure feedback. This control has output to a gap control system (such as a hydraulic system) to regulate roll position and force control in the mill stack.

[0019] Tension Control: Closed loop control of thickness via payoff strip (inlet) tension. This control provides output to the mill drive system and regulates armature current to the payoff motor. The actual strip tension is expressed in specific tension units (e.g. psi, kN / m 2 ) but in some cases the armature current is treated as if it were directly proportional to the absolute tension (in amperes).

[0020] Mill Speed ​​and Roll Speed ​​Control: Output is fed to the mill drive system to regulate the mill speed and control the speed of the mill work rolls 28, 30.

[0021] FIG. 3 shows a metal rolling system 52 including a flatness control, where the metal strip 21 coming from the left reel 62 passes through a 4-hi stand 25 including an upper backup roll 54, an upper work roll 58, a lower work roll 60, and a lower backup roll 56. A thickness gauge 66 measures the thickness of the strip 23 before it is collected on the right reel 64. Reel motor current controls 44, 42 (not shown) manage the drive of the left and right reels 62, 64, respectively. The 4-hi stand is equipped with a gap positioning system 76, which can be mechanical, hydraulic, or a combination of both. The gap positioning system 76 is a system that can vary the work roll gap and includes two screw down motors (not shown), each with a screw down or screw that clamps against the opposing ends of the two backup rolls 54, 56, respectively, to apply a roll force (pressure) to the work rolls 58, 60. The screw position actively adjusts the roll gap. A plurality of nozzles 74 spray coolant or oil onto work roll 58 and a plurality of nozzles 82 spray coolant or oil onto work roll 60. A flatness sensor roll 80 measures the flatness of exit strip 23 and generates a flatness acquisition signal. An automatic flatness control 84 receives and compares inputs including targets 70, such as from a Human-Machine Interface (HMI), and preset conditions 72, such as from an operator (not shown).

[0022] FIG. 4 shows a 4-hi stand 110 with an upper backup roll 112, an upper work roll 116, a lower work roll 118, and a lower backup roll 114. Elongated upper and lower coolant or oil distribution systems 120, 122 are disposed adjacent to the upper work roll 116 and the lower work roll 118, respectively. Each distribution system has multiple nozzles on the inside facing the 4-hi stand to spray coolant or oil along the length of the work rolls. Typically, each distribution system 120, 122 has 20-60 active nozzles along its length, which can provide spray coolant or oil for stable temperature control of the work rolls 116, 118, respectively. In addition, the spray nozzles provide zoned selective cooling along the length of the work rolls 116, 118. The 4-hi stand includes a flatness sensor roll 124 with multiple active rotors, typically ranging from 20-60 active rotors.

[0023] In particular, there are a total number of zones in the shapemeter (including the individual sensors or rotors) and the spray bar distribution system 120, 122 (including the individual spray nozzles). Based on the actual strip width of the sheet actually being rolled in that particular pass, only a certain number of rotors and spray nozzles are covered by the sheet. These rotors and spray zones covered by the rolled strip in a particular pass are referred to as the N active / used rotors / zones with M cooling spray nozzles. Only these active / used zones are used for flatness control. Typically, N is equal to M.

[0024] As an example, if there are 30 rotors (in shapemeter) and spray nozzles in a rolling mill with individual width zone widths of 50 mm each, the maximum width of metal strip that can be rolled on this particular mill is 30 x 50 = 1500 mm. For a pass where the metal strip width is 1200 mm, only 24 zones of the rotors (in shapemeter) and spray nozzles are actively covered. Thus, the first 3 and last 3 zones of the rotors and spray nozzles are outside the strip or are not covered. In this example, there are N active / used rotors / zones with M cooling spray nozzles, which is 24 zones.

[0025] The claimed invention contemplates many embodiments. The system can be cooled or heated. The spray coolant can be oil-based or water-based. The configuration can include multiple zones or rows of spray nozzles. The spray nozzles or valves can be arranged in single, double, or triple overlapping or staggered rows. The spray coolant can include continuous (e.g., constant flow) or pulsed modes. A shapemeter can be included or omitted to provide profile input. Spray zone widths, such as 25 mm or more, can allow for adjustments in impact, spray angle, and droplet size.

[0026] 5 shows a 4-hi stand configuration including an upper backup roll 90, an upper work roll 94, a lower work roll 96, and a lower backup roll 92. The work rolls 94, 96 are driven from a main drive gearbox as the metal strip passes through the roll gap between the pair of work rolls 94, 96. Roll bending jacks 98 and hydraulic cylinders 100 control the roll gap and roll forces using a combination of thermal and mechanical actuators (not shown).

[0027] Automatic Flatness Control (AFC): Automatic flatness control (or shape control) refers to the lateral measurement and control of metal strip flatness. The measurement of flatness (or shape) provides a representation of the variation in length that can occur as the reduction in strip thickness on any portion of the metal varies from one point to another across the sheet. Control of strip flatness is achieved by a combination of thermal and mechanical actuators.

[0028] Spray or Nozzle Control: Cooling sprays are used for fine adjustment of local flatness errors across the strip. This effect is the result of cooling occurring within the work rolls due to heat removal by rolling oil or water sprayed at intervals (e.g., regular or periodic) across the active rolling surfaces on the entry side of the work rolls. The cooling sprays have separate banks of spray nozzles for the upper and lower work rolls. Each of these, in turn, may have one, two, or three nozzles of different sizes.

[0029] Bending: Bending in the mill is controlled by hydraulic actuators present on both sides of the mill. The actuators act between the bearing blocks for the work rolls. When the actuators are moved between the work roll bearing blocks, a positive bending is achieved. This increases the work roll crown, i.e. decreases the distance between the work rolls at the center of the mill for the same edge of the roll gap setting. Negative bending decreases the work roll crown, which increases the distance between the work rolls at the center of the mill for the same edge of the roll gap setting.

[0030] Tilt: Tilt control operates to eliminate any side-to-side differences in shape profile. The transverse (side-to-side, cross) difference in roll gap or rolling force used to control the linear component of strip flatness.

[0031] FIG. 6 shows an apparatus with a model-based multivariable predictive controller in various embodiments of the claimed invention. The observer 144 monitors (e.g., compares) the latest inputs and latest outputs of the mill 142 to detect the presence, size, and consequences of the latest disturbances. The observer 144 then provides the latest state / information to the controller 140. The controller 140 uses the latest model of the function f(x,u,d) and the latest constraints between the specified x minimum and the specified x maximum to achieve the latest goal of maximum total productivity. The controller 140 then provides the latest inputs to the mill 142, as necessary, to compensate for the latest disturbances and achieve the latest output. The feedback continues. For example, the observer 144 provides the latest state / information to confirm or negate the validity of the latest inputs provided by the controller 140.

[0032] 7 illustrates a method including model-based multivariate predictive control (AGC) in various embodiments of the claimed invention. The exit thickness target, inlet thickness, and constraints are all fed to a model-based multivariate predictive control (AGC) 130. The AGC 130 feeds the latest roll gap / roll force and latest mill speed / strip tension to the rolling mill 132. Disturbances may affect the rolling mill 132. The latest exit thickness feedback is compared to the exit thickness target and a new exit thickness error is calculated, which is then fed to the AGC 130 along with the inlet thickness and constraints.

[0033] The MPC of the present invention uses various models for controller design. The models are derived from bump tests. The mill can be bump tested by intentionally disturbing selected actuators and detecting their response, typically with an open-loop control system. The term bump test refers to a procedure in which the mill's operating parameters, such as the mill's actuator settings, are changed and the resulting change in some dependent variable is measured. After the mill reaches steady state or stable operation, certain operating parameters are measured and recorded. A sufficient number of measurements over a length of time are made to provide representative data of the response to the bump test.

[0034] For example, bump testing in roll gap / position may change the sheet thickness from which the response / relationship between these two variables for that particular system / field device can be derived. Similarly, bump testing in spray or roll bending will affect the sheet flatness.

[0035] MPC for automatic gauge control This section describes a model-based multivariable predictive controller MPC for automatic gauge control (AGC). The following models are used in the controller design according to an embodiment of the invention: Models for roll gap, total load (rolling force), strip tension, and mill speed are derived from and tuned to bump test data.

[0036]

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[0037] The transfer function for a pure time delay is e -qs where q is the time delay. Some control system design techniques require rational transfer functions for the dynamic behavior, in which case a Padé approximation for the dead time may be used.

[0038] A first-order approximation has an inverse response with a single positive zero. A second-order approximation has a double inverse response with two positive complex conjugate zeros of the numerator transfer function.

[0039] Most ordinary differential equation numerical integrators require pure differential equations without time delays. For systems of differential equations with time delays, Pade approximations can be used to convert them into delay-free differential equations, so that they can be integrated numerically.

[0040] First, the delays are approximated by second-order Padé equations to obtain a rational transfer function. This continuous-time transfer function is then converted to a discrete-time transfer function and then to a state-space model of the form

[0041]

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[0042]

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[0043] Since the Kalman filter is an optimal filter, we want the Kalman gain that minimizes the estimated variance. To minimize the estimated variance, we minimize the main diagonal of the covariance matrix (from top left to bottom right).

[0044] Based on this predictive model, a state feedback MPC controller is designed. First, the model is expressed in differential form: x(k)u(k)d(k) and e f Instead of using (k) as the state, input, disturbance, and innovation, respectively, Δx(k+1)=x(k+1)-x(k), Δu(k)=u(k)-u(k-1), Δd(k)=d(k)-d(k-1) and Δe f (k)=e f (k)-e f We use (k-1) as the state, input, disturbance, and innovation, respectively. Using this transformation, our model becomes:

[0045]

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[0046]

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[0047] MPC uses this model for prediction of the states. There are two important controller parameters here: Prediction horizon (Np) specifies the number of future time instances the controller will make predictions for. The larger the prediction horizon, the better the closed-loop results. However, this results in a larger computation time. Similarly, control horizon (Nc) specifies the number of future inputs used to optimize the controller performance criteria. Typically, Nc is much smaller than Np. These two parameters, along with the starting state x(ki), the disturbances d(ki), and the actual output y act Using (ki) and (ki), the output prediction can be expressed as follows: Y p =Fx(ki)+ΦΔU+ΓΔd(ki)+Γ e Δe f (ki) (11) During the ceremony,

[0048]

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[0049]

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[0050]

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[0051] Consider the MPC objective function J as a combination of the control error and the control action. Specifically, it is as follows.

[0052]

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[0053]

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[0054] The MPC minimizes this objective function subject to the constraints to calculate the input move vector ΔU. The constant term can be ignored as it does not affect the optimal solution. Constraints can be placed on the actual inputs as well as the input changes. Since the receding horizontal MPC only uses the first input u(ki), the other (Nc-1) future input values ​​are discarded. Hence, only the first move can contain the constraints. This reduces the computational effort. Hence, a total of four constraints are required, namely the min and max input value constraints (u min ≦u(ki≦u max ), min and max input change constraints (Δu min ≦Δu(ki)≦Δu max ) At any time instance k i , these can be expressed as

[0055]

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[0056] Note that the first two constraints depend on the previous input values ​​and therefore update as we move along in time. These constraints can be written in the following matrix form: A con ΔU≦b (24)

[0057] Thus, at any time instance k i , the MPC solves the following constrained optimization problem:

[0058]

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[0059] MPC is a state feedback controller. However, it is not necessary that all of these states are measurable. In our case, fictitious and therefore unmeasurable states are introduced due to the Padé approximation of the delays. Therefore, a state estimator (also known as an observer) is needed that reconstructs these states from the output measurements. Here, we used a Kalman filter based observer. The observer model can be constructed from the process model as shown below: x^(k+1)=A p x^(k)+B p u(k)+B d d(k)+K ob (y act (k)-C p x^(k)) (26) where x^(k+1) is the estimate of the actual state x(k+1). It can be seen that the first part of the observer model is the same as the process model given in equation (7). The second part is the actual measurements y that are needed to converge these estimates to the actual state values. act (k) is the feedback correction term based on the observer gain K ob is selected based on the stationary Kalman filter formula. Specifically, the variance of the i-th disturbance is σ d (i) and the variance of the jth output is σ y In the case of (j), the following equation is obtained:

[0060]

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[0061] Observer Gain K ob =L is calculated by solving the following implicit equation (also known as the Riccatti equation):

[0062]

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[0063] The Riccatti equation is an interesting first-order nonlinear ordinary differential equation because it is related to a second-order homogeneous ordinary differential equation.

[0064] The above describes the design of a multivariable model-based controller MPC for automatic gauge control (AGC). The controller can use all four actuators (roll gap, roll force, inlet tension, and mill speed) simultaneously to achieve better control. The AGC MPC using disturbance measurements improves the model predictions and therefore results in better thickness control.

[0065] MPC for automatic flatness control The MPC controller for AFC is derived along similar lines. Consider the sheet has N active / used rotors / zones. Hence, there are N cooling spray nozzles. There are a total of (N+2) actuators. For each spray nozzle there is a target value for the differential gap (tilt control), difference between positive and negative bow PV (bow control) and spray duty cycle. To model the dynamic response of the flatness profile, the instantaneous flatness profile is decomposed into linear and quadratic components. The corresponding tilt model is shown below:

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[0069] Mill data is specified, e.g. the number of rotors used (active or covered by sheet) as well as the duty cycle in seconds. The former sets the problem dimension, while the latter is used as the controller execution frequency. The desired / target shape can be entered in terms of linear and quadratic components. For example, for a flat profile, these components are set to 0. The starting / initial profile (Shape-I value) needs to be considered from the actual data. This is called the raw data. This is converted to 0-mean data, which is compared to the target shape (which is also 0-mean) to calculate the overall control effort required from the AFC system. This required control effort is then decomposed into linear and quadratic components. In the default settings, the linear component control is addressed via tilt control, the quadratic component control is addressed via bend control, and the remaining effort is managed via nozzle control. However, there are two settings to modify this. There is an option to turn off the tilt and / or bend control actions completely. In this setting, that part of the control effort is transferred to the nozzle control. Second, each of the tilt, bend or nozzle control efforts has a lower limit (deadband) and an upper limit (clamping). Based on these, the final tilt, bend and nozzle targets (for each nozzle) are calculated and the set points R s It is important to note that the MPC calculations are only performed once during the duty cycle, and the inputs are held constant throughout this time.

[0070] The process of the present invention may be incorporated into plants such as cold rolling mill systems, including those having automatic gauge and flatness controls and hydraulic gap control (HGC) controllers, to improve the accuracy of thickness and flatness of the sheets produced. The mill may include outputs from a controller. The controller may include inputs from sensors and filters, which may include various models, by integrating the method of the present invention into a controller environment, such as a MATLAB script or another suitable program.

[0071] FIG. 8 illustrates one embodiment of the claimed invention including an internal mill model 800 of a material rolling process as follows.

[0072] In block 810, the mill model estimates process parameters during rolling by taking measurements.

[0073] In block 820, the mill model emulates the rolling process and predicts the thickness and flatness of the material in the roll gap.

[0074] In block 830, the mill model determines optimal controller outputs, called manipulated variables, that are independent of dead times and dynamic delays in the process.

[0075] In block 840, the mill model uses the process model to calculate manipulated variable profiles that optimize the predicted performance objectives over a future time interval, subject to the constraints.

[0076] FIG. 9 is a block schematic diagram of a computer system 150 for implementing an apparatus comprising a model-based multivariable predictive controller and method according to an exemplary embodiment. Not all components need to be used in various embodiments. One exemplary computing device in the form of a computer system 150 can include a processing unit 152, a memory 154, a removable storage 162, and a non-removable storage 164. Although an exemplary computing device is illustrated and described as a computer system 150, 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. Devices such as smartphones, tablets, and smartwatches are generally collectively referred to as mobile devices. Furthermore, although various data storage elements are illustrated as part of the computer system 150, the storage may additionally or alternatively include cloud-based storage accessible via a network such as the Internet.

[0077] Memory 154 may include volatile memory 158 and non-volatile memory 160. Computer system 150 may include or have access to a computing environment that includes a variety of computer-readable media, such as volatile memory 158 and non-volatile memory 160, removable storage 162 and non-removable storage 164. Computer storage may include random access memory (RAM), read only memory (ROM), erasable programmable read-only memory (EPROM) and electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disc read-only memory (CD ROM), Digital Versatile Disk (DVD) or other optical disk storage, magnetic cassettes, magnetic tapes, magnetic disk storage, or other magnetic storage devices capable of storing computer-readable instructions for performing the functions described herein.

[0078] The computer system 150 includes or can access a computing environment including an input 168, an output 170, and a communication interface 164. The output 170 can include a display device such as a touch screen that can also function as an input device. The input 168 can include one or more of a touch screen, a touch pad, a mouse, a keyboard, a camera, one or more device-specific buttons, one or more sensors integrated within the computer system 150 or coupled via a wired or wireless data connection, and other input devices 168. The computer system 150 can operate in a networked environment using communication connections to connect to one or more remote computers, such as database servers including cloud-based servers and storage. The remote computers can include personal computers (PCs), servers, routers, network PCs, peer devices or other common network nodes, and the like. The communication connections may include a Local Area Network (LAN), a Wide Area Network (WAN), a cellular, WiFi, Bluetooth, or other networks.

[0079] Computer-readable instructions stored on a computer-readable storage device are executable by the processing unit 152 of the computer system 150. Hard drives, CD-ROMs, and RAM are some examples of articles that include non-transitory computer-readable media, such as storage devices. The terms computer-readable media and storage devices do not include carrier waves. For example, the computer program 156 can be used to cause the processing unit 152 to perform one or more of the methods or methods described herein.

[0080] The foregoing has described the principles, preferred embodiments, and modes of operation of the present invention. However, the invention should not be construed as limited to the particular embodiments discussed. Thus, the above-described embodiments are to be considered as illustrative rather than restrictive, and it is to be understood that various modifications may be made thereto by those skilled in the art without departing from the scope of the present invention as defined by the following claims.

Claims

1. 1. A controller for controlling thickness and flatness of sheet metal in a mill exiting a roll stand including a first work roll and a second work roll positioned between a first backup roll and a second backup roll, respectively, the controller comprising a processor and code stored on a medium readable by the processor for controlling the thickness of the sheet metal, the controller comprising: inputs including the thickness and the flatness of the sheet metal; A model of the roll stand; a filter based on the model; and a controller output coupled to control a girdle gap between the first work roll and the second work roll, roll force, mill speed, and / or strip tension to produce the sheet metal.

2. The controller of claim 1 , wherein the model includes roll gap, roll force, inlet tension, mill speed, spray parameters, tilt control, and bending control.

3. 1. A method of programming a controller for automatically controlling thickness and flatness of sheet metal produced by a roll stand, comprising: generating a model of the roll stand, the model being multivariate and predictive; receiving input including variations in the thickness and the flatness of the sheet metal; generating a filter based on the model; and automatically adjusting parameters of the filter based on the input to control the thickness and the flatness of the sheet metal produced by the roll stand.

4. 1. A controller for controlling thickness and flatness of sheet metal exiting a roll stand having a first work roll and a second work roll, comprising: A processor; means for measuring the thickness of the sheet metal exiting the roll stand; means for measuring the flatness of the sheet metal exiting the roll stand; a memory device coupled to the processor, receiving an input including a variation in the thickness and the flatness of the sheet metal; generating a model of the roll stand; executing a filter based on the model; and providing an output coupled to control a roll gap between the first work roll and the second work roll, a roll force, a mill speed, and / or a strip tension.

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