Model-based multivariable predictive control for metal rolling mills

Abstract

A control system employs model-based multivariable predictive control for cold rolling mills to improve plate thickness uniformity to meet or exceed flatness specifications. Compared with a traditional control method using PID (Proportion Integration Differentiation)-based closed-loop control, the deviation between the thickness and the flatness of the metal plate and the standard requirement is obviously reduced, and meanwhile, the control precision is improved. The control system is particularly suitable for controlling the four-roller irreversible single-base metal rolling mill. The rolling mill base has a first working roll and a second working roll positioned between a first support roll and a second support roll, respectively. The plurality of sensors measure and acquire characteristic data of the material plate. A model predictive controller manipulates the actuators to adjust thickness and flatness. When rolling a metal sheet, the controller performs automatic specification control (i.e., machine direction metal control) and automatic flatness control (i.e., lateral metal sheet control).

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, for example, for a four-high irreversible single-bed metal rolling mill. Background Art

[0002] In cold rolling, the gauge or thickness of a sheet of metal material is reduced by passing the metal strip between the surfaces of rolling cylinders under applied pressure. A typical single-bed rolling mill feeds the material from an unwinding reel to a rewinding reel. The metal strip passes between working rolls, which are acted upon by corresponding backup rolls. Force is applied to at least one of the backup rolls. The rolling mill then produces a coil of thinner and constant gauge.

[0003] In metal rolling applications, centerline thickness (gauge) deviation is an important key performance indicator. There are many challenges in designing a robust and high-performance thickness control strategy. Challenges include different time delays between the mill base and the measurement equipment, as well as significant nonlinearity across the entire operating range. In addition, the requirement for fast disturbance rejection of measured disturbances (such as entry thickness and entry speed) or unmeasured internal disturbances (such as roll eccentricity, thermal expansion and thermo-mechanical wear of the work rolls) poses a constant challenge.

[0004] Current gauge and flatness control in aluminum rolling can be achieved using a proportional-integral-derivative (PID) based closed loop control. The product optimization time required to achieve acceptable results is relatively high. Gauge and flatness control during the acceleration / deceleration state of the rolling is different from gauge and flatness control during the steady state of operation. Summary of the invention

[0005] The present invention is based on the development of a control system that uses model-based multivariable predictive control for cold rolling mills to improve plate thickness uniformity to meet or exceed flatness specifications. Compared to conventional control methods using PID-based closed-loop control, deviations in metal plate thickness and flatness from standard requirements can be significantly reduced, while control accuracy is improved. The present invention is applicable to the control of a four-roll irreversible single-base metal rolling mill.

[0006] In one embodiment, the present invention relates to a system for controlling the thickness and flatness of a metal sheet in a rolling mill leaving a base, the base including a first working roll and a second working roll positioned between a first support roll and a second support roll, respectively. The metal sheet moves in a machine direction. A plurality of sensors measure and acquire characteristic data of the material sheet. A model predictive controller (MPC) manipulates an actuator to adjust the thickness and flatness. The controller performs automatic gauge control (AGC) and automatic flatness control (AFC) when rolling the metal sheet. AGC refers to metal sheet control in the machine direction, and AFC refers to transverse metal sheet control, which is nominally perpendicular to the machine direction.

[0007] In one aspect, the invention relates to a controller for controlling the thickness and flatness of a metal sheet in a rolling mill exiting a roll bed, the roll bed comprising first and second work rolls positioned between first and second support rolls, respectively, the controller comprising a processor and code stored on a medium readable by the processor to control the thickness of the metal sheet, the controller comprising:

[0008] An input end, the input end including the thickness and flatness of the metal plate;

[0009] Model of roller base;

[0010] a filter based on the model; and

[0011] A controller output is coupled to control roll force, mill speed, strip tension, and / or a roll gap between a first work roll and a second work roll to produce metal sheet.

[0012] In another aspect, the invention relates to a method of programming a controller for automatically controlling the thickness and flatness of a metal sheet produced by a roller bed, the method comprising:

[0013] Producing a model of the roll base that is multivariate and predictive;

[0014] receiving input including a variation in thickness and flatness of a metal sheet;

[0015] generating a filter based on the model; and

[0016] The parameters of this filter are automatically adjusted based on the input to control the thickness and flatness of the metal sheet produced by the roller bed.

[0017] In a further aspect, the invention relates to a controller for controlling the thickness and flatness of a metal sheet exiting a roll bed having first and second work rolls, the controller comprising:

[0018] processor;

[0019] means for determining the thickness of the metal sheet leaving the roller bed;

[0020] A device for determining the flatness of the metal sheet leaving the roller bed;

[0021] a memory device coupled to the processor and comprising a readable program executable by the processor to:

[0022] receiving input including a variation in thickness and flatness of a metal sheet;

[0023] Generate a model of the roller base;

[0024] Based on the model, performing a filter; and

[0025] An output is provided that is coupled to control roll force, mill speed, strip tension, and / or a roll gap between the first work roll and the second work roll. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 A sheet metal cold rolling mill system is shown;

[0027] Figure 2 A sheet metal cold rolling mill with automatic gauge control is shown;

[0028] Figure 3 A sheet metal cold rolling mill with automatic flatness control is shown;

[0029] Figure 4 is a perspective view of a sheet metal rolling mill system;

[0030] Figure 5 is a cross-sectional view of a rolling mill;

[0031] Figure 6 is a block diagram illustrating the operation of the controller;

[0032] Figure 7 It is the block diagram of the closed-loop MPC system;

[0033] Figure 8 A computer system implementing the controller is shown; and

[0034] Fig. 9 A flow chart showing the method of the present invention is shown. DETAILED DESCRIPTION

[0035] The present invention will describe various embodiments of apparatus and methods for a metal rolling mill system for controlling the thickness and flatness of metal sheets, such as those produced in a four-roller cold rolling mill (four-roller mill) as a benchmark. However, it should be understood that the present invention is applicable to other cold rolling mill arrangements.

[0036] Figure 1 A metal rolling mill system 2 providing thickness control is shown. The rolling mill base may include four or more vertically stacked and mounted rolls, such as two smaller diameter work rolls 8, 10, each of which is in contact with a larger diameter support roll 4, 6 mounted separately. The incoming metal strip or workpiece 1 is supplied by a material unwinding (pay-off) base 12, which is reduced to a certain thickness by a plurality of rolls 4, 8, 10 and 6, including a top support roll 4, a top work roll 8, a bottom work roll 10 and a bottom support roll 6 (collectively referred to as a four-roll base 5). The metal strip 1 may be ferrous and / or non-ferrous, such as steel, aluminum, etc. The metal strip has an entry tension that is controlled by adjusting the respective speeds of the unwinder and the coiler. The metal strip 1 passes through the roll gap between a pair of work rolls 8, 10 and leaves the roll gap as a strip 3 at a certain strip speed. The average gauge is the average thickness of the strip 3 between the two work rolls 8, 10. Roll slip refers to the speed difference between the top work roll 8 and the bottom work roll 10. Mill speed is the speed of the main mill motor connected to the work rolls. The C-frame / X-ray thickness sensor 16 measures the thickness of the strip 3 as it exits the four-axis bed before being collected by the rewind bed 14. The automatic gauge control (AGC) system 18 receives the thickness measurement (from the x-ray sensor 16) and the thickness target (such as from an operator) and transmits separate gap output signals, velocity output signals, and pay-off tension output signals.

[0037] Figure 2 A metal rolling system 22 is depicted, showing a gap positioning mechanism, wherein an incoming metal strip 11 supplied from a left mandrel 32 passes through the roll gap of a four-roller bed 15, which includes a top support roll 24, a top work roll 28, a bottom work roll 30, and a bottom support roll 26. Thickness gauges 40 and 36 measure the thickness of the incoming strip 11 and the exiting strip 13, respectively, and then collect the exiting strip 13 into the right mandrel 34. Mandrel motor current control 44 and mandrel motor current control 42 adjust the left mandrel 32 and the right mandrel 34, respectively. The four-axis bed is equipped with a gap positioning system 46, which can be mechanical, hydraulic, or a combination of both. The gap positioning system 46 that can change the gap of the work rolls includes a pair of hold-down mechanism motors or hydraulic cylinders, each of which is equipped with a hold-down mechanism or screw that clamps the opposite ends of the support rolls 24, 26, respectively, thereby applying a roll force (pressure) to the work rolls 28, 30. The output thickness of the strip 13 , such as at the centerline, is adjusted to be as close to the target thickness as possible. The automatic gauge control system 38 receives thickness measurements from the strip thickness sensors 40 , 36 and transmits signals to the hydraulic hold-down cylinder 46 .

[0038] The model-based multivariable predictive controller (MPC) of the present invention includes a multivariable controller that manipulates four actuators for automatic gauge control (AGC) to adjust: (1) roll gap, (2) roll force, (3) inlet tension, and (4) mill speed. The multivariable controller also manipulates three actuators to adjust: (5) coolant or oil spray, (6) tilt control (differential gap or differential load), and (7) bend control for automatic flatness control (AFC). The differential gap is the difference between the drive side and non-drive side roll gaps. The differential load / force is the difference between the drive side and non-drive side roll forces. The bend control adjusts the flatness between (e.g., three) actuators.

[0039] Automatic Gauge Control (AGC) The term "AGC" or "gauge control" refers to the control of the machine direction thickness of the metal. Feedback is supplied by one or more fixed point sensors.

[0040] Work roll positioning is effective in heavier passes where the ends of the rolls are not in contact, as is the case in light foil rolling. Within the working range for a particular coil, the exit strip thickness is directly related to the roll gap opening. For lighter passes, the roll gap opening cannot be easily changed because the ends of the rolls are in contact.

[0041] Mill speed is effective for AGC actuation of foil passes, where foil film thickness (which decreases with increasing speed) can significantly affect strip thickness. Mill speed is set by the mill operator and is converted to work roll angular velocity. Pay-off tension is most effective for foil and light plate. The control mode is selected before starting mill rolling (such as by the mill operator).

[0042] Roll Gap and Force Control: Closed loop control of gauge or thickness via roll gap and pressure control set points for heavier passes in mills with closed loop roll positioning systems (with roll position and pressure feedback). This control outputs to a gap control system (such as a hydraulic system) to adjust roll position and force control in the mill train.

[0043] Tension Control: Closed loop control of thickness via pay-off strip (entry) tension. This control outputs to the mill drive system to adjust the armature current to compensate the motor. Actual strip tension can be expressed in specific tension units (e.g. psi, kN / m 2 ), but sometimes the armature current is considered to be proportional to the absolute tension (amperes).

[0044] Mill Speed ​​and Roll Speed ​​Control: Output is supplied to the mill drive system to adjust the mill speed and control the speed of the working rolls 28, 30 of the mill.

[0045] Figure 3A metal rolling system 52 including flatness control is depicted, wherein a metal strip 21 entering from a left mandrel 62 passes through a four-roller base 25, the four-axis base including a top support roll 54, a top work roll 58, a bottom work roll 60, and a bottom support roll 56. A thickness gauge 66 measures the thickness of the strip 23 before being collected on the right mandrel 64. Mandrel motor current controllers 44, 42 (not shown) regulate the drive of the left mandrel 62 and the right mandrel 64, respectively. The four-axis base is equipped with a gap positioning system 76, which can be mechanical, hydraulic, or a combination of both. The gap positioning system 76 that can change the gap between the working rolls includes two hold-down mechanism motors (not shown), each of which is equipped with a hold-down mechanism or screw that clamps the opposite ends of the two support rolls 54, 56, respectively, thereby applying a roll force (pressure) to the working rolls 58, 60. The screw position effectively adjusts the roll gap. A plurality of nozzles 74 spray coolant or oil onto the work roll 58, and a plurality of nozzles 82 spray coolant or oil onto the work roll 60. A flatness sensor roll 80 measures the flatness of the exit strip 23 and generates a flatness acquisition signal. An automatic flatness control 84 receives and compares inputs including a target 70 such as from a human machine interface (HMI) and preset conditions 72 such as from an operator (not shown).

[0046] Figure 4 A four-roll base 110 is shown, which includes a top support roll 112, a top work roll 116, a bottom work roll 118, and a bottom support roll 114. Elongated upper and lower coolant or oil distribution systems 120, 122 are located adjacent to the top work roll 116 and the bottom work roll 118, respectively. Each distribution system has a plurality of nozzles on the inner side facing the four-roll base to spray coolant or oil along the length of the work rolls. Typically, each distribution system 120, 122 has 20 to 60 effective 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 four-roll base is equipped with a flatness sensor roll 124, which includes a plurality of effective rotors, which are typically in the range of 20 to 60 effective rotors.

[0047] In particular, there is a total number of zones in the shape measuring instrument (including individual sensors or rotors) and the spray bar distribution system 120, 122 (including individual spray nozzles). Based on the actual strip width of the plate actually rolled at this particular pass, the plate only covers a certain number of rotors and spray nozzles. These rotors and spray shot areas covered by the rolled strip in a particular pass are referred to as the N active / used rotors / areas with M cooling spray nozzles. Only these active / used areas are used for flatness control. Typically, N is equal to M.

[0048] For example, if there are 30 rotors (in the form meter) and spray nozzles, each with a separate width zone of 50 mm in the rolling mill, the maximum width of the metal strip that can be rolled in this particular mill is 30×50=1500 mm. For a pass with a metal strip width of 1200 mm, only 24 rotor zones (in the form meter) and spray nozzles are effectively covered. Therefore, the first three and last three zones of the rotor and spray nozzles are outside the strip or not covered. In this example, the N active / used rotors / zones with M cooling spray nozzles are 24 zones.

[0049] The present invention contemplates many embodiments. The system can cool or heat. The spray coolant can be oil-based or water-based. The configuration can include multiple zones or multiple rows of spray nozzles. The spray nozzles or valves can be arranged in a single row, double row or triple row overlapping or staggered. The spray coolant can include a continuous (such as constant flow) mode or a pulse mode. A shape meter can be included or excluded to provide a profile input. The spray zone width, such as 25 mm or greater, can allow adjustment of impact, spray angle and droplet size.

[0050] Figure 5 An arrangement 110 of a four roll stand is shown, which includes 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 and 96 are driven by a main drive gearbox as the metal strip passes through the roll gap between a pair of work rolls 94, 96. Roll bending jacks 98 and hydraulic cylinders 100 are responsible for the roll gap and roll force using a combination of thermal actuators and mechanical actuators (not shown).

[0051] Automatic Flatness Control (AFC) : Automated flatness (or shape control) refers to the lateral measurement and control of the flatness of metal strip. The measurement of flatness (or shape) provides an indication of the length variation that may result when the strip thickness reduction on any portion of the metal varies from one point to another across the plate. Control of strip flatness is accomplished by a combination of thermal and mechanical actuators.

[0052] Spray or Nozzle Control: Cooling spray is used to fine-tune local flatness errors across the strip. This effect is the result of cooling that occurs in the work rolls by spraying rolling oil or water at (e.g., regular or periodic) intervals on the effective rolling surface on the entry side of the work rolls to remove heat. The cooling spray will have separate spray nozzle groups for the top and bottom work rolls. Each of these spray nozzle groups may in turn have one, two or three nozzles of different sizes.

[0053] Bending: Bending in the mill is controlled by hydraulic actuators, which are located on both sides of the mill. The actuators act between the bearing blocks of the work rolls. When the actuators move between the bearing blocks of the work rolls, positive bending is achieved. This increases the crown of the work rolls, that is, for the same roll gap edge setting, the distance between the work rolls at the center of the mill is reduced. Negative bending reduces the crown of the work rolls, which increases the distance between the work rolls at the center of the mill for the same roll gap edge setting.

[0054] Tilt: Tilt control is used to eliminate any side-to-side differences in shape profile. It is used to control the lateral (side-to-side, cross-directional) differences in roll gap or roll load that is the linear component of strip flatness.

[0055] Figure 6 An apparatus including a model-based multivariable predictive controller in various embodiments of the present invention is depicted. An observer 144 monitors (such as compares) the latest input and the latest output of the rolling mill 142 to detect the presence, magnitude, and consequences of the latest disturbance. 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 target of maximum total productivity. The controller 140 then supplies the latest input to the rolling mill 142 to compensate for the latest disturbance so as to achieve the latest output as needed. Feedback continues. For example, the observer 144 supplies the latest state / information to confirm or reject the validity of the latest input supplied by the controller 140.

[0056] Figure 7 Methods including model-based multivariable predictive control (AGC) in various embodiments of the present invention are depicted. The exit thickness target, entry thickness, and constraints are all supplied to a model-based multivariable predictive control (AGC) 130. The AGC 130 supplies the latest roll gap / roll force and the 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 later supplied to the AGC 130 along with the entry thickness and constraints.

[0057] The MPC of the present invention employs various models for controller design. These models are derived from bump testing. A rolling mill may be bump tested by intentionally perturbing selected actuators and detecting their responses, typically with the control system in an open loop. The term bump testing refers to a procedure by which operating parameters on a rolling mill, such as the mill's actuator setpoints, are changed and the resulting changes in certain dependent variables are measured. After the mill reaches steady state or stable operation, certain operating parameters are measured and recorded. A sufficient number of measurements are made over a period of time to provide representative data on the response to the bump test.

[0058] For example, a bump test in roll gap / position can vary the board thickness, with which the response / relationship between these two variables can be derived for that particular system / field device. Similarly, bump testing in jetting or roll bending will affect the flatness of the board.

[0059] MPC for automatic specification control

[0060] This section describes a model-based multivariable predictive controller MPC for automatic gauge control (AGC). The following model is used for controller design according to an embodiment of the present invention. Models for roll gap, total load (roll force), strip tension, and mill speed are derived from and adjusted based on crash test data.

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067] The transfer function for a pure time delay is e – qs, where q is the time delay. Some control system design techniques require a rational transfer function for the dynamic behavior, in which case the Padé approximation of the dead time can be used.

[0068] The first-order approximation has an inverse response with a single positive zero. The second-order approximation has a double inverse response with two positive complex conjugate zeros of the numerator transfer function.

[0069] Most ordinary differential equation numerical integrators require pure differential equations without time delays. In systems of differential equations with time delays, the Padé approximation can be used to convert these differential equations into delay-free differential equations, making them amenable to numerical integration.

[0070] First, the delay is approximated using the second-order Pade formula, which easily yields a rational transfer function. This continuous-time transfer function is then converted to a discrete-time transfer function, and subsequently to a state-space model of the following form:

[0071] x(k+1)=Apx(k)+Bpu(k)+Bdd(k)

[0072] y(k)=Cpx(k)(7)

[0073] Where k is the discrete time sampling instant, u(k) is the vector of manipulated inputs, and d(k) is the vector of disturbance inputs. The actual mill response may not follow the model exactly. To incorporate this plant / model mismatch, an innovation deviation approach is used. The innovation signal (e(k) is calculated as the difference between the actual output and the predicted output. A filtered version of this innovation signal (ef(k)) is used to correct the prediction equation as follows.

[0074] x(k+1)=Apx(k)+Bpu(k)+Bdd(k)+Lef(k)

[0075] y(k+1)=Cpx(k+1)+ef(k)

[0076] e(k)=yact(k)-Cpx(k)

[0077] ef(k)=Φeef(k-1)+(I-Φe)e(k)(8)

[0078] where yact(k) is the actual output, L is the Kalman predictor gain, and Φe is the filter constant matrix (a diagonal matrix with each value between 0 and 1). I is the identity matrix.

[0079] The Kalman filter is an optimal filter, so we want to minimize the Kalman gain of the estimated variance. To minimize the estimated variance, we minimize the main diagonal of the covariance matrix (from top left to bottom right).

[0080] Based on this prediction model, a state feedback MPC controller is designed. First, the model is expressed in differential form. Instead of using x(k), u(k), d(k), and ef(k) as 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 Δef(k)=ef(k)-ef(k-1) are used as state, input, disturbance, and innovation, respectively. Through this transformation, the model becomes:

[0081]

[0082]

[0083] It is an augmented state system of the form (7) and can be expressed as follows:

[0084]

[0085] MPC will use this model to make state predictions. There are two important controller parameters here. The prediction horizon (Np) specifies the number of future time instances for which the controller makes predictions. The larger the prediction horizon, the better the closed-loop results. However, this will result in greater computation time. Similarly, the control horizon (Nc) specifies the number of future inputs used to optimize the controller performance criterion. Typically, Nc is much smaller than Np. Using these two parameters and the starting state x(ki), the disturbance d(ki), and the actual output y act (ki), the output prediction can be expressed as follows:

[0086] Y p =Fx(ki)+ΦΔU+ΓΔd(ki)+Γ e Δe f (ki) (11)

[0087] in,

[0088] Y p =[Y(ki+1|ki) Y(ki+2|ki)…Y(li+Np|ki)] T (12)

[0089] is the prediction of the future Np output based on the current state X(ki).

[0090] ΔU=[Δu(ki) Δu(ki+1)…Δu(ki+Nc-1)] T (13)

[0091] is the next planned Nc control action. Therefore,

[0092]

[0093]

[0094]

[0095]

[0096] The MPC objective function J is regarded as a combination of control error and control action. Specifically,

[0097] J=(R s -Y p ) T (R s -Y p )+ΔU T R ˉ ΔU (18)

[0098] Where R s is the set point trajectory along the prediction horizon, and R ˉ is a vector capturing weights of input variation and is a tuning parameter. ˉ A high value for the elements in implies a strong penalty for input movement, and thus the input will change gradually when moving from one moment to the next. On the other hand, if R ˉ →0, the controller only focuses on the error. p Substituting in, we can express J in the following quadratic form:

[0099]

[0100] The MPC will minimize this objective function under the constraints and 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 input as well as the input change. Since the backward range MPC only uses the first input u(ki), the other future (Nc-1) input values ​​will be discarded. Therefore, constraints can only be included in the first step. This reduces the computational effort. Therefore, there are four constraints in total; minimum and maximum input value constraints (umin≤u(ki)≤umax) and minimum and maximum output change constraints (umin≤Δu(ki)≤Δumax). At any time instance ki, these can be expressed as follows:

[0101] -Δu(ki)≤-umin+u(ki-1)(20)

[0102] Δu(ki)≤umax-u(ki-1)(21)

[0103] -Δu(ki)≤-Δumin(22)

[0104] Δu(ki)≤Δumax(23)

[0105] Note that the first two constraints depend on previous input values ​​and are therefore updated over time. These constraints can be written in the following matrix form:

[0106] AconΔU≤b(24)

[0107] Therefore, at any time instance ki, MPC will solve the following constrained optimization problem:

[0108]

[0109] Subject to AconΔU≤b(25)

[0110] This is a quadratic programming problem. It can be solved using Hildreth's quadratic programming algorithm. It can be noted that the optimal solution ΔUopt depends on the current state x(ki), the disturbance measurement d(ki), and the innovation signal ef(ki). In this optimal solution, only the first entry Δuopt(ki) will be sent to the process. The controller then waits until the next time instance (ki+1) and updates the state feedback vector x(ki+1), the disturbance d(ki+1), and the actual output y from the system based on the updated state feedback vector x(ki+1), the disturbance d(ki+1), and the actual output y from the system. act (ki+1) Repeat all these calculations.

[0111] MPC is a state feedback controller. However, not all of these states are measurable. For our case, due to the delayed Pade approximation, imaginary and therefore unmeasurable states are introduced. Therefore, a state estimator (also called observer) is needed to reconstruct these states based on the output measurements. Here, an observer based on a Kalman filter is used. This observer model can be constructed from the process model as follows:

[0112] 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)

[0113] where x^(k+1) is an 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 based on the actual measurement y act The feedback correction term (k) is needed to converge these estimates to the actual state value. ob is selected based on the stationary Kalman filter formula. Specifically, if the variance in the i-th disturbance is σd (i), the variance in the jth output is σ y (j), then:

[0114]

[0115]

[0116]

[0117] Observer gain K ob =L is calculated by solving the following implicit equation (also called the Riccati equation).

[0118]

[0119]

[0120] Where P represents the covariance of the estimation error.

[0121] The Riccati equation is an interesting first-order nonlinear ordinary differential equation because it is related to a second-order ordinary homogeneous differential equation.

[0122] The design of a multivariable model-based controller MPC for automatic gauge control (AGC) is described above. The controller is able to use all four actuators (roll gap, roll force, inlet tension and mill speed) simultaneously to achieve better control. AGC MPC using disturbance measurements improves model predictions and thus achieves better thickness control.

[0123] MPC for automatic flatness control

[0124] The MPC controller for AFC is derived along similar lines. Consider a board with N active / used rotors / areas. Hence, there will be N cooling spray nozzles. There will be a total of (N+2) actuators; the target value of the differential gap (tilt control), the difference between positive and negative bend PV (bend control), and the spray duty cycle for each spray nozzle. In order to model the dynamic response of the flatness curve, the instantaneous flatness curve is decomposed into linear and quadratic components. The corresponding tilt model is given below.

[0125]

[0126] Here, the output a1 represents the deviation of the linear component coefficient, and u t represents the deviation of the differential gap. Along similar lines, the bending model is given as follows.

[0127]

[0128] Here, the output a2 represents the deviation of the quadratic component coefficient, and u b The deviation represents the difference between positive and negative bend PVs. While the bend and tilt models capture the effect of the entire plate, the nozzle model is local and is given as follows.

[0129]

[0130] Here, r i captures the deviation of the shape I value at the i-th position, and u n,i Represents the deviation of the spray duty cycle at that position. The same model is used for all active areas. Similar to the AGC case, the dead time in the tilt and nozzle models is approximated using Pade's formula. Subsequently, the model is discretized and converted into state space form. These (N+2) state-space models are then combined together to obtain the main state space model in the form of equation (7). Note that while u was a scalar (one-dimensional vector) in the AGC, it is now a vector with (N+2) inputs. Therefore, the dimensions of x, Ap, Bp, and Cp are also different. The rest of the controller design process is similar to the AGC. There will be four (N+2) constraints, i.e., four constraints for each input, and these constraints are configured in the same way as the AGC.

[0131] Mill data such as the number of rotors used (active or covered by plates) and the duty cycle in seconds are specified. The former sets the dimensionality of the problem and the latter serves as the execution frequency of the controller. The desired / target shape can be entered in terms of linear and quadratic components. For example, for a flat curve, these components will be set to 0. The starting / initial curve (shape I value) needs to be considered based on the actual data. This is called the raw data. It is converted to zero-mean data, which is compared with the target shape (also zero-mean) to calculate the overall control force required for the AFC system. Next, the required control force is decomposed into linear and quadratic components. In the default setting, the linear component control problem will be solved by tilt control, the quadratic component control problem will be solved by bending control, and the remaining force will be adjusted by nozzle control. However, there are two settings that can modify this. It is possible to choose to completely turn off the tilt and / or bending control action. In this setting, this part of the control force is transferred to the nozzle control. Secondly, each of the tilt, bend or nozzle control forces has a lower limit (dead zone) and an upper limit (clamping). Based on these, the final tilt, bend and nozzle targets (for each nozzle) are calculated and passed to the MPC as the setpoint Rs. Note that the calculations of the MPC are performed only once during the duty cycle and the inputs remain constant throughout the time.

[0132] The process of the present invention can be incorporated into objects to improve the thickness and flatness accuracy of the produced plates, such as cold rolling mill systems, including those systems with automatic gauge and flatness control and hydraulic gap control (HGC) controllers. The mill can include outputs from the controller. The controller can include inputs from sensors and filters, which can include various models by integrating the method of the present invention into the controller environment, such as in the form of a MATLAB script or in the form of another suitable program.

[0133] Figure 8 An embodiment of the present invention is shown which includes an internal mill model 800 of a material rolling process as follows:

[0134] In block 810, the rolling mill model estimates process parameters during rolling by taking measurements.

[0135] In block 820, the rolling mill model simulates the rolling process and predicts the thickness and flatness of the material in the roll gap.

[0136] In block 830, the rolling mill model determines an optimal controller output that is specified as a manipulated variable that is independent of dead time and dynamic delays in the process.

[0137] In block 840, the mill model uses the process model and calculates a manipulated variable curve that optimizes the performance target predicted for the future time interval, subject to the constraints.

[0138] Fig. 9 1 is a schematic block diagram of a computer system 150 that implements an instrument and method including a model-based multivariable predictive controller according to an exemplary embodiment. Not all components need to be used in various embodiments. An exemplary computing device in the form of a computer system 150 may include a processing unit 152, a memory 154, a removable storage 162, and a non-removable storage 164. Although the exemplary computing device is shown and described as a computer system 150, the computing device may take different forms in different embodiments. For example, the computing device may alternatively be a smart phone, a tablet computer, a smart watch, or other computing device. Devices such as smart phones, tablet computers, and smart watches are generally referred to as mobile devices. In addition, although various data storage elements are shown as part of the computer system 150, the storage may also or alternatively include a cloud-based storage that can be accessed via a network such as the Internet.

[0139] Memory 154 may include volatile memory 158 and nonvolatile memory 160. Computer system 150 may include, or have access to, a computing environment that includes, various computer-readable media, such as volatile memory 158 and nonvolatile memory 160, removable storage 162, and non-removable storage 164. Computer storage includes 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 disk read-only memory (CDROM), digital versatile disk (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 the functions described herein.

[0140] The computer system 150 may include or have access to a computing environment including an input 168, an output 170, and a communication interface 164. The output 170 may include a display device that may also be used as an input device, such as a touch screen. The input 168 may include one or more of the following items: a touch screen, a touch pad, a mouse, a keyboard, a camera, one or more device-specific buttons, one or more sensors integrated into the computer system 150 or connected to the computer system via a wired or wireless data connection, and other input devices 168. The computer system 150 may operate in a networked environment using a communication connection to connect to one or more remote computers, such as a database server, including cloud-based servers and storage. The remote computer may include a personal computer (PC), a server, a router, a network PC, a peer device, or other common network nodes, etc. The communication connection may include a local area network (LAN), a wide area network (WAN), a cellular, WiFi, Bluetooth, or other network.

[0141] Computer readable instructions stored on a computer readable storage device may be executed by a processing unit 152 of a computer system 150. Hard drives, CD-ROMs, and RAM are some examples of articles of manufacture that include 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 156 may be used to cause a processing unit 152 to perform one or more methods described herein.

[0142] The foregoing describes the principles, preferred embodiments and modes of operation of the present invention. However, the present invention should not be construed as being limited to the specific embodiments discussed. Therefore, the above embodiments should be considered as exemplary rather than restrictive, and it should be understood that variations may be made in these embodiments by those skilled in the art without departing from the scope of the present invention as defined by the following claims.

Claims

1. A controller for controlling the thickness and flatness of a metal plate in a rolling mill exiting a roll bed, the roll bed comprising first and second work rolls positioned between first and second support rolls, respectively, the controller comprising a processor and code stored on a medium readable by the processor to control the thickness of the metal plate, the controller comprising: an input end, the input end comprising the thickness and the flatness of the metal plate; A model of the roller base; a filter based on the model; and A controller output coupled to control roll force, mill speed, strip tension, and / or a roll gap between the first work roll and the second work roll to produce the metal sheet.

2. The controller according to claim 1, wherein: The filter comprises an extended Kalman filter.

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

4. The controller of claim 1, wherein the model is determined by crash testing of the roller base.

5. A method of programming a controller for automatically controlling the thickness and flatness of a metal sheet produced by a roller bed, the method comprising: generating a model of the roll bed, the model being multivariate and predictive; receiving input including changes in the thickness and the flatness of the metal sheet; generating a filter based on the model; as well as Parameters of the filter are automatically adjusted based on the input to control the thickness and the flatness of the metal sheet produced by the roller bed.

6. A controller for controlling the thickness and flatness of a metal plate leaving a roll bed having a first working roll and a second working roll, the controller comprising: processor; means for determining said thickness of said metal sheet exiting said roller bed; means for determining said flatness of said metal sheet leaving said roller bed; a memory device coupled to the processor and comprising a readable program executable by the processor to: receiving input including changes in the thickness and the flatness of the metal sheet; generating a model of the roller base; Based on the model, performing a filter; as well as An output is provided that is coupled to control roll force, mill speed, strip tension, and / or a roll gap between the first work roll and the second work roll.

7. A controller according to claim 6 coupled to spray nozzles in different rotors / zones in a shape measuring machine.

8. The controller of claim 7 including a variable duty cycle for the spray nozzle.

9. The controller according to claim 6, comprising: Linear component control solved by tilt control, Secondary component control resolved by bending control, and The residual force is regulated by the nozzle control.

10. A controller according to claim 9, the controller including a desired or target shape inputted from a linear component and a quadratic component.

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