Two-dimensional web property variation modeling and control
First Claim
1. A method for determining a two-dimensional variation for a web of material as said web of material is being manufactured, said method comprising the steps of:
- measuring at least one characteristic of said web substantially across an entire width of said web to generate a two-dimensional measurement function;
selecting a series of wavelet basis functions; and
convoluting said two-dimensional measurement function with said wavelet basis functions to generate a two-dimensional variation signal representative of said web of material.
1 Assignment
0 Petitions
Accused Products
Abstract
A new two-dimensional (2D) variation modeling and control technique for a machine producing a web of material, such as paper, uses functional transformation with basis functions which are wavelets, preferably wavelets derived from and closely resembling the responses generated by actuation of cross direction (CD) actuators of the machine. By using the disclosed functional transformation together with carefully selected basis functions, memory and real-time processing requirements are substantially reduced so that practical controls can be readily implemented. In addition, the functional transformation technique of the present application expands conventional CD correction to also correct for a portion of the residual variations which, until now, have remained uncorrected. The new 2D profile is treated as the superposition of two main components: a pure machine direction (MD) variation component and a two-dimensional sheet variation component. The pure MD variation is identical to the conventional MD variation; however, the two-dimensional sheet variation represents the evolution of a sheet property being measured in both a temporal direction (TD) and a spatial direction (SD), i.e. it includes both the traditional pure CD profile and a portion of the residual variation. The TD is aligned with the MD and the SD is perpendicular to the TD or is aligned with the CD. The new 2D variation is controlled by a new 2D control arrangement which includes an optimal predictive SD controller and a model based TD controller to quickly achieve 2D web uniformity.
53 Citations
25 Claims
-
1. A method for determining a two-dimensional variation for a web of material as said web of material is being manufactured, said method comprising the steps of:
-
measuring at least one characteristic of said web substantially across an entire width of said web to generate a two-dimensional measurement function; selecting a series of wavelet basis functions; and convoluting said two-dimensional measurement function with said wavelet basis functions to generate a two-dimensional variation signal representative of said web of material. - View Dependent Claims (2, 3)
-
-
4. A method for determining a two-dimensional variation for a web of material as said web of material is being manufactured along a machine direction, said method comprising the steps of:
-
measuring at least one characteristic of said web of material as a function of the cross machine direction of said web of material to generate a measurement function; determining variation in the machine direction of the web of material which variation is substantially independent of the cross machine direction to generate a pure machine direction function; separating the pure machine direction function from the measurement function to generate a two-dimensional sheet variation function; and using wavelet basis functions to transform said two-dimensional sheet variation function into a two-dimensional variation signal representative of said web of material. - View Dependent Claims (5, 6)
-
-
7. A method for controlling a two-dimensional variation for a web of material as said web of material is being manufactured, said method comprising the steps of:
-
measuring at least one characteristic of said web substantially across an entire width of said web to generate a measurement function; determining a two-dimensional measurement function from said measurement function; transforming said two-dimensional measurement function to generate a transformed variation expression representative of said web of material; determining a reference profile function; transforming said reference profile function to generate a transformed reference expression representative of said reference profile function; subtracting said transformed variation expression from said transformed reference expression to generate a first input signal for a spatial direction controller; generating a spatial direction control signal in response to said first input signal; combining said spatial direction control signal with a modeled temporal direction feedback signal to generate a second input signal for a temporal direction controller; generating a two-dimensional process control signal in response to said second input signal; and coordinating deadtime delays to unify delay times among a series of cross direction actuators to generate a process control signal from said two-dimensional process control signal. - View Dependent Claims (8, 9, 10, 11)
-
-
12. A method for controlling a two-dimensional variation of a web of paper as said web of paper is being manufactured by a paper making machine having a headbox actuator, said method comprising the steps of:
-
measuring at least one characteristic of said web substantially across an entire width thereof to generate a measurement function; determining machine direction variations contained within said measurement function; removing said machine direction variations from said measurement function to generate a two-dimensional variation signal including both cross directional and residual variations; and controlling said headbox actuator in response to said two-dimensional variation signal. - View Dependent Claims (13, 14, 15, 16, 17)
-
-
18. A method for controlling a two-dimensional variation of a web of material as said web of material is being manufactured by a machine having a cross direction controller, said method comprising the steps of:
-
measuring at least one characteristic of said web substantially across an entire width of said web to generate a measurement function; determining machine direction variations contained within said measurement function; removing said machine direction variations from said measurement function to generate a two-dimensional variation signal including both cross directional variations and residual variations; and controlling said cross direction controller in response to said two-dimensional variation signal. - View Dependent Claims (19, 20, 21, 22, 23, 24, 25)
-
22. A method for controlling a two-dimensional variation for a web of material as said web of material is being manufactured as claimed in claim 20 further comprising the step of forming said weighting matrix to have a structure defined by the equation R=R0 +D1T R1 D1 +D2T R2 D2 + . . . where R0, R1, R2, . . . are diagonal matrices and D1, D2, . . . are band-diagonal matrices with proper dimensions.
-
23. A method for controlling a two-dimensional variation for a web of material as said web of material is being manufactured as claimed in claim 22 further comprising the steps of selecting R0, R1, R2 to provide different order of constraints for individual actuators of said cross direction controller.
-
24. A method for controlling a two-dimensional variation of a web of material as said web of material is being manufactured by a machine having a cross direction controller as claimed in claim 18 wherein said step of controlling said cross direction controller comprises the steps of:
-
selecting a series of wavelet basis functions; and decomposing said two-dimensional variation signal with said basis functions.
-
-
25. A method for controlling a two-dimensional variation of a web of material as said web of material is being manufactured by a machine having a cross direction controller as claimed in claim 24 wherein the step of selecting a series of basis functions comprises the step of selecting said basis functions to be wavelet scaling basis functions.
-
Specification