The present invention relates in general to controlling sheet forming processes and, more particularly, to improving the control of such processes.
In a sheet forming machine, the properties of a sheet vary in the two directions of the sheet, namely the machine direction (MD) which is the direction of sheet movement during production and the cross machine direction (CD), which is perpendicular to the MD and is the direction across the width of the sheet during production. Different sets of actuators are used to control the variations in each direction. The machine direction (MD) is associated with the direction of sheet moving speed, hence MD is also considered as temporal direction (TD). Similarly, the cross machine direction is associated with the width of the sheet, hence CD is also considered as spatial direction (SD).
The MD variations are generally affected by factors that impact the entire width of the sheet, such as machine speed, the source of base materials like wood fiber being formed into a sheet by the machine, common supplies of working fluids like steam, water and similar factors.
The CD variations are normally influenced by arrays of actuators located side-by-side across the width of the machine. Each actuator represents a zone of the overall actuator set. In a paper machine, the typical CD actuators are slice screws of a headbox, headbox dilution valves, steam boxes, water spraying nozzles, induction actuators, and other known devices. CD actuators present a great challenge for papermakers since a sheet-forming machine may have multiple sets of CD actuators, each with multiple numbers of zones spread across the entire width of a machine. Each set of CD actuators is installed at a different location of a sheet-making machine. There are different numbers of individual zones in each set of CD actuators. The width of each zone might also be different within the same set. Therefore, each set of CD actuators could have very different impacts on different sheet properties.
Measurements of sheet properties may be obtained from fixed sensors or from scanning sensors that traverse back and forth across the width of a sheet. The sensors are usually located downstream from those actuators that are used to adjust the sheet properties. The sensors measure the sheet properties while traveling across the sheet and use the measurement to develop a property profile across the sheet. The sheet property profile is typically discretized in a finite number of points across the sheet called “databoxes”. Presently, a sheet property profile is usually expressed in several hundreds to more than a thousand databoxes. The sheet property profiles accumulated in time form a two-dimensional matrix. The sheet property measurement at a fixed databox over a period of time can also be viewed like a profile in “temporal” direction or MD. The term “profile” is used with respect to either CD or MD. The sheet property profile is used by a quality control system (QCS) to derive control actions for the appropriate actuators so that the sheet property profile is changed toward a desired target profile. The target shape can be uniformly flat, smile, frown, or other gentle shapes. In order to control sheet property profiles with multiple set of CD actuators, it is important to measure and identify how each CD actuator influences the profiles.
Since the sensors are often located a considerable distance downstream from the CD actuators, the portion of the sheet (in the CD direction) influenced by a CD actuator zone but measured by the downstream sensors is not always perfectly aligned (in the CD direction) with the CD actuator zone, due to sheet shrinkage in the drying process or the sheet wandering sideways while the sheet is traveling through the machine. Furthermore, each CD actuator zone typically affects a portion of the profile that is wider than the portion corresponding to the width of the CD actuator zone. Thus, for controlling the CD profile of a sheet-forming machine, it is important to know which portion of the profile is affected by each CD actuator zone. The functional relationship that describes which portion of the profile is affected by each CD actuator zone is called “mapping” of the CD actuator zones.
In addition to knowing which portion of the profile is affected by which CD actuator zone, it is also important to know how each CD actuator zone affects the profile. The functional curve that illustrates how the sheet property profile is changed by the adjustment of a CD actuator zone is called the “response model” of the CD actuator zones. Conventionally, the response model for a CD actuator zone is represented with an array of discrete values or is modeled with wave propagation equations if the response is related to the spread of the slurry on the Fourdrinier wire. For a typical set of CD actuators, there are easily tens to a few hundreds of zones. For each actuator zone, if the response model is represented by an array of uniform discrete points, the model will be specified in either actuator resolution, which is the number actuator zones, or property profile resolution, which could have hundreds to more than a thousand points. Many paper machines today are equipped with multiple sets of CD actuators. The number of points needed to represent the response model for one sheet property profile for all actuator zones is the number of points per actuator zone multiplied by the total number of zones of multiple sets of CD actuators. In practice each set of actuators can change several sheet property profiles at the same time, and each sheet property profile may also be affected by multiple sets of CD actuators with different responses. These different responses are classified as different response types. The number of points needed to represent a complete response model is further multiplied by the number of sheet property profiles. A complete response model that relates the multiple sets of CD actuators and the multiple high-resolution sheet property profiles specified by the conventional approach will need a massive number of points. This is very inefficient, rigid, and subjects to errors in practice.
For specifying response models for a multivariable sheet-making process, the conventional approaches become extremely cumbersome and impractical. An effective and generalized framework for specifying the response model of all CD actuators is needed to implement a better CD control for a sheet-making machine. Therefore, it would be desirable, if a response model could be effectively described using one or a few critical points and continuous functions. The present invention is directed to such a method and apparatus for creating a generalized response model using one or a few critical points and continuous functions in an effective and user-friendly manner.