Modeling profile response from bumping multiple consecutive profiling actuators

摘要

A cross-direction feedback controller, profiler system and actuator setpoint controller are provided in communication with a plurality of actuators in a machine of a web-forming process, and with a local region detector that determines an actual profile response of a product of the web-forming process in response to consecutively bumping each of the actuators. A relationship between generated profile response data and an actuator setpoint change in the generated profile response data is represent by a profile-to-actuator general interaction matrix, which is expanded into linear equations that describe impacts of bumped actuators on different profile points of generated profile response data. The linear equations are rearranged into a bump-magnitude matrix as a function of a desired response model vector. A least-square solution is found for the bump-magnitude matrix, convolved with a window function and then optimized to minimize error between an actual and a modeled profile response.

主权项

1. A method for modeling the response of a multiple consecutive actuator bump test, wherein a processor is coupled to a memory, the method comprising executing on the processor the steps of:
generating profile response data by consecutively bumping each of a plurality of actuators in a machine of a web-forming process; representing a relationship between the generated profile response data and an actuator setpoint change in the generated profile response data by a profile-to-actuator general interaction matrix; expanding the profile-to-actuator general interaction matrix to show constituent row-column elements as a plurality of linear equations that each describe an impact of the bumped actuators on each of different respective profile points of the generated profile response data; rearranging, as a function of a desired response model vector, the plurality of linear equations into a bump-magnitude matrix that comprises zero profile responses in constituent row-column elements of each of first and last columns that do not represent multiple consecutively bumped actuator zones, and products of respective multiple consecutive actuator zones that are bumped within constituent row-column elements of at least two middle columns; finding a least-square solution for the bump-magnitude matrix; convolving the least-square solution with a window function; and optimizing the convolved least-square solution to minimize an error between the generated profile response data and a modeled profile response by: dividing the generated profile response data into a positive constituent that corresponds to a positive lobe in the modeled profile response, and a negative constituent that corresponds to a negative lobe in the modeled profile response; optimizing the positive lobe to minimize the positive error constituent; and optimizing the negative lobe to minimize the negative error constituent.