Time Dependent Structure of Profile Data

Analysis of full sheet data is useful for process performance evaluations and product value calculations. For feedback control or any other on-line application, it is necessary to continuously convert scanner data into a useful form. Consider the data vector Y ,k) for scan number k. It is separated into its MD and CD components as Y( , A ) = yM )( )+Yc )( , k) where Ymd ) s the mean of Y ,k) as a scalar and YcD -,k) is the instantaneous CD profile vector. MD and CD controllers correspondingly use these calculated measurements as feedback data for discrete time k. Univariate MD controllers are traditional in nature with only measurement delay as a potential design concern. On the other hand, CD controllers are multivariate in form and must address the challenges of controller design for large dimensional correlated systems. 

Control systems ignore short term variabilities through appropriately designed filters. Effective length of the filter window determines how quickly significant variations are actually detected. Defining a CD profile vector yc )( ) for a complete roll is perhaps the simplest form of a large window 

---