This paper extends the work of the first four parts of this series to apply the image analysis methods we have developed to characterize the fiber orientation of real non woven fabrics. The "real" fabrics chosen as typical are a carded crimped fiber web, two relatively dense overall or area bonded fabrics, a pattern or point bonded spun bonded-meltblown-spunbonded fabric, and a lightweight spunbonded nonwoven. In order to deal with real webs, it is necessary to develop a lighting system to give images with sufficient contrast along with an appropriate thresholding method to yield data suitable for analysis. The results indicate that the chord tracking method can charac terize orientation reliably when a direct measure is needed, and the information can be used to characterize and compare nonwoven laydown processes.

A robust adaptive regulator is constructed for single-inputlsingle-output discrete time systems modelled by a linear time-varying difference equation that includes an error term to incorporate model errors and/or disturbances. It is assumed that the parameters of the nominal model belong to a known bounded convex set and that the 'frozen time' nominal model is stabilizable for all possible parameter values. The estimation of the parameters of the nominal model is carried out using a standard gradient-type algorithm with a projection operation. An adaptive regulator is then constructed from the solution to a finite time Riccati equation. It is shown that the resulting closed-loop system is globally stable if the mean of the parameter time variations is sufficiently small and if the model error is sufficiently small, but where the disturbances applied to the plant may be arbitrarily large.

In this paper an indirect adaptive regulator is constructed f o r single-input single-output linear tinievarying discrete-time systems. The plant parameters are modeled as a linear combination of known bounded functions which inay be fast varying with unknown slowly-varying coefficients that are coilfined to a convex set. The unknown coefficients are estimated using a gradient type estimator with a projection operation. It is assiiined that the system is uniforiiily Nstep reachable, where N is an integer greater than or equal to the system diiiien.sion. It i s then shown that the resulting closed-loop system is globally stable for a sufficiently siiiall rate of the unknown variations. This adaptive regulator is also shown to be robust to disturbances and/or small model errors.