Step 1: Understanding Yarn Irregularity Measures: U% (Uster Percentage): A measure of yarn evenness, representing the mean deviation of the yarn's linear density. Lower U% means a more even yarn. CV% (Coefficient of Variation Percentage): Another measure of yarn evenness, representing the standard deviation of the yarn's linear density, expressed as a percentage of the mean linear density. Lower CV% means a more even yarn.
Step 2: Relationship between U% and CV% The relationship between U% and CV% isn't perfectly linear, but for most practical purposes, especially for cotton yarns, the following approximation is widely used: \[ \text{CV\%} \approx 1.25 \times \text{U\%} \] This relationship arises because U% uses the mean deviation and the distribution of yarn mass is not perfectly normal, there will be this constant factor of 1.25.
A closed-loop system has the characteristic equation given by: $ s^3 + k s^2 + (k+2) s + 3 = 0 $.
For the system to be stable, the value of $ k $ is:
A digital filter with impulse response $ h[n] = 2^n u[n] $ will have a transfer function with a region of convergence.