In a carding machine, the cylinder rotates at the highest surface speed. This high speed is essential for effective carding action. The licker-in, which initially picks up fibers from the feed, rotates at a considerably slower speed than the cylinder. The doffer, which removes the carded web from the cylinder, rotates even slower than the licker-in. This speed differential between the cylinder and the other rollers facilitates fiber transfer and alignment.
The speed arrangement (from fastest to slowest) is generally: Cylinder>Licker-in>Doffer.
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.