Question

K actuated screw thickness sensor le constant speed rollers Figure 4: Sheet metal rolling mill Q2(ii) Consider the system in Figure 4. The transfer function from the angular velocity и (rad/sec) of the actuated screw to the sheet thickness di (metres) at the roller output is given by Go(s) ko/s, with constant ko > 0. It is not physically possible to measure di for feedback control. Instead, a measurement is taken at a distance l (metres) upstream. Assuming that the positive in the upstream direction sheet velocity is v (metres/sec), determine the largest distance l > 0 for which unit gain constant feedback control (i.e. K = 1) achieves a gain margin of at least 20dB. Express the answer in terms of ko and v. [4 marks]