The function of a steel plate mill is to roll reheated slabs into plates of scheduled

Chapter 0, Problem P12.6

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The function of a steel plate mill is to roll reheated slabs into plates of scheduled thickness and dimension [5, 10). The final products are of rectangular plane view shapes having a width of up to 3300 mm and a thickness of 180 mm. A schematic layout of the mill is shown in Figure P12.6(a). The mill has two major rolling stands, denoted No. 1 and No. 2. These are equipped with large rolls (up to 508 mm in diameter), which are driven by high-power electric motors (up to 4470 kW). Roll gaps and forces are maintained by large hydraulic cylinders. Typical operation of the mill can be described as follows. Slabs coming from the reheating furnace initially go through the No. 1 stand, whose function is to reduce the slabs to the required width. The slabs proceed through the No. 2 stand, where finishing passes are carried out to produce the required slab thickness. Finally, they go through the hot plate leveller, which gives each plate a smooth finish. One of the key systems controls the thickness of the plates by adjusting the rolls. The block diagram of this control system is shown in Figure P12.6(b). The plant is represented by G(s) 1 s(s2 + 4s + 5)' The controller is a P1D with two equal real zeros, (a) Select the PID zeros and the gains so that the closed-loop system has two pairs of equal roots, (b) For the design of part (a), obtain the step response without a prefilter (Gp(s) = 1). (c) Repeat part (b) for an appropriate prefilter. (d) For the system, determine the effect of a unit step disturbance by evaluating y(t) with r(t) = 0.