Continuous casting in steel production is essentially a solidification process by which molten steel is solidified into
Question:
Continuous casting in steel production is essentially a solidification process by which molten steel is solidified into a steel slab after passing through a mold, as shown in Figure P5.41(a). Final product dimensions depend mainly on the casting speed Vp (in m/min), and on the stopper position X(in %) that controls the flow of molten material into the mold (Kong, 1993). A simplified model of a casting system is shown in Figure P5.41 (b) (Kong, 1993) and (Graebe, 1995). In the model, Hm =mold level (in mm); Ht =assumed constant height of molten steel in the tundish; Dz= mold thickness = depth of nozzle immerged into molten steel; and Wt= weight of molten steel in the tundish.
For a specific setting let Am = 0.5 and
Also assume that the valve positioning loop may be modeled by the following second-order transfer function:
and the controller is modeled by the following transfer function:
The sensitivity of the mold level sensor is β = 0.5 and the initial values of the system variables at t= 0- are: R(0-) = 0; YC (0-) = X(0-) = 41.2; ΔHm = (0-) = 0; Hm(0-) = -75; ΔVp (0-) = 0; and Vp (0-) = 0. Do the following:
a. Assuming vp(t) is constant [vp = 0] , find the closed-loop transfer function T(s) = ΔHm(s)/R(s).
b. For r(t) = 5 u(t); vp(t) = 0.97 u(t); and Hm(0-) = 75 mm, use Simulink to simulate the system. Record the time and mold level (in array format) by connecting them to Workspace sinks, each of which should carry the respective variable name. After the simulation ends, utilize MATLAB plot commands to obtain and edit the graph of hm(t) from t = 0 to 80 seconds.
Step by Step Answer: