Process and Disturbance Models The rolling mill is used to shape rectangular beams of hot metal. The desired outgoing shape is sketched below. Figure 1 Beam Shaping by Rolling Cylinders. This shape is impressed by two pairs of rolling cylinders (one per axis) positioned by hydraulic actuators. The gap between the two cylinders is called the roll gap. Figure 2 Rolling Mill Stand. The objective is to maintain the beam thickness along the x- and y-axes within the quality assurance tolerances. Variations in output thickness can arise from the following: • Variations in the thickness/hardness of the incoming beam • Eccentricity in the rolling cylinders Feedback control is necessary to reduce the effect of these disturbances. Because the roll gap delta cannot be measured close to the mill stand, the rolling force is used instead for feedback. The input thickness disturbance is modelled as a low pass filter driven by white noise. The eccentricity disturbance is approximately periodic and its frequency is a function of the rolling speed. A reasonable model for this disturbance is a second-order bandpass filter driven by white noise. This leads to the following generic model for each axis of the rolling process. Figure 3 Open-Loop Model. The measured rolling force variation f is a combination of the incremental force delivered by the hydraulic actuator and of the disturbance forces due to eccentricity and input thickness variation. Note that: The outputs of H(s), Fe(s), and Fi(s) are the incremental forces delivered by each component. • An increase in hydraulic or eccentricity force reduces the output thickness gap δ. • An increase in input thickness increases this gap. Cross-Coupling Effects Rolling mills have some amount of cross-coupling between axes because an increase in force along x compresses the material and causes a relative decrease in force along the y axis. Cross-coupling effects are modelled as shown in the figure below with gxy=0.1 and gyx=0.4. Figure 4 Cross-Coupling Model.   Assignment Requirements: You are required to write a report of 2,500 words maximum (excluding
references). This Project will include a progress report; literature review, hypothesis, and proposed solution with concept workings for the following: Select and apply different control strategies from fundamental PID, multivariable control, and model predictive control for a rolling mill plant. Consider / discuss the following in the report: • Block diagrams • Type of control PID, MPC, LQG? • Configuration: MIMO vs SISO? • Use of Statistical Process Control • Discrete vs continuous. Notes: • No implementation or results needed, as this is a proposal type report. • A minimum 3-4 supporting references and correct use of in-text citation. Citation and referencing format should conform to the EIT Marking Guidelines. Please see details of the use of IEEE citation within Moodle • Research readings, articles, MATLAB software help files, or other sources for guidance and information on this topic.