u1,% 4 (15 pts). Consider the open-loop step responses shown below. Find the MIMO process transfer...

  

Transcribed Image Text:

u1,% 4 (15 pts). Consider the open-loop step responses shown below. Find the MIMO process transfer function matrix. Please show the units associated with each gain. Show your work. 50, y1, deg C 32 30 28 26 24 y2, mol% 35 45 22 20 100 150 200 t, min 56 51 55 50.5 54 53 52 u2, 1pm 50 51 49.5 50 49 49 0 50 100 t, min 150 200 50 0 55 50 45- 52 51 50 49 40- 35- 30 25 t, min y2, mol% 60 55- 50 451 401 100 150 200 50 48 100 t, min 150 200 u2, 1pm 56 100 t, min 100 t, min 100 150 200 t, min 150 200 150 200 50 100 t, min 150 200 a. Estimate a first-order + deadtime model for each input-output relationship and state the units for the process gain, time constant and deadtime in each case. Include the proper subscripts for each transfer function. 5 b. Write the matrix transfer function relationship y(s) = G(s) u(s) c. Find the RGA and suggest the best input-output pairing u1,% 4 (15 pts). Consider the open-loop step responses shown below. Find the MIMO process transfer function matrix. Please show the units associated with each gain. Show your work. 50, y1, deg C 32 30 28 26 24 y2, mol% 35 45 22 20 100 150 200 t, min 56 51 55 50.5 54 53 52 u2, 1pm 50 51 49.5 50 49 49 0 50 100 t, min 150 200 50 0 55 50 45- 52 51 50 49 40- 35- 30 25 t, min y2, mol% 60 55- 50 451 401 100 150 200 50 48 100 t, min 150 200 u2, 1pm 56 100 t, min 100 t, min 100 150 200 t, min 150 200 150 200 50 100 t, min 150 200 a. Estimate a first-order + deadtime model for each input-output relationship and state the units for the process gain, time constant and deadtime in each case. Include the proper subscripts for each transfer function. 5 b. Write the matrix transfer function relationship y(s) = G(s) u(s) c. Find the RGA and suggest the best input-output pairing