Problem 2. Consider Example 14.3 from the textbook, the mixing tank, with level and temperature as controlled variables. Hot stream Cold stream (disturbance) "2 Cold stream LC TC 12 Read and understand how the inputs and outputs were scaled to achieve the following scaled transfer function relationship [ y(s) H y(s) 1.667 1.667 20s+1 20s+1 u(s) 0.5 -0.5 10s+1 10s+1 u(s) 1 a. Perform a singular value decomposition to find the strongest and weakest input and output directions. Is it easier to move in the y1 or y2 direction? Explain. b. Use the file svdio.m to plot a "circle" of inputs to an output "ellipse" (figure 6 from the file). c. Calculate the RGA for this process. Can you recommend input/output pairings? Why or why not?