Data have been collected from a chemical process unit. The feed rate was the only variable that changed when the data were collected. The input and output data are given in the table below. Time (min) Input (% open) Output (C) 9210 30 50.0 50 49.8 4 50 49.6 6 50 49.6 8 50 56.8 10 50 61.2 12 30 64.2 14 30 65.8 16 30 67.4 18 30 61.6 20 30 57.6 (a) Use the least squares method to estimate the gain and time constant in a first-order-plus- dead-time model, considering possible dead times of 2 and 4 minutes. The matrices X and vectors y used in your parameter estimation calculations should be given, and you should show clearly the procedure followed in order to determine which of the candidate dead time estimates is most appropriate for your model. Assume that the first data point corresponds to steady-state conditions. (b) Plot the residuals for the proposed model and discuss your observations. (e) Plot the model response curve and data on the same graph. Be sure to use actual inputs and predicted outputs for calculating the model predictions.