The following data were collected from a cell concentration sensor measuring absorbance in a biochemical stream. The input u is the flow rate deviation (in dimensionless units) and the sensor output y is given in volts. The flow rate (input) is piece wise constant between sampling instants. The process is not at steady state initially, so y can change even though u = 0.

Fit a first order model, y(k) = a₁y(kˆ’1) + b₁ u(kˆ’1), to the data using the least-squares approach. Plot the model response and the actual data. Can you also find a first-order continuous transfer function G(s) to fit the data?

Table E7.14 Time (s) y 3.000 3 2.456 2 5.274 3 6.493 4 6.404 5 5.243 6. 4.293 3.514 2.877 2.356 10 1.929 1,