Recall that a transfer function matrix relates the inputs and outputs

The input/output transfer function matrix is found from

using the MATLAB routine `SS2TF` (see Appendix), we find

The poles of the characteristic polynomial

are -0.191 and -4.709. The transfer function relating output 1 (tank temperature) to input 1 (jacket flowrate) is

dividing

by 0.9, we find

which can be factored into

which is the gain-time constant form. Any of these forms can be used, however we will generally use the gain-time constant form.

The transfer function relating output 2 (jacket temperature) to input 1 (jacket flowrate) is

Similarly, we find (dividing

by 0.9)

Also,

can be factored into

B. Wayne Bequette, bequeb@rpi.edu