Appendix M8.1

For Equations (M8.12) we develop a linear state space model, with the states, outputs, input, and disturbances as the following deviation variables:

The Jacobian matrix elements are

where

The first column of the B matrix is (this column is related to input 1, the jacket feed flow rate)

If both the reactor temperature (state 2) and the jacket temperature (state 3) are measured for a cascade control structure, the measured output matrix is