
The problem before us is to estimate the reaction constant k and reaction order n. We will do this
by simulating the response for the chemical concentration starting with guessed values for k and n.
The observed and simulated responses are used to compute the sum of squared errors, that is,
SSE ¼ f (k, n) ¼
X
60
i¼0
[
^
x
i
x
i
]
2
(7:69)
where
x
i
¼x(t
i
), i ¼0, 1, 2, . . . , 60 are simulated concentrations a minute apart
^
x
i
¼
^
x(t
i
), i ¼0, 1, 2, . . . , 60 are values of concent ration measured at one-minute intervals, some
of which are shown in Table 7.5
Minimizing the objective function f(k, n) yields the opti mal estimates of the reaction parameters.
Observed ...