Project $1.$ Linear Model for Dynamic Behavior of a CSTR$.$

Refer to Chapter $3$ in the text Chemical Reactor Design and Control by William Luyben. Section $3\mathrm{.}1\mathrm{.}1$

summarizes a nonlinear dynamic model for a CSTR with a cooling jacket.

Section $3\mathrm{.}1\mathrm{.}2$ shows the equations for a linearized model based upon the Taylor$-$series expansion.

Section $3\mathrm{.}1\mathrm{.}3$ shows the results of various simulations where the effect of conversion on open loop and

closed loop stability is examined.

Starting from the nonlinear model given in section $3\mathrm{.}1\mathrm{.}2,$ show the derivation of the linearized

model given in section $3\mathrm{.}1\mathrm{.}2.$ This should include the development of eq$.3\mathrm{.}12$ and the various

terms defined by eq$.3\mathrm{.}15.$

Show how the transfer function defined by eq$.3\mathrm{.}17$ is obtained from the above analysis and the

inclusion of the two first$-$order temperature measurements lags.

Recreate the Matlab codes shown in Figure $3\mathrm{.}1$ and Figure $3\mathrm{.}5,$ and then use them to reproduce

Figures $3\mathrm{.}2,3\mathrm{.}3,3\mathrm{.}5,3\mathrm{.}6$ and $3\mathrm{.}7.$ Note that these codes can be modified slightly as needed to

generate the indicated graphs.