Question: help generate a matlab code for this example that will show results like the graphs provided? To illustrate how the CSTR can exhibit nonlinear dynamic

To illustrate how the CSTR can exhibit nonlinear dynamic behavior, we simulate the effect of a step change in the coolant temperature Tc in positive and negative directions. Table 2.3 shows the parameters and nominal operating condition for the CSTR based on Eqs. 2-66 and 2-68 for the exothermic, irreversible first-order reaction AB. The two-state variables of the ODEs are the concentration of A(cA) and the reactor temperature T. The manipulated variable is the jacket water temperature, TC Two cases are simulated, one based on increased cooling by changing Tc from 300K to 290K and one reducing the cooling rate by increasing Tc from 300K to 305K. These model equations are solved in MATLAB with a numerical integrator (ode15s) over a 10min horizon. The decrease in Tc results in an increase in CA. The results are displayed in two plots of the temperature and reactor concentration as a function of time (Figs. 2.7 and 2.8 ). At a jacket temperature of 305K, the reactor model has an oscillatory response. The oscillations are characterized by apparent reaction run-away with a temperature spike. However, when the concentration drops to a low value, the reactor then cools until the concentration builds, then there is another temperature rise. It is not unusual for chemical reactors to exhibit such widely different behaviors for different directional changes in the operating conditions. Table 2.3 Nominal Operating Conditions for the CSTR Figure 2.7 Reactor temperature variation with step changes in cooling water temperature from 300K to Figure 2.8 Reactant A concentration variation with step 305K and from 300K to 290K. changes in cooling water temperature to 305K and to 290K
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