(Solved): Consider a constant-volume continuous stirred tank reactor (CSTR) shown in Figure P6.6. The follo ...

Consider a constant-volume continuous stirred tank reactor (CSTR) shown in Figure P6.6. The following reaction takes place isothermally in the CSTR: with the reaction rate being first order in both directions: $r_1=k_1{C}_R,r_{?1}=k_{?1}{C}_P$. The inlet concentration of the reactant $C_{R0}$ is the input of the system, the concentration of species $P$ in the reactor $C_P$ is the output. (a) Write down a state-space model for this system, consisting of mole balances for species $R$ and $P$. Put your model in standard matrix form $\begin{array}{l}\frac{dx}{dt}=Ax+bu\\ y=cx+du\end{array}$ (b) Derive the transfer function of the CSTR using the formula $G(s)=c(sI?A{)}^{?1}b+d$.