Consider the AB process. The reaction occurs in 5 identical CSTRS connected in series. To maximize conversion, the CSTRS are operated at maximum hold-up with PI level controllers manipulating the respective CSTR outflows. The reactor effluent is a mixture of A and B and is separated in a column to recover pure B product down the bottoms and recycle pure unreacted A up the top. The recycle stream is mixed with the pure fresh A feed stream and then fed to the first CSTR. Since the reaction is very slow, the CSTRs are very large and the column dynamics may be treated as instantaneous relative to the CSTR dynamics. The level controllers on the CSTR are tuned aggressive such that the outflow to inflow transfer function is second-order underdamped with = 0.5 and 7 = 1 h. The TPM is at the fresh A feed. If the nominal steady state recycle rate to product rate ratio is a (a) Obtain the transfer function relating the recycle rate R to the fresh feed rate F. (b) What is the maximum value of a for which the process is stable.