The product quality from a catalytic tubular reactor is controlled by the (low rate of the entering stream, utilizing composition measurements from a process gas chromatograph. The catalyst decays over time and once its overall activity drops below 50%, it must be recharged. Deactivation usually takes two to three months to occur. One measure of catalyst activity is the average of three temperature measurements that are used to estimate the peak temperature. Discuss how you would employ an adaptive control scheme to maintain product quality at acceptable levels. What transfer functions would need to be determined and why?