The temperature control system for a chemical process shown in Figure Q$2($a$).$ The uncompensated system is operating with a rise time approximately the same as a second$-$order system with a peak time of $16$ second and $5\%$ overshoot. Suggest and design a suitable controller so that the compensated system will have a rise time approximately equivalent to a second order system with a peak time of $8$ second or less and $5\%$ overshoot, and zero steady$-$state error for a step$-$input.