$3$ Feedback control loop with PID

$G_p(s)=\frac{5*{10}^{-4}\frac{C}{k}ca\frac{l}{m}in}{(4s+1)(2s+1)},G_d(s)=\frac{1\frac{C}{}C}{4s+1},G_s(s)=\frac{\frac{16}{100}\frac{mA}{}C}{s+1},$

$G_v(s)=\frac{600\mathrm{.}000\text{k}\text{c}\text{a}\frac{l}{m}in}{16(mA)}.$

a$)$ Find the optimum controller parameters to control this sysytem by using Tyreus$-$Luyben method

b$)$ If the feed temperature, which is the disturbance variable, increases by $50C,$ how much of an offset is seen in the system?