4. Consider a process transfer function $\tilde{G}_p(s) = \frac{8(1-3s)}{s}$, $G_v = 1$, $G_m = 1$
1) Design a IMC controller $G_c^*$ using a filter $f = 1/(\tau s + 1)$.
2) Based on the result of part 1), design a PID controller $G_c$ that can be used in the classical
feedback control configuration. Write down the expression for $G_c$ and report the relevant
control parameters (e.g., proportional gain, integral time, derivative time).