Problem 4. The closed-loop system is shown below. We want to draw its root-locus and design the positive constant K to achieve closed-loop stability. ) Find the departure angles at

pi and p2, and the arrival angle at z1. \text { Departure angle: } \phi_{d e p}=\sum_{j=1}^{m} \psi_{j}-\sum_{i \neq d e p}^{n} \phi_{i}-180(2 k+1) \text { Arrival angle: } \psi_{a r r}=\sum_{i=1} \phi_{i}-\sum_{j \neq a r r}^{m} \psi_{j}+180(2 k+1) (2) (2.5 points) Find the range of K for closed-loop stability using the Routh stability criterion.