Consider the transfer function model in Eq. 12-10 with K = 2, = 5 and = 1.

Consider the transfer function model in Eq. 12-10 with K = 2, τ = 5 and θ = 1. Compare the PID controller settings obtained from the Ziegler-Nichols and Tyreus-Luyben tuning relations in Table 12.6. Simulate the closed-loop responses for a unit step change in the set point.