Answer Happy

A) Determine whether each of the following open-loop systems are stable or not (has all roots in the open left half plan (OLHP) using the Hurwitz criteria) 1) R(s) → G() = ++382 +252 +28+9 3 →Y(s) 2) R(s) → G(s) = 5* +1052 +31s+30 1 →Y(S) 3) R(s) → G(8) = x3 +234 +238 +682 +11s+10 Y(s) B) Consider the following unstable open loop system a R(s) → Go(s) = (x+2)(5-1) Y(s) ) | - We want to stabilize the system by closing the loop via a proportional controller as shown in Figure 1. Note that, the transfer function of the closed-loop system KG(8) is given by G(S) = 1 + KG(s) 1. Compute the range of K that stabilize the system 2. For K = 4, Compute the performance characteristics of the closed-loop system: T, (settling time), T, (rise time), T, (peak time) and OS (over- shoot). 3. For K = 10, Compute the performance characteristics of the closed-loop system: T, (settling time), T,(rise time), T, (peak time) and OS. (over- shoot). 4. What is the effect of increasing K on the performance characteristics of the system?