Question

E. If you double the value of kp, what are the new closed-loop pole locations and [5 points] how much overshoot does the step response have? Hint: It is possible to determine the original value for kp. However, with the knowledge at this point, you can compute the pole locations without actually knowing kp (simply double the zero-order term in the denominator polyno- mial). Problem 2 You are confronted with a process that has the unknown transfer function G(s). It is embedded in a feedback loop whose feedback path has the adjustable gain kp Figure 2A). Y(s) Figure 2: (A): A feedback control system with a process whose transfer function GG) is unknown. (B): Unit step response in the time domain. The step response indicates a critically damped system. Some facts are known about the closed-loop system: . A step input, x(1)-a(1) or correspondingly (s) = 1/s causes the system response shown in Figure 2B. . The response indicates that G(s) is a second-order system. .The gain kp is adjusted to obtain a critically damped response, meaning, the closed-loop system has a double pole on the real axis . One additional detail is known: One pole of G(s) is in the origin

Answer 1