Answer Happy

Use matlab for all sections, please and thank you.
Experiment 2 Consider the system shown in the figure below. R(S) E(S) C(s) G(s) H(s) Where, K G(s) = (s + 4)(8 + 7) s2 - 68 +16 HS) = S2 + 4s + 10 In this experiment we are going to investigate the effect of increasing system gain K on the resulting response, closed-loop pole locations, and the stability of the system. a) For some K value, find the closed-loop transfer function, and the closed-loop poles. b) Determine from the location of those poles, whether your system is stable. Output a message like: "Stable / Unstable at < Kvalue > with largest pole at < polevalue >" c) Have your program run in a loop for K values ranging from 0 to 40 (steps of 0.1). 3 2 d) Determine the gain Kcr , that takes the system to critical oscillations. To do this, determine the K value between that resulting in stable and unstable system. e) Plot the step response and pole locations for a value of K = Kcr – 2. f) Plot the step response and pole locations for a value of K = Kcr. Hint: use the Matlab command "step(Ts,tfinal)" where Ts is your closed-loop transfer function and tfinal is the final time value in seconds. g) Plot the step response and pole locations for a value of K = Kcr + 2. h) Plot the system poles (on one graph) for 40 values of K, starting with K = 1 to K = 40, to create a path of the system pole changes.

Experiment 3 a) Modify your program from experiment 2 to automatically determine the critical gain K, and report a message such as: "Change in stability at K =< Kvalue >" where Kvalue is the mean of K values either side of the stability boundary. b) Now modify your program report a message such as "Stability region: K <or > < Kvalue >"