Question

. (15 points) An unstable system can be stabilized by using negative feedback with a gain K in the feedback loop. For instance, consider an unstable system with transfer function which has a pole in the right-hand s-plane, making the impulse response of the system h) grow as increases. Use negative feedback with a gain K> 0 in the feedback loop, and put H) in the forward loop. Draw a block diagram of the system. Obtain the transfer function Gus) of the feedback system and determine the value of K that makes the overall system BIBO stable Ge, its poles in the open left-hand s-plane)

Answer 1

H(s) = 2/s - 1 Pole - zero plot for H(s): Left hand side Right hand side of s - plane rightarrow A system is said to be stable from its zero plot is all poles of given transfer function is on left hand side of s - plane. One plane is allowed at origin rightarrow On j w - axis non - repeated poles are also accept but that can be called as marginally stable system. rightarrow If any repeated poles on j w - axis (or) more than one pole at origin (or) any pole found to be Right - side of s - plane than that system can be called as unstable stable system. \r\n rightarrow for given unstable system. We can make it as stable system by apply feedback from system output to i/p rightarrow For given problem. Negative feedback system rightarrow From above block diagram E(s) = R(s) - k. C(s) rightarrow (1) C(s) = E(s). H(s) rightarrow (2) So from (1) & (2) C(s)/H(s) = R(s) - k C(s) C(s) = R(s). H(s) - k. C(s). H(s)