Question

Problem 1: Given the transfer function from input u(t) to output y(t), Y (s) U(s) = s 2 − 4s + 3 (s 2 + 6s + 8)(s 2 + 25) (a) Develop a state space model for this transfer function, in the standard form x˙ = Ax + Bu y = Cx + Du (b) Suppose that zero input is applied, such that u = 0. Perform a modal analysis of the state response for this open-loop system. Your analysis should include the nature of the time response for each mode, as well as how each element of the state vector x contributes to that mode. Which mode dominates the time response? (c) Now suppose that input of the form u = Ky is applied, where K = −15. Repeat the modal analysis of part (b) for this closed-loop system.

Answer 1

Y(3) sul 2)