Consider the system of Problem 11.4-4.

(a) Find the feedback gain required to minimize the given cost function for the infinite-time problem.

(b) Find the closed-loop system characteristic equation.

(c) Find the closed-loop time constant v as a function of the sample period T.

Problem 11.4-4

Given the first-order plant described by

(a) Calculate the feedback gains required to minimize the cost function, using the partial-differentiation procedure of Section 11.3.

(b) Repeat part (a) using the difference-equation approach of Section 11.4.

(c) Find the maximum magnitude of u(k) as a function of x(0).

Transcribed Image Text:

with the cost function x(k+ 1) = 0.6x(k) + 0.5u(k) 3 J3 = [2x(k) + 7u(k)] k=0