Consider the system of Problem 11.4-10. (a) Find the feedback gain required to minimize the given cost
Question:
Consider the system of Problem 11.4-10.
(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.
(d) Compare the gain in part (b) with the value in Problem 11.6-3(a). Explain the difference.
Problem 11.4-10
Given the plant of Problem 11.4-4, with the cost function
(a) Calculate the feedback gains required to minimize the cost function, using the difference-equation approach of Section 11.4.
(b) Find the maximum magnitude of u(k) as a function of x(0).
(c) Compare the maximum magnitude of u(k) in part
(b) with the value in Problem 11.4-4(c). Explain the difference.
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).
Problem 11.6-3(a)
(a) Find the feedback gain required to minimize the given cost function for the infinite-time problem.
Step by Step Answer:
Digital Control System Analysis And Design
ISBN: 9780132938310
4th Edition
Authors: Charles Phillips, H. Nagle, Aranya Chakrabortty