Consider the satellite control system of Problem 11.4-6. (a) By computer, find the feedback gains required to
Question:
Consider the satellite control system of Problem 11.4-6.
(a) By computer, find the feedback gains 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 constants as a function of the sample period T.
Problem 11.4-6
A satellite control system is modeled as shown in Fig. P11.4-6. This system is described in Problem 1.4-1.
For this problem, ignore the sensor gain and let D(z) = 1. In addition, K = 1, T = 1 s, and J = 4. As stated in Problem 9.2-4, a state model for this system is given by
where x1(k) is angular position and x2(k) is angular velocity.
(a) Determine by hand the gains required to minimize the cost function
with N = 1. The value of N is chosen to be unity to limit the calculations.
(b) Use MATLAB to solve part (a) for N = 20. Sketch the calculated gains versus k.
Problem 1.4-1
Step by Step Answer:
Digital Control System Analysis And Design
ISBN: 9780132938310
4th Edition
Authors: Charles Phillips, H. Nagle, Aranya Chakrabortty