Consider the satellite control system of Problem 9.2-4. Problem 9.2-4 A satellite control system is modeled as

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Consider the satellite control system of Problem 9.2-4.

Problem 9.2-4

A satellite control system is modeled as shown in Fig. P9.2-4. This system is described in Problem 1.4-1.
For this problem, let D(z) = 1. In addition, K = 1, T = 1 s, J = 4, and Hk = 1. From the z-transform
tables,I - 2 N 45 0.125(z + 1) (z  1)

(a) Design a predictor observer for this system, with the time constant equal to one-half the value of Problem 9.2-4(b) and with the observer critically damped.

(b) To check the results of part (a), use (9-46) to show that these results yield the desired observer characteristic equation.

(c) Find the control-observer transfer function Dce(z)Dce(z) in Fig. 9-8. Use the control gain matrix of Problem 9.2-4(b), K=[0.38931.769]K=[0.38931.769].


(d) The characteristic equation of the closed-loop system of Fig. 9-8 is given by
1+Dce(z)G(z)=01+Dce(z)G(z)=0
Use G(z)G(z) as given and Dce(z)Dce(z) in part (c) to show that this equation yields the same characteristic equation as αc(z)αe(z)=0αc(z)αe(z)=0

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Digital Control System Analysis And Design

ISBN: 9780132938310

4th Edition

Authors: Charles Phillips, H. Nagle, Aranya Chakrabortty

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