Consider the pole-placement design of Problem 9.2-2. Problem 9.2-2 Consider the plant of Problem 9.2-1, which has

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Consider the pole-placement design of Problem 9.2-2.

Problem 9.2-2

Consider the plant of Problem 9.2-1, which has the transfer function, from Example 9.5,G(z.) N N 1 [s (s + 1)] = 0.00484Z+0.00468 z1.905z + 0.905

Problem 9.2-1

The plant of Example 9.1 has the state equations given (9-1). Find the gain matrix K required to realize the
closed-loop characteristic equation with zeros which have a damping ratio 1 of 0.46 and a time constant v
of 0.5 s. Use pole-assignment design.

(a) Design a predictor observer for this system, with the time constant equal to one-half the value of Problem 9.2-2(a) 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 control gain matrix of Problem 9.2-2(a).

(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)=0

Consider the plant of Problem 9.2-1, which has the transfer function, from Example 9.5,

Consider the plant of Problem 9.2-1, which has the transfer function, from Example 9.5,αc(z)αe(z)=0

Problem 9.2-2Problem 9.2-2Problem 9.2-2Problem 9.2-2Problem 9.2-2Problem 9.2-2Problem 9.2-2

Problem 9.2-2Problem 9.2-2

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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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