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Asked Jun 12, 2019
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Feedback Control of Dynamic Systems (7th edition) - Problem 7.25

Consider the system in Fig. 7.87.
7.25
Figure 7.87
System for Problem 7.25
-o Y
s2+4
(a) Write a set of equations that describes this system in the standard canonical
control form as x = AxBu and y Cx
(b) Design a control law of the form
u
Ki K2
2j
which will place the closed-loop poles at s= -2
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Consider the system in Fig. 7.87. 7.25 Figure 7.87 System for Problem 7.25 -o Y s2+4 (a) Write a set of equations that describes this system in the standard canonical control form as x = AxBu and y Cx (b) Design a control law of the form u Ki K2 2j which will place the closed-loop poles at s= -2

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Expert Answer

Step 1

 First, find out the canonical form from the given transfer function    and after that design a control law of form mentioned in the second part.

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Y (s) U (s) s2+4

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Step 2

First, break the transfer function into two part using cascading. Consider a point Z(s)  between two transfer functions as shown in the figure below.

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Y (s) s24 z (s)

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Step 3
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Z(s)Y(s) (1) U(s) Us)Z(s), Since - s) U(s) 1 (2) 't+,5 Comparing the equation (1) with equation (2) we get, Z (s) 1 (3) _(s) And Y (s (4) Z (s)

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