Q3 (a) Consider the transfer function system below. Y(s) s2 + 4s + 6 U(s) s3 + 6s2 + 4s + 2 Obtain a state-space representation of this system showing all intermediate steps. Briefly describe the characteristics of signal flow diagrams, and explain how you convert the state equations of a system (for example, a system like in part (a)) into a signal flow diagram. (b) It is required to design a state-feedback controller for the system defined in part (a) with the desired closed-loop poles at: (c) s = -1+ 2j; s = -5 Determine the gain values of the state feedback vector for this design.

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Q3
(a)
Consider the transfer function system below.
s2 + 4s + 6
Y(s)
U(s) s3 + 6s2 + 4s + 2
Obtain a state-space representation of this system showing all intermediate
steps.
Briefly describe the characteristics of signal flow diagrams, and explain how
you convert the state equations of a system (for example, a system like in part
(a)) into a signal flow diagram.
(b)
It is required to design a state-feedback controller for the system defined in part
(a) with the desired closed-loop poles at:
(c)
s = -1+ 2j;
s = -5
Determine the gain values of the state feedback vector for this design.
Transcribed Image Text:Q3 (a) Consider the transfer function system below. s2 + 4s + 6 Y(s) U(s) s3 + 6s2 + 4s + 2 Obtain a state-space representation of this system showing all intermediate steps. Briefly describe the characteristics of signal flow diagrams, and explain how you convert the state equations of a system (for example, a system like in part (a)) into a signal flow diagram. (b) It is required to design a state-feedback controller for the system defined in part (a) with the desired closed-loop poles at: (c) s = -1+ 2j; s = -5 Determine the gain values of the state feedback vector for this design.
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