## [answered] MEM 255 - Fall 2016 Homework 5 November 18, 2016 Name: Redu

Pleas solve the following questions in detail. MATLAB may be used.

MEM 255 - Fall 2016 Homework 5 November 18, 2016 Name:

1. Reduce the following block diagram to a single transfer function G(s) = C(s)

R(s) : 2. Reduce the following block diagram to a single transfer function G(s) = C(s)

R(s) : 3. For the following state space systems draw a signal flow graph: 0

0

1

0

0

1 x + 0 u

x? = 0

1

?2 ?4 ?6





y= 1 1 0 x 0

1

0

0

x? = 0 ?3 1 x + 1 u

?3 ?4 ?6

1





y= 1 2 0 x

4. Reduce the following signal flow graph determine the transfer function G(s) = C(s)

R(s) : 5. Draw the signal flow graph for the following T.F. and find the state space notation:

G(s) = s3 s2 + 2s + 6

+ 5s2 + 2s + 1 6. Draw the signal flow graph for the following block diagram and find the state space notation: 7. Draw the signal flow graph for the following block diagram and find the state space notation assuming

?2 is the output: 8. Determine how many roots are in the LHP, RHP, and on jw-axis using Routh-Hurwitz:

P (s) = s5 + 3s4 + 5s3 + 4s2 + s + 3

P (s) = s5 + 6s3 + 5s2 + 8s + 20

9. For the following block diagram and transfer funciton, determine the value of K for closed-loop stability. G(s) = MEM 255 - Fall 2016 K(s + 2)

s(s ? 1)(s + 3) Homework 5 Page 2 of 2

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