UCF Dynamics and Control Questions
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Problem #1 (20 points)
Find the Laplace Transform of the following set of differential equations representative of a
control actuator for an aerospace system. Assume zero initial conditions.
0.897??? ? 0.154?? + 2.634?? + 0.23?? = 0
??? ? 0.122?? ? ?? + 0.011?? = 0
Problem #2 (50 points)
For the frictionless mass-spring-damper system given, where k1, k2, c1, and c2 are constant
scalars, obtain the differential equations of motion. Moreover, find the A, B, C, and D matrices.
??2
Let the output be ?? = [??? ].
1
Hint: ??1 = ??1 , ??2 = ??2 , ??3 = ???1 , ??4 = ???2
Bonus (10 points). Obtain the equations of motion now using a different approach
(Lagrangeàequations / Newtonà2nd law).
Problem #3 (30 points)
Given the Dutch Roll mode approximation for the Convair 880 jet,
????? = ?0.1193???? ? 784.9638??? + 21.0382?????
???? = 0.0002???? ? 5.9369??? + 0.0097?????? ? 0.0926??????
Calculate the following transfer functions:
????
??????
,
????
??????
Purchase answer to see full
attachment
Find the Laplace Transform of the following set of differential equations representative of a
control actuator for an aerospace system. Assume zero initial conditions.
0.897??? ? 0.154?? + 2.634?? + 0.23?? = 0
??? ? 0.122?? ? ?? + 0.011?? = 0
Problem #2 (50 points)
For the frictionless mass-spring-damper system given, where k1, k2, c1, and c2 are constant
scalars, obtain the differential equations of motion. Moreover, find the A, B, C, and D matrices.
??2
Let the output be ?? = [??? ].
1
Hint: ??1 = ??1 , ??2 = ??2 , ??3 = ???1 , ??4 = ???2
Bonus (10 points). Obtain the equations of motion now using a different approach
(Lagrangeàequations / Newtonà2nd law).
Problem #3 (30 points)
Given the Dutch Roll mode approximation for the Convair 880 jet,
????? = ?0.1193???? ? 784.9638??? + 21.0382?????
???? = 0.0002???? ? 5.9369??? + 0.0097?????? ? 0.0926??????
Calculate the following transfer functions:
????
??????
,
????
??????
Purchase answer to see full
attachment
Explanation & Answer:
3 Questions
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