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Example A rotational mechanical system is shown schematically as follows. Given that: Do the following for the system Find the differential equation. ( ) Find the transfer function G ( s ) = θ ( s )/ T (s). ( ) - PowerPoint PPT Presentation
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Example A rotational mechanical system is shown schematically asfollows. Given that:
Do the following for the system
1. Find the differential equation. ( )
2. Find the transfer function G(s) = θ(s)/T(s). ( )
3. Find the poles.( )
4. Is this system stable or not? Why? (Stable as all poles are in the LHP)
5. Find ζ and ωn.( )
6. Evaluate %OS, Ts, Tp, and Tr of the step response.
( )
7. Find the analytical expressions for the frequency response.
( )
7. Determine the system ouptut, θ(t), in the steady state if the system input is . ( )
8. Suppose this system is the plant of a unity feedback system, find the steady-state error of the feedback system if the input is a step. (8/9)
,T
D
K
J
m/radN 8 and ,s/radm-N 4 ,mkg 2 2 KDJ
)2sin(5)( ttT
T 842
842
1)(
2
sSsG
js 31
rad/s 2 ,5.0
sec82.0 sec,8.1 sec,4 ,3.16% rps TTTOS
21
222 28
4tan)( ,
16)28(
1)(
jwGjwG
)2
2sin(8
5)(
tt