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MEM 255 Midterm Sample Problems
- For the system shown, determine:
a. The transfer function U ( s ) → Y ( s ),
b. The impulse and step responses
U s ( ) (^) Y s ( )
2 ( s +4)
2 2
s s +
3 2 6
s s
- Consider a system with transfer function
G s s
a. Compute the response to the input u t ( ) = cos( t ),
b. Sketch the bode plot, c. Repeat part a) for the transfer function
s G s s
- Consider a dc motor driving a mechanical load, similar to an antenna positioning servo. The equations of motion are:
2 2
b B
a a a a b a
m T a
m
d t v t K dt di t R i t L v t v t dt T t K i t d t d t J C T t dt dt
Construct the state equations where the applied armature voltage is the input, and the angular position is the output.
va ( ) t
θ ( ) t
Nomenclature v b Motor back emf i a Armature current v a Armature voltage
θ Load angular position
T m Mechanical torque R a Armature resistance L a Armature inductance K (^) B Motor back emf coefficient K (^) T Motor torque coefficient J Motor & load inertia C Friction constant
- Using the partial fraction expansion method compute the step input response of the system shown below. U ( s ) Y ( s ) 2 12 1 7 12
s s s
- Consider the ship shown. A model used to study the yaw dynamics for a variety of stable and unstable ships is
T T 1 2 ψ ^ + ( T 1 + T 2 ) ψ + ψ = K ( δ + T 3 δ)
where the parameters are determined
for each specific ship. Determine state variable and a transfer function models that relate the output
T T 1 , 2 (^) , T 3 , K
ψ to the input δ.
- Find the transfer function for a system described by the state space model:
[ ] =[ ]
0 0 1 1 1 0 0 , 0 , 1 1 1 , 0 0 1 0 0
A b c d
⎡ −⎤ ⎡ ⎤ = ⎢^ ⎥^ = ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ ⎢⎣ ⎥⎦ ⎢ ⎥⎣ ⎦
V , velocity
, heading
β , sideslip
ψ
δ , rudder
- Consider the magnetically suspended ball shown below. An equilibrium voltage V
maintains a current that induces a magnetic field sufficient to hold the ball at a gap
. The linearized equations governing the motion of the ball are:
eq i eq h eq
