. Figure Ql shows a block diagram of the positioning control system of the Hubble space telescope. Given that K = 100 and K1 = 12, derive the closed loop transfer functions relating angular position C(s) to both the commanded input R(s) and a general disturbance D(s). Determine the response of the telescope (1) to a unit step input in R(s). Hence deduce the telescope's response to a unit step disturbance D(s). D(s) R(s) C(s) K KI Figure QI.

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1. Figure Q1 shows a block diagram of the positioning control system of the Hubble space telescope. Given
that K = 100 and K1 = 12, derive the closed loop transfer functions relating angular position C(s) to
both the commanded input R(s) and a general disturbance D(s). Determine the response of the telescope
c(t) to a unit step input in R(s). Hence deduce the telescope's response to a unit step disturbance D(s).
D(s)
R(s)
C(s)
K
s2
Figure Q1.
2. The ailerons of a large airliner are positioned through an angle da by servo actuators which respond to
the pilot's lateral stick displacement y, Figure Q2. Derive the closed loop transfer function of
relating the aileron displacement to the pilot's stick motions.
system
y(s)
8«(8)
1
0.1s + 1
Figure Q2.
3. Figure Q3 shows the block diagram of an electric locomotive motor where wd is the desired angular
velocity of motor as set by the driver whilst w is the actual angular velocity achieved. The block G2(s)
represents the load transfer function (i.e. the locomotive) whilst G,(s) is the armature controller transfer
function. The locomotive motor can experience torque disturbances due to braking, given by Ta(s).
Derive the transfer functions relating output angular velocity to desired angular velocity,
and output
angular velocity to torque disturbance,
T given
10
G|(s) =
1
G2(s) =
s+ 1
2s + 0.5
Ta(s)
wa(s)
w(s)
540
G|(s)
G2(s)
0.1
Figure Q3.
Transcribed Image Text:1. Figure Q1 shows a block diagram of the positioning control system of the Hubble space telescope. Given that K = 100 and K1 = 12, derive the closed loop transfer functions relating angular position C(s) to both the commanded input R(s) and a general disturbance D(s). Determine the response of the telescope c(t) to a unit step input in R(s). Hence deduce the telescope's response to a unit step disturbance D(s). D(s) R(s) C(s) K s2 Figure Q1. 2. The ailerons of a large airliner are positioned through an angle da by servo actuators which respond to the pilot's lateral stick displacement y, Figure Q2. Derive the closed loop transfer function of relating the aileron displacement to the pilot's stick motions. system y(s) 8«(8) 1 0.1s + 1 Figure Q2. 3. Figure Q3 shows the block diagram of an electric locomotive motor where wd is the desired angular velocity of motor as set by the driver whilst w is the actual angular velocity achieved. The block G2(s) represents the load transfer function (i.e. the locomotive) whilst G,(s) is the armature controller transfer function. The locomotive motor can experience torque disturbances due to braking, given by Ta(s). Derive the transfer functions relating output angular velocity to desired angular velocity, and output angular velocity to torque disturbance, T given 10 G|(s) = 1 G2(s) = s+ 1 2s + 0.5 Ta(s) wa(s) w(s) 540 G|(s) G2(s) 0.1 Figure Q3.
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