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A closed-loop servomechanism is designed in order to control the angular position of a rotatable turbine blade in a nuclear plant and is stabilised by means of additional acceleration feedback (see figure.Q1 below):
The moment of inertia of the turbine blade is 1kg/m2, with the viscous damping torque constant, c, per radian per second being 10.0N.m. The motor torque is given by T = 400 [? + k d2θout] N.m. Where:
? = (θin - θout) is the angular positional error in radians between the input and output shafts and k. d2θout/(dt2) defines the additional feedback signal.
a. Show that the system equation is defined as: G(t)-1= 2.5 x 10-3{(1 - 400k)D2 + 10D + 400}
b. Finally, determine the value that is to be assigned to k, in order that the damped natural frequency of the transient response will be 6.37 Hz and also calculate the damping constant. [Note: a hint for solution for this part of the problem is shown overpage].
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Find the value for required Q for the first filter.
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