Page 71 - Modern Control Systems

Advanced Problems 45

Light Iron-
snai oojeci MEMS actuator
Kv (not 10 scale)

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mirror
Wavefront sensor
Controller
and algorithms
FIGURE AP1.4 Extremely large optical telescope with deformable mirrors
for atmosphere compensation.

AP1.4 Adaptive optics has applications to a wide variety of control one of the deformable mirrors to compensate for
key control problems, including imaging of the human the distortions in the incoming light. Figure AP1.4 shows
retina and large-scale, ground-based astronomical a diagram of the telescope with a single deformable mir-
observations [98]. In both cases, the approach is to use a ror. Suppose that the mirror has an associated MEMS
wavefront sensor to measure distortions in the incoming actuator that can be used to vary the orientation. Also,
light and to actively control and compensate to the er- assume that the wavefront sensor and associated algo-
rors induced by the distortions. Consider the case of an rithms provide the desired configuration of the de-
extremely large ground-based optical telescope, possi- formable mirror to the feedback control system.
bly an optical telescope up to 100 meters in diameter.
The telescope components include deformable mirrors AP1.5 The Burj Dubai is the tallest building in the world
actuated by micro-electro-mechanical (MEMS) devices [94]. The building, shown in Figure API.5, stands at
and sensors to measure the distortion of the incoming
iight as it passes through the turbulent and uncertain at-
mosphere of Earth.
There is at least one major technological barrier
to constructing a 100-m optical telescope.The numeri-
cal computations associated with the control and
compensation of the extremely large optical telescope
10
can be on the order of 10 calculations each 1.5 ms.To
date, this computational power is unachievable. If we
assume that the computational capability will ulti-
mately be available, then one can consider the design
of a feedback control system that uses the available
computational power. We can consider many control
issues associated with the large-scale optical tele-
scope. Some of the controls problems that might be
considered include controlling the pointing of the
main dish, controlling the individual deformable mir-
rors, and attenuating the deformation of the dish due
to changes in outside temperature.
Employing Figure 1.3 as a model for the block dia- FIGURE AP1.5 The world's tallest building in
gram, describe a closed-loop feedback control system to Dubai. (Photo courtesy of Alamy Images.)