Page 323 - Modern Control Systems

Design Problems 297
Load
disturbance
Controller G(s)
LO lt(s)
Desired irv-* K I io(s)
FIGURE DP4.1 X —rA-* s + 4 Actual
Speed control speed speed
system. I

that 10 < /C < 25. Determine a suitable value for [17]. The laser allows the ophthalmologist to apply
the gain K. heat to a location in the eye in a controlled manner.
Many procedures use the retina as a laser target. The
DP4.2 The control of the roll angle of an airplane is
achieved by using the torque developed by the ailerons. retina is the thin sensory tissue that rests on the inner
A linear model of the roll control system for a small surface of the back of the eye and is the actual trans-
experimental aircraft is shown in Figure DP4.2, where ducer of the eye, converting light energy into electrical
pulses. On occasion, this layer will detach from the
G(.v) = . wall, resulting in death of the detached area from lack
2
.v + 45 + 9 of blood and leading to partial or total blindness in
The goal is to maintain a small roll angle 6 due to dis- that eye. A laser can be used to "weld" the retina into
turbances. Select an appropriate gain KK X that will its proper place on the inner wall.
reduce the effect of the disturbance while attaining a Automated control of position enables the oph-
desirable transient response to a step disturbance, with thalmologist to indicate to the controller where lesions
0 f/(/) = 0. To obtain a desirable transient response, let should be inserted. The controller then monitors the
KK : < 35. retina and controls the laser's position so that each
DP4.3 The speed control system of Figure DP4.1 is altered lesion is placed at the proper location. A wide-angle
so that G(s) = l/(.v + 5) and the feedback is K u as video-camera system is required to monitor the
shown in Figure DP4.3. movement of the retina, as shown in Figure DP4.4(a).
If the eye moves during the irradiation, the laser
(a) Determine the range of /(| allowable so that the must be either redirected or turned off. The position-
steady state is e ss ^ 1 %. control system is shown in Figure DP4.4(b). Select an
(b) Determine a suitable value for K^ and K so that appropriate gain for the controller so that the tran-
the magnitude of the steady-state error to a wind sient response to a step change in r{t) is satisfactory
disturbance T d{i) - 2t mrad/s, 0 < t < 5 s, is and the effect of the disturbance due to noise in the
less than 0.1 mrad. system is minimized. Also, ensure that the steady-state
DP4.4 Lasers have been used in eye surgery for more error for a step input command is zero. To ensure
than 25 years. They can cut tissue or aid in coagulation acceptable transient response, require that K < 10.

TAs)

FIGURE DP4.2 0(s)
Control of the roll Roll angle
angle of an
airplane.

TAs)
1 G(s)
K 1
IO.I(S) -ti- — • s + 5
k Speed
FIGURE DP4.3
Speed control
system. * i Tachome ter