Large microwave antennas have become increasingly important for radio astronomy and satellite tracking. A large antenna with a diameter of 60 ft, for example, is subject to large wind gust torques. A proposed antenna is required to have an error of less than 0.10° in a 35 mph wind. Experiments show that this wind force exerts a maximum disturbance at the antenna of 200,000 ft lb at 35 mph, or the equivalent to 10 volts at the input Td(s) to the amplidyne. One problem of driving large antennas is the form of the system transfer function that possesses a structural resonance. The antenna servo system is shown in Figure P4.5. The transfer function of the antenna, drive motor, and amplidyne is approximated by

where Ï‚ = 0.707 and wn = 15. The transfer function of the power amplifier is approximately

where Ñ‚ = 0.15 second.
(a) Determine the sensitivity of the system to a change of the parameter ka.
(b) The system is subjected to a disturbance Td(s) = 10/s. Determine the required magnitude of ka in order to maintain the steady-state error of the system less than 0.10° when the input R(s) is zero.
(c) Determine the error of the system when subjected to a disturbance Td(s) = 10/s when it is operating as an open-loop system (ks = 0) with R(s) = 0.
Figure P4.5
Antenna control system.

Transcribed Image Text:

Gi(s) = Ts + 1. Tts) Power amplifier Gl(s) s) Position (radians) CAntenna, drive motor +and amplidyne Gs) Sensor