Design Problem 4 MAE 171A
Due: June 4, 2014
We consider the design of a satellite attitude control system. The satellite is
assumed to be in drag free space. We are interested in controlling rotation about
its axis of rotational symmetry. We do this by means of a motor and an inertia
wheel mounted on the satellite. The configuration is given in figure 1.
The motor applies a torque to the inertia wheel, and the resulting reaction
torque, acting on the satellite, is used to control its attitude. Angles θ and φ denote
rotational motion of the satellite and the wheel, respectively, relative to inertially
fixed references. Our goal is to design a system to control θ.
A gyro sensor package provides θ as a feedback signal. The controller compares
the input command θc to the feedback signal θ and generates, through a compensator
gain Ka, the voltage v to the motor, i. e. v/e = Ka where e = θc − θ.
The motor applies torque to the inertial wheel, and the resulting torque applied
to the satellite controls its motion.We assume the simple motor model where the
torque and current equations are
M = K1i − K2(
˙θ + φ˙)
i = v/R
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