834 D. W. CHILDS J. SPACECRAFT2) Simplicity. The control logic cited in Eq. (28) is extremely simple, and the results of this study indicate that the servomechanism requirements for implementation of the system are modest, both in terms of peak force and frequency response requirements. Sensor requirements are also modest, since only w and co y must be measured. The implementation of this system would be considerably simpler than competitive systems such as fluid-displacement systems, movable mass on boom arrangements, inertia wheels, CMG's, etc.3) Power Requirements. The low level of peak and sustained force levels required for the controller indicates a quite low level of power consumption. A movable mass controller has a significant advantage, in this respect, over CMG's or inertia wheels.Future communications satellites will employ multiple narrow-beam antennas covering widely separated areas of the Earth. Some of these narrow beams must cover more than one ground station, necessitating coverage of stations located at the fringes of the antenna beams. This imposes a requirement for high pointing accuracies; current estimates for satellites to be put into service in 1972 and beyond being for beam pointing accuracies of 0.1° or less. An additional requirement for future satellites will be longer life-times; operating lives of 10 yr are presently being considered. Attitude stabilization systems using momentum and reaction wheels in various combinations are evaluated based on these requirements. The candidate wheel stabilization systems are discussed in terms of their respective design parameters and performance characteristics. Comparisons are made between the systems on the basis of wheel size, weight, and power required to achieve high pointing accuracies.
Nomenclature
B= antenna beam width E = antenna elevation angle in radians H z = yaw wheel momentum h = angular momentum of pitch wheel HR = required control momentum I X) I y ,I z = principal moments of inertia K = autopilot gain Ke,Ke,Ki = controller rate, position and integral gain, respectively KD = desaturation gain k = factor relating required momentum to peak disturbance torque, or ratio of yaw gain to roll gain M Xc ,M Zc = control moments about roll and yaw axes, respectively N = correction factor n = number of days between momentum desaturation PP,PA = peak and average power, respectively P™,PR -momentum wheel power and three-axis reaction wheel system power, respectively s = Laplace operator T c = cyclic disturbance torque TM,TMP = motor torque for disturbances and peak motor torque, respectively T p = peak disturbance torque Ts = inertial fixed disturbance torque T X) Tz = disturbance torques about roll and yaw axes, respectively W = weight of momentum control system a = offset angle of roll-yaw coupled control thruster € = attitude pointing error = roll angle \l/ = yaw angle 6 = pitch angle T = lead time constant in control system r m -motor time constant T Z = nonminimum phase zero time constant wo = orbital rate, 7.29 X 10~5 rad/sec for sy...
