Small-Satellite Attitude Control Using Continuous But Only Piecewise-Continuously Differentiable Sinusoidal Controls

We consider attitude control of a rigid body (e.g., small satellite) with internal rotating-mass actuators that, unlike reaction wheels, cannot perform complete rotations. Instead, these actuators are limited to γ radians of total rotation. We present and analyze attitude-feedback control algorithms for this system, where the controls are continuous but only piecewise-continuously differentiable sinusoids, that is, signals that are continuous and piecewise sinusoidal but whose derivatives contain discontinuities. The main analytic results show these attitude-feedback controls achieve asymptotic setpoint tracking for a constant attitude command and approximate command following for a time-varying attitude command. We also demonstrate the setpoint tracking algorithm in simulation. Finally, we present single-axis closed-loop attitude control experiments for a small-satellite system on a three-dimensional air bearing.