Small-Satellite Attitude Control Using Continuous Sinusoids With Strict Amplitude Constraints

This article considers attitude control of a rigid body (e.g., small satellite) with internal rotating-mass actuators that, unlike reaction wheels, cannot perform unrestricted rotations. Instead, the rotational stroke of each actuator is limited to $[-\alpha,\alpha]$ rad, where $\alpha > 0$. We present two attitude-feedback control methods. The first method addresses setpoint tracking of constant attitude commands, whereas the second approach addresses command following of time-varying attitude commands. Both methods use control signals that are continuous and piecewise sinusoidal but whose derivatives can contain discontinuities. The main analytic results show that these attitude-feedback controls achieve asymptotic setpoint tracking for a constant attitude command and approximate command following for a time-varying attitude command. The results also show that the controls satisfy the strict actuator amplitude constraint. Each control method is demonstrated in numerical simulations of a small satellite in deep space. Finally, we present single-axis closed-loop attitude control experiments for a small-satellite system on an air bearing.