Time Efficient Rate Feedback Tracking Controller with Slew Rate and Control Constraint

TL;DR

This work tackles time-efficient attitude tracking for Earth-observation satellites under slew-rate and control-torque constraints by formulating a finite-time sliding-mode controller that explicitly shapes the body-frame rate via a regulating rate aligned with the instantaneous eigen-axis. The method defines a sliding surface $\mathbf{s}=\boldsymbol{\omega}_D+\boldsymbol{\omega}_R-\boldsymbol{\omega}_B$ and derives a robust control law that drives $\mathbf{s}$ to zero in finite time while respecting bounds on $\boldsymbol{\omega}_B$ and $\mathbf{u}$. A regulating-rate design combines maximum-acceleration limits, rate saturation, and an eigen-axis trajectory to realize a trapezoidal (and modified trapezoidal) rate-profile that remains practical under low control frequency and reduces actuator chatter. The approach is validated through simulations of rest-to-rest maneuvers and two practical imaging sequences (SPOT and STRIP), demonstrating effective constraint satisfaction and comparable reorientation times to bang-bang-like profiles, with the modified trapezoidal profile offering smoother torque profiles for real implementations.

Abstract

This paper proposes a time-efficient attitude-tracking controller considering the slew rate constraint and control constraint. The algorithm defines the sliding surface, which is the linear combination of command, body, and regulating angular velocity, and utilizes the sliding surface to derive the control command that guarantees finite time stability. The regulating rate, which is an angular velocity regulating the attitude error between the command and body frame, is defined along the instantaneous eigen-axis between the two frames to minimize the rotation angle. In addition, the regulating rate is shaped such that the slew rate constraint is satisfied while the time to regulation is minimized with consideration of the control constraint. Practical scenarios involving Earth observation satellites are used to validate the algorithm's performance.

Figures (10)

• Figure 1: Trapezoidal acceleration profile for (a) $\tau_2>0$ (b) $\tau_2 < 0$
• Figure 2: Sample $(\theta_e - \omega_R)$ profile for (a) large $\tau_1$, $\tau_3$ (b) small $\tau_1$, $\tau_3$
• Figure 3: Result of Trapezoidal Profile (a) $\theta_e$, $\lVert \boldsymbol{\omega}_e\rVert$ (b) $\lVert \boldsymbol{\omega}_\mathcal{B} \rVert$ (c) $u_i,\ i=x,y,z$ (d) $\lVert \textbf{u} \rVert$
• Figure 4: Result of Modified Trapezoidal Profile (a) $\theta_e$, $\lVert \boldsymbol{\omega}_e\rVert$ (b) $\lVert \boldsymbol{\omega}_\mathcal{B} \rVert$ (c) $u_i,\ i=x,y,z$ (d) $\lVert \textbf{u} \rVert$
• Figure 5: Norm of torque command comparison when control frequency is 100 Hz