Actuator Saturation

Definition

Actuator (input) saturation is the hard bound on commanded control effort: the applied torque $\mathrm{sat}(\tau )$ equals the demand $\tau$ only while $|{\tau }_i|\le {\tau }_m$ and clips beyond it, so the realized dynamics differ from the commanded ones by a residual term. In yao2021adaptive’s free-flying space-manipulator tracking controller the saturation is folded multiplicatively into the equation of motion and the resulting residual is absorbed by the adaptive (RBF-network) compensation, preserving the prescribed-performance guarantee under bounded actuation.

Key Equations

Saturated Euler–Lagrange dynamics (canonical inertia $M$, Coriolis $C$):
$M(q)\ddot{q}+C(q,\dot{q})\dot{q}=\mathrm{sat}(\tau )+d.$
The saturation is factored multiplicatively, $\mathrm{sat}(\tau )=\Theta (\tau )\tau$, yielding
$M\ddot{q}+C\dot{q}=\tau +\Delta \tau +d,\Delta \tau =(\Theta (\tau )-I_n)\tau ,$
where the residual $\Delta \tau$ is the saturation deficit — gloss: lumped with the disturbance/uncertainty and approximated by the adaptive law so closed-loop boundedness (SGUUB) survives the input limit.

Source Support

• yao2021adaptive — the multiplicative saturation model $\mathrm{sat}(\tau )=\Theta (\tau )\tau$ (Eqs. 2–4), the residual $\Delta \tau$, and its absorption into the BLF/RBFNN backstepping controller with a guaranteed prescribed-performance envelope under ${\tau }_m$ limits.

Related Topics

• trajectory_tracking — saturation degrades the tracking loop unless its residual is compensated.
• prescribed_performance_control — the envelope that must survive the input limit.
• barrier_lyapunov_function — the BLF enforcing that envelope in yao2021adaptive.
• ffsm_dynamics — the free-flying manipulator dynamics the saturated torque drives.

Open Questions

• yao2021adaptive hides base/arm coupling inside the uncertain $M,C$; for a fully-actuated 6-DOF base with explicit coupling, how should the saturation budget be allocated between base-translation and arm actuators?