Sliding Mode Control

A control method that forces the state onto a designed ‘sliding surface’ via switching, then slides it to the target with strong robustness.

Sliding mode control belongs to the broader family of variable structure control, first studied in the early 1950s by Soviet researchers including Emelyanov and later systematized by Vadim Utkin and others. The design starts with a sliding surface — for instance, using tracking error e to construct s = ė + λe (λ > 0): once s = 0, the error decays to zero as e(0)·exp(−λt). The control law combines an equivalent control term (which holds the state on the surface, computed from the nominal model) with a switching term −k·sign(s) that forces the state back onto the surface whenever it strays. The system first reaches the sliding surface, then slides along it toward the target. As long as k exceeds the upper bound of the disturbance, any disturbance or model error entering through the control channel doesn't change the behavior during the sliding phase, which makes this approach more robust than PID or computed-torque control. The cost is chattering: actuator delay and discrete sampling make the sign function switch rapidly back and forth, producing high-frequency vibration, usually mitigated with a boundary layer (replacing sign with a saturation function) or higher-order sliding modes such as super-twisting.

ExampleFor position tracking on an arm joint with an unknown payload: take s = ė + λe and torque τ = τ_eq − k·sat(s/φ). τ_eq is computed from the nominal model, k is set large enough to cover the upper bound of friction and payload error, sat is the saturation function, and φ is the boundary-layer thickness used to suppress chattering.

Also called

SMC, Variable Structure Control

Related

Robust Control · Adaptive Control · Lyapunov Stability · Feedback Linearization · Active Disturbance Rejection Control · Disturbance Observer

Sources

Sliding mode control - Wikipedia
Variable structure control - Wikipedia