Sliding-Mode Control in Detail
Sliding-mode control forces the state onto a designed surface and holds it there, giving strong robustness to matched uncertainty at the cost of chattering.
The sliding surface
Sliding-mode control defines a surface in state space, a sliding manifold, on which the desired reduced-order dynamics live. The controller drives the state to this surface and then keeps it there. Once confined to the surface, the closed-loop behavior is governed entirely by the surface's definition, independent of the plant's uncertain parameters and matched disturbances. This invariance is the method's signature strength.
Reaching and sliding
Design has two phases. The reaching law ensures the state approaches the surface from any initial condition; a common choice makes the surface variable and its derivative satisfy a reaching condition, guaranteeing the surface is hit in finite time. On the surface, the equivalent control keeps the state sliding. Robustness comes from a high-gain switching term that dominates any matched uncertainty within a known bound, forcing the surface variable to zero regardless of the disturbance.
Chattering and remedies
The discontinuous switching that provides robustness also excites high-frequency oscillation, chattering, which stresses actuators and can excite unmodeled dynamics. Remedies include a boundary layer that smooths the switch, at the price of a small steady-state region, higher-order sliding modes such as the super-twisting algorithm that hide the discontinuity in a derivative and produce continuous control with finite-time convergence, and observer-based schemes. Only matched uncertainty is rejected; unmatched uncertainty requires structural methods like backstepping.
- State is forced onto and held on a sliding surface
- On-surface dynamics are invariant to matched uncertainty
- Discontinuous switching gives robustness but causes chattering
- Boundary layers and higher-order modes reduce chattering
Sliding-mode control also underlies robust observers, sliding-mode observers, which reconstruct states and even estimate disturbances from the equivalent injection. It is closely related to Lyapunov redesign with a discontinuous term.
For a design-stage nonlinear loop with bounded matched disturbances, a higher-order sliding-mode controller would give robust finite-time regulation with reduced chattering, evaluated in simulation.