01
Sliding Surface
State motion target; once reached, provides robustness.
Hyperplane s(x)=0 in state space defining the desired reduced-order dynamics.
Sliding Mode Control
Enforcing state trajectories to slide along a switching surface in state space, rendering system dynamics insensitive to a defined class of disturbances and model uncertainties.
Category
Abstraction level
Manipulator control under unknown loadsFTC — fault tolerance as disturbance rejectionElectric vehicles — motor controlRobotic aerial vehicles (quadrotors, VTOL)Maximum power point tracking in photovoltaic systemsSpeed control in electric drives
Define a sliding surface s(x) = 0. Choose a control law u = u_eq + u_sw, where u_eq satisfies the dynamics on the surface and u_sw = -K·sgn(s) enforces the reaching phase. Once s = 0 is reached, the system slides along the surface and its dynamics become insensitive to disturbances satisfying the matching condition.
How to design controllers robust to model uncertainties and disturbances without knowing their exact values — only an upper bound needs to be known.
02
Reaching Law
Reaching phase.
Control component u_sw = -K·sgn(s) ensuring the surface is reached in finite time.
03
Equivalent Control
Sliding mode dynamics.
Control component u_eq that keeps the trajectory on the sliding surface once reached.
Common pitfalls
ChatteringHIGH
Rapid sgn(s) switching generates control oscillations that damage mechanical drive elements and excite high-frequency dynamics.
Boundary layer (replacing sgn with sat), Higher-Order SMC, super-twisting.
K Selection — robustness vs. chattering trade-offMEDIUM
Excessively large K damages drives; too small fails to ensure robustness.
Adaptive gain (adaptive K), estimation of the disturbance upper bound.
1960
Utkin — origins of VSS in the USSR
breakthroughV. I. Utkin and colleagues formalise VSS and SMC theory at the Moscow Institute of Cybernetics.
1977
Utkin — "Variable Structure Systems with Sliding Modes"
breakthroughUtkin's IEEE TAC paper introduces SMC to the Western literature.
1993
Higher-Order SMC (Levant)
breakthroughA. Levant proposes HOSMC eliminating chattering by extending to higher orders; super-twisting algorithm (STA).
2003
SMC for robots — standard tool
SMC becomes a standard robust control method for manipulators and drones in the robotics literature.
CPU AVXPRIMARY
SMC runs on RT CPU; high sampling frequency (>1 kHz) is key for chattering reduction.
FPGAGOOD
FPGAs for ultra-high frequencies (>10 kHz) in electric drives.
ALTERNATIVE TO
H-infinity
H∞ Control (H-infinity) is a robust control method whose design criterion is the minimisation of the H∞-norm of the transfer function from disturbance w to controlled output z: ||T_{zw}||_∞ = sup_ω σ_max(T_{zw}(jω)) < γ. This means output energy is at most γ times the disturbance input energy — the controller is best in the worst case (minimax). The theoretical foundations were laid by Zames (1981); practical Riccati-based synthesis methods were developed by Doyle, Glover, Khargonekar, and Francis (1989). More general LMI (Linear Matrix Inequalities) frameworks — Gahinet & Apkarian (1994) — enable H∞ synthesis for broader system classes. In FTC, H∞ is used as the baseline robust controller (Passive FTC) tolerating small faults subsumed into the uncertainty model. Typical design uses Robust Control Toolbox (MATLAB), Slycot, or cvxpy (Python LMI). Applications: aviation, manipulators, power systems, active vibration isolation.
GO TO CONCEPT| Title | Publisher | Type |
|---|---|---|
| Variable Structure Systems with Sliding Modes V. I. Utkin, 1977. The canonical paper introducing SMC to the Western literature. | IEEE Transactions on Automatic Control | scientific article |
| Sliding Mode Control in Electromechanical Systems (Utkin, Guldner, Shi) Standard SMC reference manual (2nd ed. 2009). | Taylor & Francis / CRC | documentation |
Variable Structure Systems with Sliding Modes
V. I. Utkin, 1977. The canonical paper introducing SMC to the Western literature.
scientific articleIEEE Transactions on Automatic Control
Sliding Mode Control in Electromechanical Systems (Utkin, Guldner, Shi)
Standard SMC reference manual (2nd ed. 2009).
documentationTaylor & Francis / CRC