Sliding Mode Control

Author: CislunarSpace

Site: https://cislunarspace.cn

Definition

Sliding Mode Control (SMC) is a variable structure control method that drives system states to a predefined sliding surface in finite time and maintains them there, achieving robust control against uncertainties and external disturbances.

Basic Principles

Sliding Surface Design

For an n-th order nonlinear system:

x˙=f(x)+g(x)u\dot{x} = f(x) + g(x)u

Design the sliding surface:

s(x)=(ddt+λ)n−1es(x) = \left(\frac{d}{dt} + \lambda\right)^{n-1}e

Where e=x−xde = x - x_d is tracking error, λ>0\lambda > 0 is the design parameter.

Reaching Condition

Using exponential reaching law:

s˙=−εsgn(s)−ks,ε>0,k>0\dot{s} = -\varepsilon \text{sgn}(s) - ks, \quad \varepsilon > 0, k > 0

Chattering Problem

Chattering is an inherent issue caused by high-frequency switching:

IssueImpact
High-frequency switchingActuator wear
Energy consumptionReduced efficiency
Thermal effectsController overheating

Suppression Methods

MethodPrinciple
Boundary layerSaturated function replaces sign function
Higher-order SMCHigher-order switching smoothing
Observer-basedEstimate uncertainties to reduce switching
Fuzzy smoothingFuzzy logic for smooth switching

Applications in Stratospheric Airships

Stratospheric airships face uncertainties including:

  • Aerodynamic parameter perturbation (velocity, temperature changes)
  • Wind disturbances (gusts, turbulence)
  • Buoyancy variations (helium leakage, thermal effects)

References

  • Gao W. Variable Structure Control Theory[M]. Science Press, 2023.
  • Utkin V I. Sliding Mode Control in Electro-Mechanical Systems[M]. CRC Press, 2024.