Backstepping Sliding Mode Control

Author: CislunarSpace

Site: https://cislunarspace.cn

Definition

Backstepping sliding mode control combines backstepping methodology with sliding mode control. Backstepping handles strict-feedback nonlinear systems through recursive virtual control design, while sliding mode provides robustness against uncertainties and disturbances.

Design Principles

Standard Backstepping

For a strict-feedback system:

x˙1=x2+f1(x1)x˙2=x3+f2(x1,x2)⋮x˙n=fn(x)+g(x)u\begin{aligned} \dot{x}_1 &= x_2 + f_1(x_1) \\ \dot{x}_2 &= x_3 + f_2(x_1, x_2) \\ &\vdots \\ \dot{x}_n &= f_n(x) + g(x)u \end{aligned}

Sliding Mode Enhancement

Introduce sliding mode terms at each Lyapunov design step:

Vi=Vi−1+12si2V_i = V_{i-1} + \frac{1}{2}s_i^2

Applications in Stratospheric Airships

Attitude Control System

ChannelModel CharacteristicControl Strategy
PitchLongitudinal motion couplingBackstepping SMC
YawAffected by crosswindBackstepping SMC + Feedforward
RollIndependent controlSMC

References

  • Krstic M, et al. Nonlinear and Adaptive Control Design[M]. Wiley, 1995.
  • Wang H, et al. Backstepping Sliding Mode Control for Stratospheric Airship[J]. AIAA Guidance, Navigation, and Control Conference, 2024.