Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Chattering Reduction for a Second-Order Actuator via Dynamic Sliding Manifolds

Patricia Nöther, Lars Watermann, Johann Reger

Abstract

We analyze actuator chattering in a scalar integrator system subject to second-order actuator dynamics with an unknown time constant and first-order sliding-mode control, using both a conventional static sliding manifold and a dynamic sliding manifold. Using the harmonic balance method we proof that it is possible to adjust the parameters of the dynamic sliding manifold so as to reduce the amplitude of the chattering in comparison to the static manifold. The proof of concept is illustrated with an example.

Chattering Reduction for a Second-Order Actuator via Dynamic Sliding Manifolds

Abstract

We analyze actuator chattering in a scalar integrator system subject to second-order actuator dynamics with an unknown time constant and first-order sliding-mode control, using both a conventional static sliding manifold and a dynamic sliding manifold. Using the harmonic balance method we proof that it is possible to adjust the parameters of the dynamic sliding manifold so as to reduce the amplitude of the chattering in comparison to the static manifold. The proof of concept is illustrated with an example.
Paper Structure (8 sections, 2 theorems, 37 equations, 4 figures, 1 table)

This paper contains 8 sections, 2 theorems, 37 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Chattering Analysis for a Static Sliding Manifold
  4. Dynamic Sliding Manifold
  5. Stability Constraints
  6. Chattering Analysis
  7. Example
  8. Conclusion

Key Result

Theorem 1

For system eq:system subject to actuator dynamics eq:actuator_SOL with $\tau$ unknown, a dynamic sliding manifold eq:DSM can be chosen such that the chattering amplitude of the sliding variable $\sigma$ is smaller than for the static sliding manifold eq:SM_static.

Figures (4)

  • Figure 1: Block diagram of the sign-function and the partially closed loop $\Sigma_{\star}$ with $\star \in \left\lbrace \mathrm{S}, \mathrm{D} \right\rbrace$.
  • Figure 2: Harmonic Balance analysis for SMC and DSM each with $\tau = 0.01s$ and $\tau = 0.1s$
  • Figure 3: Simulation with $\tau = 0.01s$
  • Figure 4: Simulation with $\tau = 0.1s$

Theorems & Definitions (6)

  • Theorem 1
  • proof
  • Remark 1
  • Remark 2
  • Theorem 2
  • proof