Understanding Chattering in Control Systems: Causes and Stability Analysis

Feb 09, 2026

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Chattering is a phenomenon observed in control systems, primarily caused by unmodeled dynamics and limitations in switching frequency. This document explores the underlying causes of chattering, emphasizing the effects of fast dynamics that are typically ignored in ideal models. It presents the Singular Perturbation Theory, establishing that if a system's equilibrium point is asymptotically stable, it remains so despite chattering influences. An example based on an inverted pendulum system illustrates these concepts, highlighting the implications for plant dynamics and stability analysis.

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Understanding Chattering in Control Systems: Causes and Stability Analysis

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m n chattering INTRODUCTION ■ Causes of Chattering 1. Fast dynamics disregarded in an ideal model (unmodeled dynamics) 2. Switching frequency limitation * Discrete time system (discretization chattering)

Singular Perturbation Theory << 1 Formally: Preposition: If the equilibrium point of the system is asymptotically stable, then

Example where a and b are negative constant while c and d are positive constant values. Those equations govern a simple ‘inverted pendulum’ system when is angular displacement and the system is known to be unstable for .