Nonlinear-Dependent Equivalent Input Disturbance Method for Disturbance Rejection in Nonlinear Systems

Abstract

Nonlinear systems in industrial applications are often subject to unknown and time-varying external disturbances, which pose significant challenges to disturbance rejection design. To address this issue, this paper proposes a nonlinear-dependent equivalent input disturbance (ND-EID) method that enhances disturbance rejection performance while explicitly preserving their intrinsic nonlinear dynamics. Unlike conventional EID-based approaches, the proposed method introduces a dual-error compensation mechanism that explicitly accounts for estimation errors induced by both the observer dynamics and the disturbance filtering process, thereby improving estimation accuracy and compensation effectiveness. A Lyapunov-based stability criterion is established for the resulting nonlinear closed-loop system and reformulated as a tractable linear matrix inequality using convex optimization techniques. Moreover, a frequency-domain analysis framework incorporating nonlinear information is developed to reveal the disturbance attenuation mechanism and clarify the influence of observer gain on disturbance rejection performance. Comparative simulation studies on a two-inertia torsional system demonstrate that the proposed ND-EID method achieves enhanced disturbance rejection and better preservation of the system’s intrinsic nonlinear dynamics compared with conventional EID-based techniques. Note to Practitioners—Industrial motion-control systems, such as high-speed drives and robotic mechanisms, often experience performance degradation caused by load variations, nonlinear effects, and time-varying external disturbances. The proposed nonlinear-dependent equivalent input disturbance method provides a disturbance-rejection solution for nonlinear systems with affine input structures by retaining known nonlinear dynamics instead of treating them as part of the disturbance. This feature is useful when an accurate nonlinear model is available but the external disturbance is difficult to characterize. For implementation, the controller and observer gains can be obtained offline by solving the proposed linear matrix inequalities, while the dual-error compensation parameters can be tuned to enhance disturbance attenuation. The resulting observer and disturbance-compensation structure can then be implemented online without requiring an inverse plant model, a strict-feedback transformation, or a Takagi–Sugeno fuzzy representation. Experimental results on a two-inertia torsional system show that incorporating the nonlinear dependence reduces disturbance-induced output fluctuations compared with the corresponding EID-based method.