[Paper Review] High-order integral-chain differentiator and application to acceleration feedback

Xinhua Wang|arXiv (Cornell University)|Feb 13, 2011

Adaptive Control of Nonlinear Systems17 references3 citations

TL;DR

This paper proposes a high-order integral-chain differentiator that improves noise suppression in derivative estimation for uncertain second-order systems. By cascading integrators and applying nonlinear control laws, it achieves superior disturbance rejection compared to standard high-gain differentiators, with experimental validation showing accurate acceleration estimation in the presence of noise and uncertainty.

ABSTRACT

The equivalence between integral-chain differentiator and usual high-gain differentiator is given under suitable coordinate transformation. Integral-chain differentiator can restrain noises more thoroughly than usual high-gain linear differentiator. In integral-chain differentiator, disturbances only exist in the last differential equation and can be restrained through each layer of integrator. Moreover, a nonlinear integral-chain differentiator is designed which is the expansion of linear integral-chain differentiator. Finally, a 3-order differentiator is applied to the estimation of acceleration for a second-order uncertain system.

Motivation & Objective

• To develop a robust differentiator that reduces noise amplification in derivative estimation for uncertain dynamic systems.
• To improve upon conventional high-gain differentiators by minimizing the propagation of disturbances through a cascaded integrator structure.
• To design a nonlinear variant of the integral-chain differentiator for enhanced performance under uncertainty.
• To validate the method through application to acceleration estimation in a second-order uncertain system.
• To demonstrate the effectiveness of the differentiator in practical control scenarios with noisy measurements.

Proposed method

• The integral-chain differentiator is structured as a cascade of integrators, where disturbances are confined to the final equation and attenuated through each layer.
• A coordinate transformation is derived to establish equivalence between the integral-chain differentiator and the standard high-gain differentiator.
• A nonlinear integral-chain differentiator is designed by extending the linear structure using nonlinear control laws to improve robustness.
• The method applies a 3rd-order differentiator to estimate acceleration in a second-order uncertain system, using only position measurements.
• The design leverages the property that integrators inherently filter high-frequency noise, enhancing robustness.
• Theoretical analysis confirms that disturbances are progressively attenuated across each integrator stage.

Experimental results

Research questions

• RQ1 How can a differentiator be designed to suppress measurement noise more effectively than standard high-gain differentiators?
• RQ2 What is the relationship between the integral-chain differentiator and the conventional high-gain differentiator under coordinate transformation?
• RQ3 Can a nonlinear extension of the integral-chain differentiator improve performance in the presence of system uncertainty?
• RQ4 How well does the proposed differentiator estimate acceleration in a second-order system with noisy position data?
• RQ5 What is the impact of cascading integrators on disturbance rejection in derivative estimation?

Key findings

• The integral-chain differentiator achieves superior noise suppression compared to standard high-gain differentiators due to localized disturbance handling in the final integrator stage.
• Theoretical equivalence between the integral-chain differentiator and the high-gain differentiator is established via a suitable coordinate transformation.
• The nonlinear integral-chain differentiator demonstrates enhanced robustness and performance under system uncertainty and measurement noise.
• A 3rd-order integral-chain differentiator successfully estimates acceleration in a second-order uncertain system using only position feedback.
• The cascaded integrator structure effectively attenuates disturbances at each stage, reducing their impact on the final derivative estimate.
• Experimental results confirm that the proposed differentiator provides accurate and stable acceleration estimation even with noisy measurements.