Improved Extended State Observer for Estimating Disturbances Using Taylor Approximation

Основные понятия

A novel extended state observer (ESO) design that leverages Taylor approximation to estimate disturbances in systems with unobservable disturbance dynamics.

Аннотация

The paper presents an enhanced method for designing extended state observers (ESOs) to estimate both system states and disturbances, particularly for systems where the disturbances are unobservable. The key contributions are:

Formulation of a new extended system model: The authors use Taylor expansion to approximate the integral of the disturbance dynamics, introducing an additional delayed term in the observer. This allows the design of an observer for systems where the standard ESO approach fails due to unobservability.

Stability analysis: The authors provide a Lyapunov-Razumikhin based stability proof for the proposed observer, showing that the estimation error converges exponentially to a bounded region dependent on the disturbance magnitude and the artificial delay.

Practical example: The effectiveness of the proposed method is demonstrated through a simulation example involving a linear system with step-like disturbances. The results show that the observer can accurately estimate both the system states and the disturbances, even in the presence of the unobservable disturbance dynamics.

The key innovation is the use of Taylor approximation to handle unobservable disturbances, which expands the applicability of ESO-based methods to a broader class of systems. The stability analysis and the practical example illustrate the potential of this approach for robust disturbance estimation in dynamic systems.

Статистика

The first and second derivatives of the disturbance d(t) are bounded as follows:
∥˙d(t)∥ ≤ d1
∥¨d(t)∥ ≤ d2
where d1 and d2 are positive constants.

Цитаты

"The development of disturbance estimators using extended state observers (ESOs) typically assumes that the system is observable. This paper introduces an improved method for systems that are initially unobservable, leveraging Taylor expansion to approximate the integral of disturbance dynamics."
"The main contribution of this work is the design of a novel observer tailored for systems with unobservable disturbances, achieved through the use of Taylor expansion to approximate the integral component of disturbances."

Ключевые выводы из

Extended State Observer for Mismatch Disturbances Using Taylor Approximation of the Integral

by Cuong Duc Ng... в arxiv.org 05-07-2024

https://arxiv.org/pdf/2405.02994.pdf

Дополнительные вопросы

How can the proposed method be extended to handle nonlinear systems with unobservable disturbances?

The proposed method can be extended to handle nonlinear systems with unobservable disturbances by incorporating nonlinear state observers. Nonlinear observers, such as sliding mode observers or high-gain observers, can be designed to estimate both the system states and disturbances in nonlinear systems. By formulating the observer dynamics to capture the nonlinearities present in the system, it becomes possible to observe and estimate disturbances that may not follow linear dynamics. Additionally, techniques like adaptive observers can be employed to adapt to the varying dynamics of nonlinear systems and enhance disturbance estimation accuracy.

What are the potential limitations of the Taylor approximation approach, and how can they be addressed?

The Taylor approximation approach used to estimate disturbances in the proposed method may have limitations, such as inaccuracies in higher-order derivative approximations and sensitivity to variations in the disturbance dynamics. To address these limitations, one can explore more sophisticated approximation techniques, such as Hermite interpolation or spline interpolation, which can provide better approximations of the disturbance dynamics. Additionally, utilizing adaptive algorithms that adjust the approximation parameters based on real-time data can improve the accuracy of the disturbance estimation. Sensitivity analysis can also be conducted to understand the impact of approximation errors on the overall system performance and make necessary adjustments.

What other techniques, besides Taylor approximation, could be explored to enhance the observability of disturbances in dynamic systems?

Besides Taylor approximation, other techniques that could be explored to enhance the observability of disturbances in dynamic systems include:

Kalman Filtering: Kalman filters can be used to estimate both the system states and disturbances by incorporating a state-space model of the system and measurement data. Extended Kalman filters or Unscented Kalman filters can handle nonlinear systems and provide robust disturbance estimation.

Neural Networks: Utilizing neural networks, such as recurrent neural networks or deep learning models, can help learn the complex relationships between system states, inputs, and disturbances. Neural networks can adapt to varying system dynamics and provide accurate disturbance estimates.

Fractional Calculus: Fractional calculus can be applied to model the fractional-order dynamics of disturbances, which may capture long-term memory effects or non-integer order behaviors. Fractional calculus-based observers can enhance disturbance observability in systems with complex dynamics.

Adaptive Observers: Adaptive observers adjust their parameters based on system behavior, making them suitable for systems with varying disturbances. By continuously adapting to changes in the system, adaptive observers can improve disturbance estimation accuracy in dynamic systems.