State-Feedback Control in Descriptor Discrete-Time Fractional-Order Linear Systems: A Superstability-Based Approach

Borawski, Kamil

doi:10.3390/app112210568

Applied Sciences

2021

DOI: 10.3390/app112210568

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State-Feedback Control in Descriptor Discrete-Time Fractional-Order Linear Systems: A Superstability-Based Approach

Kamil Borawski¹

Abstract: In this article, the superstabilizing state-feedback control problem in descriptor discrete-time fractional-order linear (DDFL) systems with a regular matrix pencil is studied. Methods for investigating the stability and superstability of the considered class of dynamical systems are presented. Procedures for the computation of the static state-feedback (SSF) and dynamic state-feedback (DSF) gain matrices such that the closed-loop DDFL (CL-DDFL) system is superstable are presented. A numerical example is used … Show more

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Cited by 3 publications

References 26 publications

(39 reference statements)

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Simultaneous Stabilization of Second Order Linear Switched Systems Based on Superstability and D-Decomposition Technique

Shatov

2024

ARC

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The considered problem is to simultaneously stabilize a family of second order linear systems by static linear state feedback when applied to switched systems. The proposed synthesis approach is based on a known design method where a static regulator is found as a solution to the linear programming problem. This regulator makes all matrices from the family forming switched systems superstable in the closed loop state, which in turn guarantees exponential stability of the switched system. This approach is generalized for the case where not all matrices in the family can simultaneously be made superstable: for non-superstabilizable matrices one determines using D-decomposition linear bounds on the set of stabilizing regulators, which are used in the linear programming problem. The designed switched system properties are briefly studied. An example of a design problem solution using the proposed approach is presented.

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Simultaneous Stabilization of Second Order Linear Switched Systems Based on Superstability and D-Decomposition Technique

Shatov

2024

ARC

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Simultaneous Stabilization of Second Order Linear Switched Systems Based on Superstability and D-Decomposition Technique

Shatov

2024

Avtomatika i telemehanika

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Design and Analysis of an Active Disturbance Rejection Robust Adaptive Control System for Electromechanical Actuator

Chen

Zhu

et al. 2021

Actuators

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Airline electromechanical actuators (EMAs), on the task of controlling flight surfaces, hold a great promise with the development of more- and all-electric aircraft. Notwithstanding, the deficiencies in both robustness and adaptability of control algorithms prevent EMAs from extensive use. However, the state-of-the-art control schemes fail to precisely compensate the system nonlinear uncertainties of servo control. In this paper, from the innovation point of view, we tend to put forward the foundation of devising an active disturbance rejection robust adaptive control (ADRRAC) strategy, whose main purpose is to deal with the position servo control of EMA. Specifically, an adaptive control law is designed and deployed for resolving not only the nonlinear disturbance, but also the parameter uncertainties. In addition, an extended disturbance estimator is employed to estimate the external disturbance and thus eliminate its impact. The proposed controlling algorithm is deemed best able to address the external disturbance based on the nonlinear uncertainty compensation. With the input parameters and control commands, the ADRRAC strategy maintains servo system stability while approaching the controlling target. Following the algorithm description, a proof of the controlling stability of ADRRAC strategy is presented in detail as well. Experiments on a variety of tracking tasks are conducted on a prototype of an EMA to investigate the working performance of the proposed control strategy. The experimental outcomes are reported, which verify the effectiveness of the ADRRAC strategy, compared to widely applied control strategies. According to the data analysis results, our controller is capable of obtaining an even faster system response, a higher tracking accuracy and a more stable system state.

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State-Feedback Control in Descriptor Discrete-Time Fractional-Order Linear Systems: A Superstability-Based Approach

Cited by 3 publications

References 26 publications

Simultaneous Stabilization of Second Order Linear Switched Systems Based on Superstability and D-Decomposition Technique

Simultaneous Stabilization of Second Order Linear Switched Systems Based on Superstability and D-Decomposition Technique

Simultaneous Stabilization of Second Order Linear Switched Systems Based on Superstability and D-Decomposition Technique

Design and Analysis of an Active Disturbance Rejection Robust Adaptive Control System for Electromechanical Actuator

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