Merging Flatness, GPI Observation, and GPI Control with ADRC

Sira‐Ramírez, Hebertt; Luviano‐Juárez, Alberto; Ramírez‐Neria, Mario; Zurita-Bustamante, Eric William

doi:10.1016/b978-0-12-849868-2.00003-4

Cited by 12 publications

(19 citation statements)

References 24 publications

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“…Secondly, considering the system in (21) and either of state and output dependent uncertainty models in (22), we construct augmented system (5a) with r = 1, using (5b) or its modified version (20) for state and output dependent uncertainty models, respectively. Next, we design two actuator fault estimators of the form (7), one for each of cases considering state-and output-dependent uncertainty models, by solving the semi-definite problem in Theorem 3.1.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…where ζ j ∈ R n f . As you see, the accuracy of the approximated model (3) increases as f (r) goes to zero (entry-wise), and it is exact for f (r) = 0 (since we have ζr = ζ(r) 3) is used to construct a fault estimator filter that ultra-locally [20], [21] acts as a selfupdating polynomial spline approximating the actual value of the fault. To design such a filter, in the following section, we extend the system state, x(t), with the states of the actual fault internal state ζ j (t), j ∈ {1, .…”

Section: Ultra Local Fault Representationmentioning

confidence: 99%

“…We propose a fault estimation scheme for process and sensor faults that allows to guarantee zero error in the absence of uncertainty, external disturbances, and measurement noise for some classes of faults and ensures robust fault estimate in the presence of perturbations. This scheme incorporates an internal representation of the fault vector, where we use the notion of ultra-local models [20], [21] phenomenological models valid for short time intervals. We then extend the system dynamics with the (internal) ultra-local state-space of the fault vector to construct an augmented dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Ultra Local Nonlinear Unknown Input Observers for Robust Fault Reconstruction

Farhad

Murguia

Esfahani

et al. 2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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This paper proposes a nonlinear estimator for the robust reconstruction of process and sensor faults for a class of uncertain nonlinear systems. The proposed fault estimation method augments the system dynamics with an ultra-local (in time) internal state-space representation (a finite chain of integrators) of the fault vector. Next, a nonlinear state observer is designed based on the known parts of the augmented dynamics. This nonlinear filter (observer) reconstructs the fault signal as well as the states of the augmented system. We provide sufficient conditions that guarantee stability of the estimation error dynamics: firstly, asymptotic stability (i.e., perfect fault estimation) in the absence of perturbations induced by fault model mismatch (mismatch between internal, ultralocal model for the fault and the actual fault characteristics), uncertainty, external disturbances, and measurement noise and, secondly, Input-to-State Stability (ISS) of the estimation error dynamics is guaranteed in the presence of these perturbations. In addition, to support performance-based estimator design, we provide Linear Matrix Inequality (LMI) conditions for L2-gain and L2 − L∞ induced norm and cast the synthesis of the estimator gains as a semi-definite program where the effect of model mismatch and external disturbances on the fault estimation error is minimized in the sense of L2-gain, for an acceptable L2 − L∞ induced norm with respect to measurement noise. The latter result facilitates a design that explicitly addresses the performance trade-off between noise sensitivity and robustness against model mismatch and external disturbances. Finally, numerical results for a benchmark system illustrate the performance of the proposed methodologies.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Ultra Local Fault Representationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Ultra Local Nonlinear Unknown Input Observers for Robust Fault Reconstruction

Farhad

Murguia

Esfahani

et al. 2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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“…On the one hand, in the past 20 years much progress has been made on the theoretical foundation of ADRC for uncertain systems including the convergence analyses of ESO and ADRC's closed-loop, see for instance the convergence analysis of ESO for a class of uncertain systems in [2], the convergence analysis of ADRC's closed-loop of a class of uncertain stochastic systems in [3], and more all-round designs and theoretical analyses of ADRC for uncertain systems in the monographs [4], [5] and the references therein. On the other hand, networked control systems (NCSs) with spatially distributed sensors, actuators, and controllers transmitting data over a communication data channel, of superiority in reducing installation costs, achieving higher reliability, and increasing system agility, has been applied extensively.…”

Section: Introductionmentioning

confidence: 99%

Event-Triggered Active Disturbance Rejection Control for Uncertain Lower Triangular Stochastic Systems

Wu¹,

Deng²,

Zeng³

et al. 2023

Preprint

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In this paper, the event-triggered active disturbance rejection control (ADRC) is first addressed for a class of uncertain lower triangular stochastic systems driven by bounded noise and colored noise. The eventtriggered extended state observer (ESO) and ADRC controller are designed, where two respective event-triggering mechanisms with a fixed positive lower bound for the inter-execution times for every sample path solution of the stochastic systems are proposed. The stochastic total disturbance representing the coupling of nonlinear unmodeled dynamics, external deterministic disturbance, bounded noise, and colored noise is estimated in real time by the event-triggered ESO and compensated in the event-triggered feedback loop. Both the mean square and almost surely practical convergence of the closed-loop systems is shown with rigorous theoretical analysis. Finally, some numerical simulations are presented to validate the theoretical results.

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“…Active disturbance rejection control has been studied extensively in the last years. Numerous recent approaches have been developed to address a large variety of academic and industrial problems such as motion control by Zhao and Gao (2013), Sen et al (2019), Hernández-Melgarejo et al (2019), and Touhami et al (2019), power electronics by Wu et al (2017), Huangfu et al (2019), Sun et al (2019), and Zheng and Gao (2018), robotics by Ramírez-Neria et al (2015), Gutiérrez-Giles and Arteaga-Pérez (2019), and Gutiérrez-Giles et al (2019), industrial process by Zheng and Gao (2012), Zheng et al (2018), and Zheng and Gao (2018), vibration suppression by Madonski et al (2019), and underactuated systems by Sira-Ramirez et al (2018) and Ramírez-Neria et al (2020a, 2020b). In previous studies, ADRC has been applied on various types of mechanical systems, showing excellent performance in terms of accuracy, repeatability, energy efficiency, easy implementation, and intuitiveness of each control term.…”

Section: Introductionmentioning

confidence: 99%

Active vibration control of building structure using active disturbance rejection control

Ramírez‐Neria

Morales‐Valdez

2021

Journal of Vibration and Control

Self Cite

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This article presents an active vibration control of seismically excited building structures. The control scheme is based on active disturbance rejection control, which is an attractive alternative technique for structural vibration suppression and practical motion control solution in the presence of parametric uncertainties and disturbances. The proposed active disturbance rejection control scheme uses a generalized proportional integral observer, which allows us to estimate in real time the unknown dynamics and disturbances in the building structure to cancel their effect using a part of the control signal. First, the active disturbance rejection control provides a proportional derivative controller with robustness to external disturbances and uncertainties, and its structure is expressed in a compact error-based form. An important advantage with respect to other methods is that the proposed scheme does not need the system parameters. Moreover, supposing that displacement and velocity cannot be measured directly, an online robust adaptive observer is introduced to estimate both data, required for the proportional derivative controller. The adaptive observer removes constant disturbance and attenuates measurement noise in acceleration data. Under this line, a second active disturbance rejection control scheme is introduced based on a proportional controller that, unlike proportional derivative, it only needs the velocities that can be directly estimated by integrating the acceleration signals and does not require the adaptive observer. An advantage of this scheme is its simplicity to be implemented because it only needs to tune the proportional gain. Furthermore, this scheme has a similar performance of the proportional derivative controller. The effectiveness of the proposed active disturbance rejection control schemes is demonstrated through experimental results of a reduced scale five-story building structure. The results are found to be a good step in that direction, confirming that the proposed method is promising for practical applications.

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Merging Flatness, GPI Observation, and GPI Control with ADRC

Cited by 12 publications

References 24 publications

Ultra Local Nonlinear Unknown Input Observers for Robust Fault Reconstruction

Ultra Local Nonlinear Unknown Input Observers for Robust Fault Reconstruction

Event-Triggered Active Disturbance Rejection Control for Uncertain Lower Triangular Stochastic Systems

Active vibration control of building structure using active disturbance rejection control

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