Delta-Operator-Based Extended Disturbance Observer and Its Applications

In this paper, we present an output feedback based design of event-triggered sliding mode control for delta operator systems. For discretetime systems, multi-rate output sampling based state estimation technique is very useful if the output information is available. But at high sampling rates, the discrete-time representation of the system using shift operator becomes numerically ill-conditioned and as a result, the observability matrix becomes singular as the sampling period tends to zero. Here, a new formulation of multi-rate state estimation (MRSE) for a small sampling period is presented. We first propose a new observability matrix and then discuss its relationship with the observability matrix defined in the conventional sense. For the delta operator system with matched uncertainty, we have presented the design of MRSE based sliding mode control (SMC). Additionally, to make the control efficient in terms of resource utilization, MRSE based event-triggered SMC is proposed. The absence of Zeno phenomenon is guaranteed as the control input is inherently discrete in nature. Finally, the effectiveness of the proposed method is illustrated through numerical simulations, considering a ball and beam system and a general linear system as a numerical example.

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“…After reaching QSMB, we have |s(k)| < Ω, using this in the above equation gives δV 1 (x 1 (k)) ≤ − λ min (Q) x 1 (k) 2 + τλ max (P) Ā 12 2 Ω 2…”

Section: Design Of Smc Using Mrse Techniquementioning

confidence: 99%

“…where β 1 = PĀ 12 + τA ⊤ cl PĀ 12 Ω 1 , β 2 = τλ max (P) Ā 12 2 Ω 2 1 , b 4 = β 1 /a 2 , and c 4 = β 2 /a 2 + β 2 1 /a 2 2 . PROOF.…”

Section: Remarkmentioning

confidence: 99%

Output feedback based event-triggered sliding mode control for delta operator systems

et al. 2019

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“…The paper [6], authored by Ginoya et al, proposes a delta operator based discrete-time disturbance observer for a class of uncertain systems, which can not only estimate the disturbances but also their derivatives. Own to the use of the delta operator, the proposed design technique unifies the design of continuous-time and discrete-time time disturbance observers.…”

Section: A Disturbance Observer Based Techniquementioning

confidence: 99%

Advances in Disturbance/Uncertainty Estimation and Attenuation [Guest editors' introduction]

Chen

Ohnishi

Guo

2015

IEEE Trans. Ind. Electron.

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“…To unify the continuous-time and discrete-time systems, Goodwin and Middleton establish a delta operator system theory. 34,35 Such a unified description is a natural correspondence between continuous-time and discrete-time systems and has successfully attracted wide attention [36][37][38][39][40][41][42] and the references therein. As shown in Goodwin et al 35 and Yang et al, 43 the main advantages of the delta operator method lie in that it is able to effectively avoid the ill-conditioned problems under fast sampling, and it requires smaller word length when implemented in fixed-point digital control processers than shift operator.…”

Section: Introductionmentioning

confidence: 99%

Quantized sliding mode control in delta operator framework

Zheng

Xue

2017

Intl J Robust & Nonlinear

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Summary This paper is concerned with quantized sliding mode control in the unified delta operator system framework. To solve the quantization measurement saturating problem, a dynamic quantization strategy including discrete on‐line open‐loop zooming‐out and closed‐loop zooming‐in policies is presented. By analyzing the sign relation between the traditional linear switching function and the quantized linear switching function, a novel quantized sliding mode control method is proposed, and both the amplitude of the control gain and the value of the quantization measurement saturating parameter are reduced compared with previous results. Some simulation results are presented to verify the effectiveness of the proposed method.

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Delta-Operator-Based Extended Disturbance Observer and Its Applications

Cited by 42 publications

References 40 publications

Output feedback based event-triggered sliding mode control for delta operator systems

Output feedback based event-triggered sliding mode control for delta operator systems

Advances in Disturbance/Uncertainty Estimation and Attenuation [Guest editors' introduction]

Quantized sliding mode control in delta operator framework

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