The Ultimate Bound of a Sampled-Data Sliding Mode Control System with Short Sampling Period

Heum-Yong Park,Young-Hun Jo,Kang-Bak Park 제어로봇시스템학회 2009 제어로봇시스템학회 국제학술대회 논문집 Vol.2009 No.8

Almost all of control methods proposed so far have been designed in the continuous-time domain. Actual systems, however, have been implemented in the discrete-time domain since MCU and/or microprocessors have been used for the control system, that is, the overall system turned to be a sampled-data system. In this case, the ultimate error cannot converge to zero in the actual system even though the proposed control algorithm showed the asymptotic stability in the continuous-time domain. In this paper, therefore, the ultimate error bound of a sampled data system has been investigated. The ultimate error is shown to be related in the sampling period.

Sampled-Data System의 信號흐름線圖에 관한 解析的 考察

趙範峻 朝鮮大學校 動力資源硏究所 1982 動力資源硏究所誌 Vol.4 No.1

In this paper, the signal flow graph technique is expanded so that one can apply it directly to the sampled-data system. A new symbol is introduced to define topological structure and shape. The signal flow graph technique is used for theoretical analysis because of its topological nature which makes it possible to get the input-output relation. Mason's theorem is the easiest and simplest expression of input-output relation, Analytical research using a mathematical model is carried out for unsampled and sampled-data response, very important factors for control system design using a signal flow graph which is equivalently transformed from a block diagram a control system as a result, by inseitiun of the black node which is a new symbol representing a sampler, it is proved to be much easier and simpler than the conventional mathematical method to get the unsampled and sampled-data response.

Sampled-Data Models and ZeroDynamics for Nonlinear Systems

Masatoshi Nishi,Mitsuaki Ishitobi 제어로봇시스템학회 2009 제어로봇시스템학회 국제학술대회 논문집 Vol.2009 No.8

For sampled-data controller design of nonlinear continuous-time systems, it is important to derive a good approximate sampled-data model because the exact sampled-data model for nonlinear system sis often unavailable to the controller designers. Recently, Yuz and Good win have proposed an accurate approximate model which includes extrazero dynamics corresponding to the relative degree of the continuou-time nonlinear system. Such extra zero dynamic sarecalled sampling zero dynamics. A more accurate sampled-data modelis, however, required when the relative degree of a continuous-time nonlinear plant is two. The reasonis that the closed-loop system becomes unstable when the more accurate sampled-data model has unstable sampling zero dynamics and a controller design method based on the assump-tion of the stability of the zero dynamics is applied. This paper derives the sampling zero dynamics of the more accurate sampled-data model and shows a condition which assurest he stability of the sampling zero dynamics of the model.

Sampled-data H_~ fuzzy filtering for nonlinear systems with missing measurements

Koo, G.B.,Park, J.B.,Joo, Y.H. North-Holland ; Elsevier Science Ltd 2017 FUZZY SETS AND SYSTEMS Vol.316 No.-

<P>In this paper, a sampled-data H-infinity fuzzy filtering problem is considered for nonlinear systems with missing measurements. The nonlinear sampled-data system and missing measurements are assumed to be represented by a Takagi-Sugeno (T-S) fuzzy system and an independent, identically distributed Bernoulli random process, respectively. Based on the fuzzy system, the H-infinity fuzzy filtering problem is formulated to design the sampled-data fuzzy filter. By using the exponential mean-square stability definition, the stability condition with an H-infinity performance is guaranteed for the fuzzy system with the sampled-data fuzzy filter, and its sufficient condition is converted into the linear matrix inequality (LMI) format. Finally, an example is provided to verify the effectiveness of the proposed fuzzy filtering technique. (C) 2016 Elsevier B. V. All rights reserved.</P>

An Improved H∞ Fuzzy Filter for Nonlinear Sampled-data Systems

김호준,주영훈,박진배 제어·로봇·시스템학회 2017 International Journal of Control, Automation, and Vol.15 No.3

This paper presents an H∞ fuzzy filter design method for nonlinear sampled-data systems that are representedby a Takagi–Sugeno (T–S) fuzzy model. An error system between the T–S fuzzy system and the fuzzyfilter is obtained to analyze the sampled-data system and solve the filter synthesis problem. To enhance the feasibilityof the sampled-data fuzzy filter, an improved approach is proposed that not only captures the characteristicsof the sampled-data system, but also eliminates a complex discretized model of the sampled-data system using aLyapunov function and two null terms. In the sense of Lyapunov, relaxed sufficient conditions, which are derivedin terms of linear matrix inequalities (LMIs), are obtained for both asymptotic stability and H∞ disturbance attenuationperformance of the error system with less conservatism. Finally, simulation examples are presented to showthe effectiveness of the proposed method.

Consensus for a Class of Sampled-data Heterogeneous Multi-agent Systems

Huanyu Zhao,Lei Wang,Hongbiao Zhou,Dongsheng Du 제어·로봇·시스템학회 2021 International Journal of Control, Automation, and Vol.19 No.5

This paper investigates the problem of consensus for one kind of sampled-data heterogeneous multiagent system. We first discretize the continuous-time networked system by the method of sampled-data. Then we use a system transformation to transform the multi-agent system into the reduced-order error system. Two consensus algorithms with and without velocity measurement will be considered respectively. We obtain two sufficient conditions for the networked systems with and without velocity measurement to reach consensus through analyzing the stable problem of the reduced-order systems. Simulations are given to verify the effectiveness of the results.

Synchronization criteria for delayed Lur’e systems and randomly occurring sampled-data controller gain

Lee, S.H.,Park, M.J.,Kwon, O.M. Elsevier 2019 Communications in nonlinear science & numerical si Vol.68 No.-

<P><B>Abstract</B></P> <P>In this paper, the synchronization problem for delayed Lur’e systems with sampled-data control is investigated. To reflect noises and perturbations of a designed controller gain, Bernoulli sequence and random variables are applied to sampled-data scheme. By constructing some novel Lyapunov-Krasovskii functionals and utilizing some mathematical techniques such as Wirtinger-based integral inequalities, a sampled-data synchronization method for delayed Lur’e systems under a sampled-data control with randomly occurring perturbations is proposed as the framework of linear matrix inequalities. As a special case of the first result, a sampled-data synchronization criterion without considering randomly occurring perturbations is derived. Finally, via three numerical examples, the superiority and validity of the proposed results will be verified through comparing with the existing results.</P> <P><B>Highlights</B></P> <P> <UL> <LI> A concept of stochastic parameter uncertainties is applied to a sampled-data control method to present a realistic system. </LI> <LI> A novel <I>t<SUB>k</SUB> </I>-dependent double integral term of LKFs, ( <SUB> t k + 1 </SUB> − t ) ∫ <SUB> t k </SUB> t ∫ s t ω 3 T ( u ) R <SUB> ω 3 </SUB> ( u ) d u d s , is proposed and a bound of its time derivative is estimated by utilizing Wirtinger-based double inequality and a maximum value of a function. </LI> <LI> Two novel LKFs, 2 ( <SUB> t k + 1 </SUB> − t ) ∑ i = 1 l ∫ 0 d i T x ( t ) [ <SUB> k 1 , i </SUB> ( <SUB> ψ i </SUB> ( s ) − γ i − s ) + <SUB> k 2 , i </SUB> ( γ i + s − <SUB> ψ i </SUB> ( s ) ) ] d s , and 2 ( t − <SUB> t k </SUB> ) ∑ i = 1 l ∫ 0 d i T x ( t ) [ <SUB> k 3 , i </SUB> ( <SUB> ψ i </SUB> ( s ) − γ i − s ) + <SUB> k 4 , i </SUB> ( γ i + s − <SUB> ψ i </SUB> ( s ) ) ] d s , are proposed for the first time through a condition of a nonlinear function to enhance the feasible region of synchronization criteria. </LI> <LI> The effectiveness and less conservatism of our results are illustrated via three numerical examples. </LI> </UL> </P>

Sampled-data Output Feedback Control of a Class of Uncertain Nonlinear Systems

Jian Zhang,Xiaoshuai Xin,Hongbing Xu 제어·로봇·시스템학회 2013 International Journal of Control, Automation, and Vol.11 No.1

In this paper, we study the problem of sampled-data output feedback control for a class of uncertain nonlinear systems. The main contributions of this work are two-fold: (i) we develop a systematic design procedure of sampled-data output feedback controller; and (ii) we provide a theoretical analysis of the sampled-data closed-loop system, which shows that the state of the plant can be regu-lated into any given neighborhood of the origin by an appropriate choice of design parameters and sampling period. Furthermore, the bound of the neighborhood is proportionally dependent on the sam-pling period. Finally, an illustrative example is given to demonstrate the effectiveness of the presented method.

Sampled-data Fuzzy Observer Design for an Attitude and Heading Reference System and Its Experimental Validation

Han Sol Kim,Jin Bae Park,Young Hoon Joo 대한전기학회 2017 Journal of Electrical Engineering & Technology Vol.12 No.6

In this paper, a linear matrix inequality-based sampled-data fuzzy observer design method is proposed based on the exact discretization approach. In the proposed design technique, a numerically relaxed observer design condition is obtained by using the discrete-time fuzzy Lyapunov function. Unlike the existing studies, the designed observer is robust to the uncertain premise variable because the fuzzy observer is designed under the imperfect premise matching condition, in which the membership functions of the system and observer are mismatched. In addition, we apply the proposed method to the state estimation problem of the attitude and heading reference system (AHRS). To do this, we derive a Takagi-Sugeno fuzzy model for the AHRS system, and validate the proposed method through the hardware experiment.

슬라이딩 모드 제어기가 적용된 샘플치 시스템에 대한 안정도 판별 조건

박흠용(Heum-Yong Park),조영훈(Young-Hun Jo),박강박(Kang-Bak Park) 제어로봇시스템학회 2011 제어·로봇·시스템학회 논문지 Vol.17 No.2

Although most of control methods have been studied in the continuous-time domain, the actual control systems have been implemented using MCU (Micro Control Unit) and/or microprocessors so that the overall systems turn to be sampled-data systems. In this case, the stability criterion of the closed-loop system is not easy to derive. In this paper, a simple stability criterion for the sampled-data system with sliding mode controller is derived.