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1
Content available Practical Mittag-Leffler stability of quasi-one-sided Lipschitz fractional order systems
Basdouri Imed, Kasmi Souad, Lerbet Jean
Archives of Control Sciences
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2023
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Vol. 33, No. 1
55--70
EN
This paper focuses on the global practical Mittag-Leffler feedback stabilization problem for a class of uncertain fractional-order systems. This class of systems is a larger class of nonlinearities than the Lipschitz ones. Based on the quasi-one-sided Lipschitz condition, firstly, we provide sufficient conditions for the practical observer design. Then, we exhibit that practical Mittag-Leffler stability of the closed loop system with a linear, state feedback is attained. Finally, a separation principle is established and we prove that the closed loop system is practical Mittag-Leffler stable.
2
Content available Discrete-time Takagi-Sugeno singular systems with unmeasurable decision variables: state and fault fuzzy observer design
Aitdaraou Khaoula, Essabre Mohamed, El Assoudi Abdellatif, El Yaagoubi El Hassane
Archives of Control Sciences
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2023
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Vol. 33, No. 2
321--338
EN
The studied problem in this paper, treat the issue of state and fault estimation using a fuzzy observer in the case of unmeasurable decision variable for Discrete-Time Takagi-Sugeno Singular Sytems (DTSSS). First, an augmented system is introduced to gather state and fault into a single vector, then on the basis of Singular Value Decomposition (SVD) approach, this observer is designed in explicit form to estimate both of state and fault of a nonlinear singular system. The exponential stability of this observer is studied using Lyapunov theory and the convergence conditions are solved with Linear Matrix Inequalities (LMIs). Finally a numerical example is simulated, and results are given to validate the offered approach.
3
Content available An observer design for Takagi-Sugeno fuzzy bilinear control systems
Delmotte François, Hadj Taieb Nizar, Hammami Mohamed Ali, Meghnafi Houria
Archives of Control Sciences
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2023
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Vol. 33, No. 3
631--649
EN
In this paper, the observer design problem for a T-S fuzzy bilinear control system is investigated. First, an observer of Kalman type is designed to estimate the system states for the linear case. Then, some new sufficient conditions are derived to show the exponential convergence of the solutions of the error equation for fuzzy bilinear systems. Furthermore, we consider some uncertainties of the system that are bounded and satisfy a certain condition where an observer is designed. Moreover, an application to Van de Vusse system is given.
4
Content available remote TP transformation based ocntroller and observer design of the inverted pendulum
Wéber Andrea, Kuczmann Miklós
Przegląd Elektrotechniczny
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2022
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R. 98, nr 10
34--39
EN
The paper discusses that applying of CNO and IRNO type weighting functions results different TP models, including controller and observer. Selection of weighting functions has influence on the TP model transformation and the LMI based design. Present paper introduces the LMI based observer and controller design of the inverted pendulum via the TP model transformation based method using CNO and IRNO type weighting functions. The TP transformation is accomplished by qLPV modeling and HOSVD method. The paper gives a conclusion and a comparison of the original and estimated state variables and the impact of applying two types of weighting functions. The aim of present paper is to prove that using different type of weighting functions influences the TP models and LMI methods, but LMIs still result feasible solution for controller and observer design. Furthermore the modification allows to choose the better controller/observer.
PL
W artykule wykazano, ze zastosowanie funkcji wagowych typu CNO i IRNO skutkuje różnymi modelami TP, w tym kontrolerem i ˙ obserwatorem. Wybór funkcji wagowej ma wpływ na transformację modelu TP i konstrukcję w oparciu o LMI. W niniejszym artykule przedstawiono projekt obserwatora i kontrolera w oparciu o LMI odwróconego wahadła za pomocą metody opartej na transformacji modelu TP z wykorzystaniem funkcji wagowych typu CNO i IRNO. Transformacja TP realizowana jest za pomocą modelowania qLPV i metody HOSVD. Artykuł zawiera wnioski i porównanie pierwotnych i oszacowanych zmiennych stanu oraz wpływu zastosowania dwóch typów funkcji wag. Celem niniejszego artykułu jest wykazanie, ze zastosowanie różnego rodzaju funkcji wagowych wpływa na modele TP i metody LMI, ale LMI nadal dają wykonalne rozwiązanie dla konstrukcji kontrolera i obserwatora. Ponadto modyfikacja pozwala wybrac lepszego kontrolera/obserwatora.
5
Content available On the state estimation for nonlinear continuous-time fuzzy systems
Delmotte Francois, Hammami Mohamed Ali, Rettab Nour El Houda
Archives of Control Sciences
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2022
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Vol. 32, No. 1
57--72
EN
A large class of nonlinear systems can be represented or well approximated by Takagi-Sugeno (TS) fuzzy models, which in theory can approximate a general nonlinear system to an arbitrary degree of accuracy. The TS fuzzy model consists of a fuzzy rule base. The rule antecedents partition a given subspace of the model variables into fuzzy regions, while the consequent of each rule is usually a linear or affine model, valid locally in the corresponding region. In this paper, the observer design problem for a T-S fuzzy system subject to Lypschitz perturbation is investigated. First, an observer of Kalman type is designed to estimate the unknown system states. Then, the class of one-sided Lipschitz for a TS fuzzy system subject to a sufficient condition on the bound is studied. The challenges are discussed and some analysis oriented tools are provided. An example is given to show the applicability of the main result.
6
Content available Observer design estimating the propofol concentration in PKPD model with feedback control of anesthesia administration
Ilyas Muhammad, Khan Awais, Khan Muhammad Abbas, Xie Wei, Riaz Raja Ali, Khan Yousaf
Archives of Control Sciences
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2022
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Vol. 32, No. 1
85--103
EN
Propofol infusion in anesthesia administration requires continual adjustment in the manual infusion system to regulate the hypnosis level. Hypnotic level is based on Bispectral Index Monitor (BIS) showing the cortical activity of the brain scaled between 0 to 100. The new challenging aspect of automation in anaesthesia is to estimate the concentration of hypnotic drugs in different compartments of the body including primary, rapid peripheral (muscle), slow peripheral (bones, fat) and effect site (brain) compartment based on Pharmacokinetics (PK) and Pharmacodynamics (PD) model. This paper aimed to regulate the hypnosis level with estimating the Propofol concentrations using a linear observer in feedback control strategy based on Integral Super-Twisting Sliding Mode Controller (ISTSMC). The drug concentration in plasma of the silico patients accurately estimated in nominal transient. The results show that tracking errors between the actual output in form of BIS level and linearized output nearly approaches to zero in the maintenance phase of anesthesia to ensure the controller response on sliding phase with optimum performances by achieving desired hypnotic level 50 on BIS. The robustness of control strategy is further ensured by adding measurement noise of electromagnetic environment of operation theatre distracting signal quality index of the output BIS level.
7
Content available Robust sensor fault estimation for descriptor-LPV systems with unmeasurable gain scheduling functions: Application to an anaerobic bioreactor
López-Estrada F. R., Ponsart J. C., Theilliol D., Astorga-Zaragoza C. M., Camas-Anzueto J. L.
International Journal of Applied Mathematics and Computer Science
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2015
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Vol. 25, no. 2
233--244
EN
This paper addresses the design of a state estimation and sensor fault detection, isolation and fault estimation observer for descriptor-linear parameter varying (D-LPV) systems. In contrast to where the scheduling functions depend on some measurable time varying state, the proposed method considers the scheduling function depending on an unmeasurable state vector. In order to isolate, detect and estimate sensor faults, an augmented system is constructed by considering faults to be auxiliary state vectors. An unknown input LPV observer is designed to estimate simultaneously system states and faults. Sufficient conditions to guarantee stability and robustness against the uncertainty provided by the unmeasurable scheduling functions and the influence of disturbances are synthesized via a linear matrix inequality (LMI) formulation by considering H∞ and Lyapunov approaches. The performances of the proposed method are illustrated through the application to an anaerobic bioreactor model.
8
Content available Real-time implementation of an interconnected observer design for p-cells chopper
Laidi K., Benmansour K., Ferdjouni A., Bouchhida O.
Archives of Electrical Engineering
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2010
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Vol. 59, nr 1-2
5-20
EN
This paper deals with an observer design for a p-cell chopper. The goal is to reduce drastically the number of sensors in such system by using an observer in order to estimate all the capacitor voltages. Furthermore, considering an instantaneous model of a p-cell chopper, an interconnected observer is designed in order to estimate the capacitor voltages. This is realized by using only the load current measurement. Simulation results are given in order to illustrate the performance of such observer. To demonstrate the validity of our approach, experimental results based on Digital Signal Processor (DSP) are presented.
9
Content available remote Observer design using a partial nonlinear observer canonical form
Röbenack K., Lynch A. F.
International Journal of Applied Mathematics and Computer Science
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2006
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Vol. 16, no 3
333-343
EN
This paper proposes two methods for nonlinear observer design which are based on a partial nonlinear observer canonical form (POCF). Observability and integrability existence conditions for the new POCF are weaker than the well-established nonlinear observer canonical form (OCF), which achieves exact error linearization. The proposed observers provide the global asymptotic stability of error dynamics assuming that a global Lipschitz and detectability-like condition holds. Examples illustrate the advantages of the approach relative to the existing nonlinear observer design methods. The advantages of the proposed method include a relatively simple design procedure which can be broadly applied.
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