High-Gain Nonlinear Observer Using System State Augmentation

2021 ◽

Author(s):

Khaled Laib ◽

Minh Tu Pham ◽

Xuefang LIN-SHI ◽

Redha Meghnous

Keyword(s):

Closed Loop ◽

Sliding Mode ◽

High Gain ◽

Observer Design ◽

Nonlinear Observer ◽

State Model ◽

Pressure Measurements ◽

Pneumatic Actuators ◽

Nonlinear Observers ◽

Piston Position

Abstract This paper presents an averaged state model and the design of nonlinear observers for an on/off pneumatic actuator. The actuator is composed of two chambers and four on/off solenoid valves. The elaborated averaged state model has the advantage of using only one continuous input instead of four binary inputs. Based on this new model, a high gain observer and a sliding mode observer are designed using the piston position and the pressure measurements in one of the chambers. Finally, their closed-loop performances are verified and compared on an experimental benchmark.

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Unknown Inputs Nonlinear Observer for an Activated Sludge Process

Mathematical Problems in Engineering ◽

10.1155/2018/1382914 ◽

2018 ◽

Vol 2018 ◽

pp. 1-12 ◽

Cited By ~ 5

Author(s):

Feten Smida ◽

Taoufik Ladhari ◽

Salim Hadj Saïd ◽

Faouzi M’sahli

Keyword(s):

Activated Sludge ◽

High Gain ◽

The Other ◽

Nonlinear Observer ◽

Dynamics Simulation ◽

Activated Sludge Process ◽

Unknown Inputs ◽

Simulation Results ◽

Economic Concentration ◽

Substrate Concentrations

This paper deals with the jointly estimation problem of unknown inputs and nonmeasured states of one altering aerated activated sludge process (ASP). In order to provide accurate and economic concentration measures during aerobic and anoxic phases, a cascade high gain observer (HGO) approach is developed. Only two concentrations are available; the other process’s states are assumed unavailable. The observer converges asymptotically and it leads to a good estimation of the unavailable states which are the ammonia and substrate concentration, as well as a quite reconstruction of the unknown inputs, which are the influent ammonia and the influent substrate concentrations. To highlight the efficiency of the proposed HGO with this MIMO system’s dynamics, simulation results are validated with experimental data.

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Lucid Analysis of Periodically Forced Nonlinear Systems via Normal Forms

Volume 6: 15th International Conference on Multibody Systems, Nonlinear Dynamics, and Control ◽

10.1115/detc2019-97100 ◽

2019 ◽

Author(s):

Peter M. B. Waswa ◽

Sangram Redkar

Keyword(s):

Nonlinear Systems ◽

Ad Hoc ◽

Normal Forms ◽

Numerical Results ◽

Duffing Equation ◽

System State ◽

Periodic Forcing ◽

Periodic Coefficients ◽

Duffing’S Equation ◽

State Augmentation

Abstract This paper presents a straightforward methodology to analyze periodically forced nonlinear systems with constant and periodic coefficients via normal forms. We demonstrate how the intuitive system state augmentation facilitates construction of normal forms by avoiding ad-hoc addition of equation variables, book-keeping parameters and detuning parameters. Moreover, this technique directly connects the periodic forcing terms and periodic coefficients of the nonlinearity with the augmented states — making it applicable to all periodically forced nonlinear systems. Accuracy of this approach is successfully verified via fulfilled compliance between analytical and numerical results of forced Duffing’s equation and Mathieu-Duffing equation.

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Output feedback boundary control of a flexible marine riser system

Journal of Vibration and Control ◽

10.1177/1077546317708516 ◽

2017 ◽

Vol 24 (16) ◽

pp. 3617-3630 ◽

Cited By ~ 6

Author(s):

Yu Liu ◽

Fang Guo

Keyword(s):

Boundary Control ◽

Closed Loop ◽

Vibration Suppression ◽

High Gain ◽

Loop System ◽

System State ◽

Marine Riser ◽

Closed Loop System ◽

Observer Error ◽

System States

This paper is concerned with the design of boundary control for globally stabilizing a flexible marine riser system. The dynamics of the riser system are represented in the form of hybrid partial–ordinary differential equations. Firstly, when the system state available for feedback is unmeasurable, an observer backstepping method is employed to reconstruct the system state and then design the boundary control for vibration suppression of the riser system. Subsequently, for the case that the system states in the designed control law cannot be accurately obtained, the high-gain observers are utilized to estimate those unmeasurable system states. With the proposed control, the uniformly ultimately bounded stability of the closed-loop system is demonstrated by the use of Lyapunov’s synthetic method and the state observer error is converged exponentially to zero as time approaches to infinity. In addition, the disturbance observer is introduced to track external environmental disturbance. Finally, the control performance of the closed-loop system is validated by carrying out numerical simulation.

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A Fractional High-Gain Nonlinear Observer Design—Application for Rivers Environmental Monitoring Model

Mathematical and Computational Applications ◽

10.3390/mca25030044 ◽

2020 ◽

Vol 25 (3) ◽

pp. 44

Author(s):

Abraham Efraim Rodriguez-Mata ◽

Yaneth Bustos-Terrones ◽

Victor Gonzalez-Huitrón ◽

Pablo Antonio Lopéz-Peréz ◽

Omar Hernández-González ◽

...

Keyword(s):

Fractional Order ◽

Oxygen Demand ◽

Environmental Water ◽

High Gain ◽

Observer Design ◽

Nonlinear Observer ◽

Distribution Models ◽

Luenberger Observer ◽

Monitoring Model ◽

Numerical Studies

The deterioration of current environmental water sources has led to the need to find ways to monitor water quality conditions. In this paper, we propose the use of Streeter–Phelps contaminant distribution models and state estimation techniques (observer) to be able to estimate variables that are very difficult to measure in rivers with online sensors, such as Biochemical Oxygen Demand (BOD). We propose the design of a novel Fractional Order High Gain Observer (FOHO) and consider the use of Lyapunov convergence functions to demonstrate stability, as it is compared to classical extended Luenberger Observer published in the literature, to study the convergence in BOD estimation in rivers. The proposed methodology was used to estimated Dissolved oxygen (DO) and BOD monitoring of River Culiacan, Sinaloa, Mexico. The use of fractional order in high-gain observers has a very effective effect on BOD estimation performance, as shown by our numerical studies. The theoretical results have shown that robust observer design can help solve problems in estimating complex variables.

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Prescribed-Time High-Gain Nonlinear Observer Design for Triangular Systems

10.1109/icsc50472.2021.9666587 ◽

2021 ◽

Author(s):

Ania Adil ◽

Ibrahima N'Doye ◽

Abdelghani Hamaz ◽

Ali Zemouche ◽

Taous-Meriem Laleg-Kirati

Keyword(s):

High Gain ◽

Observer Design ◽

Nonlinear Observer ◽

Triangular Systems

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A high-gain-based global finite-time nonlinear observer

International Journal of Control ◽

10.1080/00207179.2012.760045 ◽

2013 ◽

Vol 86 (5) ◽

pp. 759-767 ◽

Cited By ~ 8

Author(s):

Yunyan Li ◽

Xiaohua Xia ◽

Yanjun Shen

Keyword(s):

Finite Time ◽

High Gain ◽

Nonlinear Observer

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Adaptive Regulation of a Class of Uncertain Nonlinear Systems with Nonstrict Feedback Form

Mathematical Problems in Engineering ◽

10.1155/2016/9748489 ◽

2016 ◽

Vol 2016 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Jian-xiong Li ◽

Chong-yi Gao ◽

Yi-ming Fang ◽

Cui Guo ◽

Wen-bo Zhang

Keyword(s):

Nonlinear Systems ◽

Control Algorithm ◽

Closed Loop ◽

High Gain ◽

Design Parameters ◽

System State ◽

Closed Loop System ◽

Feedback Form ◽

Semiglobal Stabilization ◽

Adaptive Control Algorithm

This paper focuses on the semiglobal stabilization for a class of nonlinear systems with nonstrict feedback form. Based on a generalized scaling technique, an adaptive control algorithm with dynamic high gain is developed for a class of nonstrict feedback nonlinear systems. It can be proved that, under some appropriate design parameters, all signals of the resulting closed-loop system are bounded semiglobally, and the system state will be convergent to origin exponentially. Finally, a numerical simulation is provided to confirm the effectiveness of the proposed method.

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