Design of H_/H∞ fault detection observer for closed-loop nonlinear system with disturbance

2020 ◽  
Vol 40 (4) ◽  
pp. 589-599
Author(s):  
Zhengquan Chen ◽  
Lu Han ◽  
Yandong Hou
Keyword(s):  
Fault Detection ◽  
Closed Loop ◽  
External Disturbance ◽  
Adaptive Threshold ◽  
Linear Matrix ◽  
Content Type ◽  
Non Linear ◽  
Runge Kutta ◽  
Non Linear System ◽  
Residual Generator

Purpose This paper proposes a novel method of fault detection, which is based on H_/H∞ Runge–Kutta observer and an adaptive threshold for a class of closed-loop non-linear systems. The purpose of this paper is to improve the rapidity and accuracy of fault detection. Design/methodology/approach First, the authors design the H_/H∞ Runge–Kutta fault detection observer, which is used as a residual generator to decouple the residual from the input. The H_ performance index metric in the specified frequency domain is used to describe how sensitive the residual to the fault. The H∞ norm is used to describe the residual robustness to the external disturbance of the systems. The residual generator is designed to achieve the best tradeoff between robustness against unknown disturbances but sensitivity to faults, thus realizing the accurate detection of the fault by suppressing the influence of noise and disturbance on the residual. Next, the design of the H_/H∞ fault detection observer is transformed into a convex optimization problem and solved by linear matrix inequality. Then, a new adaptive threshold is designed to improve the accuracy of fault detection. Findings The effectiveness and correctness of the method are tested in simulation experiments. Originality/value This paper presents a novel approach to improve the accuracy and rapidity of fault detection for closed-loop non-linear system with disturbances and noise.

Suppressing the Noise in Measured Signals for the Control of Helicopters

2019 ◽  
Vol 18 (01) ◽  
pp. 1950002 ◽  
Author(s):  
Deepali Y. Dube ◽  
Hiren G. Patel
Keyword(s):  
Adaptive Filter ◽  
Mimo Systems ◽  
Sliding Mode ◽  
Euler Angle ◽  
Linear Matrix ◽  
Frequency Spectra ◽  
Non Linear ◽  
The Future ◽  
The Stability ◽  
Non Linear System

This paper concerns with the non-linear system having multiple-inputs multiple-outputs (MIMO). The plant mainly comprises: bench-top helicopter, tail and main rotor of a helicopter system. The dynamics are presented with control methodologies where a conventional strategy proves the instability of the system while the deadbeat and sliding mode control with linear matrix inequality regulates the future estimates. There have been disturbances like presence of unwanted ripples in the output of the non-linear systems (in case of stability also after 100[Formula: see text]s) and in the tracking of states accurately by updating the minimization error regularly. These problems originate mainly from the rotor section and are visited carefully by studying the dynamics of the blade, whereas, the design of filter makes the solution more appealing. The adaptive filter is capable of handling the frequency spectra of noise (reducing noise by 10[Formula: see text]dB), Euler angle deviations and travel angle accurately. Also, the stability analysis does not confirm the behavior in the case of bounded and a varying range of initial angular velocity. Hence, the problem of fluctuations is overcome by deadbeat and SMC-LMI approach which not only improved the ripples but also allowed the final response of the future states to be more exact and noiseless. As the previous research involved in position tracking (either translational or rotational) of these MIMO systems was concerned with software tools like MATLAB. This paper justifies its validation tested experimentally on OPAL RT hardware. The key findings involve the comparison of frequency spectra, the Euler deviation plot compared to CSL Helicopter and the three set-point variations providing accuracy in results in four modes — desired, actual, with controller-without filter and with controller-with filter. The use of adaptive filter with controllers have encouraged the suppression of noisy waveforms in the bench-top system very smoothly. The details regarding hardware setup are also discussed.

A two-dimensional simulation of solidification processes in materials with thermo-dependent properties using XFEM

2016 ◽  
Vol 26 (6) ◽  
pp. 1661-1683 ◽  
Author(s):  
Pawel Stapór
Keyword(s):  
Finite Element ◽  
Phase Change ◽  
Dimensional Space ◽  
Benchmark Problems ◽  
Liquid Region ◽  
Two Dimensional ◽  
Linear Phase ◽  
Content Type ◽  
Non Linear ◽  
Non Linear System

Purpose – The purpose of this paper is to carry out a finite element simulation of a physically non-linear phase change problem in a two-dimensional space without adaptive remeshing or moving-mesh algorithms. The extended finite element method (XFEM) and the level set method (LSM) were used to capture the transient solution and motion of phase boundaries. It was crucial to consider the effects of unequal densities of the solid and liquid phases and the flow in the liquid region. Design/methodology/approach – The XFEM and the LSM are applied to solve non-linear transient problems with a phase change in a two-dimensional space. The model assumes thermo-dependent properties of the material and unequal densities of the phases; it also allows for convection in the liquid phase. A non-linear system of equations is derived and a numerical solution is proposed. The Newton-Raphson method is used to solve the problem and the LSM is applied to track the interface. Findings – The robustness and utility of the method are demonstrated on several two-dimensional benchmark problems. Originality/value – The novel procedure based on the XFEM and the LSM was developed to solve physically non-linear phase change problems with unequal densities of phases in a two-dimensional space.

An L1 adaptive closed-loop guidance law for an orbital injection problem

2009 ◽  
Vol 223 (6) ◽  
pp. 753-761 ◽  
Author(s):  
J Roshanian ◽  
M Zareh ◽  
H H Afshari ◽  
M Rezaei
Keyword(s):  
Closed Loop ◽  
Adaptive Strategy ◽  
Analytical Form ◽  
Open Loop ◽  
Control Input ◽  
Guidance Law ◽  
Non Linear ◽  
Non Linear System ◽  
Orbital Injection

The current paper presents the determination of a closed-loop guidance law for an orbital injection problem using two different approaches and, considering the existing time-optimal open-loop trajectory as the nominal solution, compares the advantages of the two proposed strategies. In the first method, named neighbouring optimal control (NOC), the perturbation feedback method is utilized to determine the closed-loop trajectory in an analytical form for the non-linear system. This law, which produces feedback gains, is in general a function of small perturbations appearing in the states and constraints separately. The second method uses an L1 adaptive strategy in determination of the non-linear closed-loop guidance law. The main advantages of this method include characteristics such as improvement of asymptotic tracking, guaranteed time-delay margin, and smooth control input. The accuracy of the two methods is compared by introducing a high-frequency sinusoidal noise. The simulation results indicate that the L1 adaptive strategy has a better performance than the NOC method to track the nominal trajectory when the noise amplitude is increased. On the other hand, the main advantage of the NOC method is its ability to solve a non-linear, two-point, boundary-value problem in the minimum time.

scholarly journals Bibo Stabilisation of Continuous–Time Takagi–Sugeno Systems under Persistent Perturbations and Input Saturation

2018 ◽  
Vol 28 (3) ◽  
pp. 457-472 ◽  
Author(s):  
José V. Salcedo ◽  
Miguél Martínez ◽  
Sergio García-Nieto ◽  
Adolfo Hilario
Keyword(s):  
Continuous Time ◽  
Closed Loop ◽  
Input Saturation ◽  
Fuzzy Model ◽  
Maximum Volume ◽  
Ts Fuzzy Model ◽  
Non Linear ◽  
Non Linear System ◽  
Takagi Sugeno ◽  
Fuzzy State

Abstract This paper presents a novel approach to the design of fuzzy state feedback controllers for continuous-time non-linear systems with input saturation under persistent perturbations. It is assumed that all the states of the Takagi-Sugeno (TS) fuzzy model representing a non-linear system are measurable. Such controllers achieve bounded input bounded output (BIBO) stabilisation in closed loop based on the computation of inescapable ellipsoids. These ellipsoids are computed with linear matrix inequalities (LMIs) that guarantee stabilisation with input saturation and persistent perturbations. In particular, two kinds of inescapable ellipsoids are computed when solving a multiobjective optimization problem: the maximum volume inescapable ellipsoids contained inside the validity domain of the TS fuzzy model and the smallest inescapable ellipsoids which guarantee a minimum *-norm (upper bound of the 1-norm) of the perturbed system. For every initial point contained in the maximum volume ellipsoid, the closed loop will enter the minimum *-norm ellipsoid after a finite time, and it will remain inside afterwards. Consequently, the designed controllers have a large domain of validity and ensure a small value for the 1-norm of closed loop.

Decentralized fuzzy C-means robust algorithm for continuous systems

2019 ◽  
Vol 92 (2) ◽  
pp. 222-228
Author(s):  
Tim Chen ◽  
J.C.Y. Chen
Keyword(s):  
Stability Criterion ◽  
Large Scale ◽  
Clustering Algorithm ◽  
Closed Loop ◽  
Linear Matrix ◽  
Model Description ◽  
Continuous Systems ◽  
Content Type ◽  
Fuzzy C Means ◽  
The Stability

Purpose This paper aims to address the robust controller design problem for a class of fuzzy C-means clustering algorithm that is robust against both the plant parameter perturbations and controller gain variations. Based on Takagi–Sugeno (T-S) fuzzy model description, the stability and control problems of nonlinear systems are studied. Design/methodology/approach A recently proposed integral inequality is selected based on the free-weight matrix, and the less conservative stability criterion is given in the form of linear matrix inequalities (LMIs). Findings Under the premise that the controller and the system share the same, the method does not require the number of membership functions and rules. Practical implications Furthermore, the modified controller in a large-scale nonlinear system is utilized as a stability criterion for a closed-loop T-S fuzzy system obtained by LMI, and is rearranged by a machine learning membership function. Originality/value The closed-loop controller criterion is derived by energy functions to guarantee the stability of systems. Finally, an example is given to demonstrate the results.

scholarly journals LPV robust servo control of aircraft active side-sticks

2020 ◽  
Vol 92 (4) ◽  
pp. 599-609
Author(s):  
Guang Rui Zhou ◽  
Shi Qian Liu ◽  
Yuan Jun Sang ◽  
Xu Dong Wang ◽  
Xiao Peng Jia ◽  
...  
Keyword(s):  
Control Method ◽  
Linear Time ◽  
External Disturbance ◽  
Servo System ◽  
Slip Angle ◽  
Content Type ◽  
Civil Aircraft ◽  
Non Linear ◽  
Lpv Control ◽  
The Impact

Purpose This paper aims to focus on the variable stick force-displacement (SFD) gradience in the active side stick (ASS) servo system for the civil aircraft. Design/methodology/approach The problem of variable SFD gradience was introduced first, followed by the analysis of its impact on the ASS servo system. To solve this problem, a linear-parameter-varying (LPV) control approach was suggested to process the variable gradience of the SFD. A H∞ robust control method was proposed to deal with the external disturbance. Findings To validate the algorithm performance, a linear time-variant system was calculated to be used to worst cases and the SFD gradience was set to linear and non-linear variation to test the algorithm, and some typical examples of pitch angle and side-slip angle tracking control for a large civil aircraft were also used to verify the algorithm. The results showed that the LPV control method had less settling time and less steady tracking errors than H∞ control, even in the variable SFD case. Practical implications This paper presented an ASS servo system using the LPV control method to solve the problem caused by the variable SFD gradience. The motor torque command was calculated by pressure and position feedback without additional hardware support. It was more useful for the electronic hydraulic servo actuator. Originality/value This was the research paper that analyzed the impact of the variable SFD gradience in the ASS servo system and presented an LPV control method to solve it. It was applicable for the SFD gradience changing in the linear and non-linear cases.

scholarly journals Data-driven models for fault detection using kernel PCA: A water distribution system case study

2012 ◽  
Vol 22 (4) ◽  
pp. 939-949 ◽  
Author(s):  
Adam Nowicki ◽  
Michał Grochowski ◽  
Kazimierz Duzinkiewicz
Keyword(s):  
Fault Detection ◽  
Distribution System ◽  
Water Distribution ◽  
Water Distribution System ◽  
Principal Component ◽  
Data Driven ◽  
Kernel Principal Component Analysis ◽  
Non Linear ◽  
Non Linear System ◽  
Water Leakage Detection

Kernel Principal Component Analysis (KPCA), an example of machine learning, can be considered a non-linear extension of the PCA method. While various applications of KPCA are known, this paper explores the possibility to use it for building a data-driven model of a non-linear system-the water distribution system of the Chojnice town (Poland). This model is utilised for fault detection with the emphasis on water leakage detection. A systematic description of the system’s framework is followed by evaluation of its performance. Simulations prove that the presented approach is both flexible and efficient.

scholarly journals Fault Detection of Markov Jumping Linear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Wei Li ◽  
Fan Jiang ◽  
Zhongqiu Wang ◽  
Gongbo Zhou ◽  
Zhencai Zhu
Keyword(s):  
Fault Detection ◽  
Linear Systems ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Reference Model ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Residual Generator ◽  
Stochastic Properties ◽  
Residual Generation

In this paper, the fault detection (FD) problems of discrete-time Markov jumping linear systems (MJLSs) are studied. We first focus on the stationary MJLS. The proposed FD system consists of two steps: residual generation and residual evaluation. A new reference model strategy is applied to construct a residual generator, such that it is robust against disturbances and sensitive to system faults. The generated residual signals are then evaluated according to their stochastic properties, and a threshold is computed for detecting the occurrences of faults. The upper bound of the corresponding false alarm rate (FAR) is also given. For the nonstationary MJLS, similar results are also obtained. All the solutions are presented in the form of linear matrix inequalities (LMIs). Finally, a numerical example is used to illustrate the results.

scholarly journals New Criterion of Robust Hܣ Stabilization for Uncertain Neutral Systems

2021 ◽  
pp. 1-12
Author(s):  
Jiyong Lu
Keyword(s):  
Closed Loop ◽  
External Disturbance ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Asymptotically Stable ◽  
Neutral Systems ◽  
Closed Loop Systems ◽  
Delay Dependent ◽  
New Criterion ◽  
Robust Stability And Stabilization

The problems of delay-dependent robust stability and stabilization for a class of uncertain neutral systems are investigated in this paper. At first, by constructing a new Lyapunov functional and using the Lyapunov stability theory, a new delay-dependent condition which renders the system with no external disturbance and input to be asymptotically stable is obtained and given by a linear matrix inequality. Then, based on the obtained condition, a state feedback stabilize law is designed, which guarantees closed-loop neutral systems are asymptotically stable for all the permitted uncertainties when the external disturbance is naught, and it can also guarantee the closed-loop systems have  performance under the external disturbance. The model of neutral systems with both the uncertainty and the disturbance discussed in this paper has rarely been considered before.

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