Takagi-Sugeno fuzzy regulator design for nonlinear and unstable systems using negative absolute eigenvalue approach

Gandhi, Ravi V.; Adhyaru, Dipak M.

doi:10.1109/jas.2019.1911444

Cited by 17 publications

(10 citation statements)

References 44 publications

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“…There are periodic oscillations and damping in the response of e 1 and e 3 in the initial phase for 2 to 3 s from t = 4. This phenomenon can be co-related with the nonlinear second-order underdamped nature of the mechanical sub-system of the MLS [20]. The proposed controller can adapt to the change, which is introduced at 4 s and ensures convergence of the error between the two responses to zero within a short time of 2 s. The error, which was already zero before the change in parameters, re-converges to zero after short transience, thereby demonstrating the controller's robustness, as shown in Figure 8.…”

Section: Design Of Parameter Adaptation Mechanismmentioning

confidence: 97%

“…wherep i , i = 1, 2, 3 are the parameter estimates,û(t) is the control action taken by the reference stabilizer described later in Equation (20), andx i , i = 1, 2, 3 are the reference states. Subtracting Equation ( 5) from Equation ( 7), the tracking-error dynamics with e i =…”

Section: Model-assisted Adaptive Control Designmentioning

confidence: 99%

“…A multi-surface sliding-mode control (SMC) approach [16] handles the mismatched type of parametric uncertainties due to external disturbance. Similarly, the performance robustness of MLS is improved by control approaches, like robust control [17,18], SMC [19], Takagi-Sugeno fuzzy control [20], feedback linearizing control [21], etc. In most of the MLS, the position (x) of moving object and current (i) passing from the coil are measurable variables.…”

Section: Introductionmentioning

confidence: 99%

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A Reference Model Assisted Adaptive Control Structure for Maglev Transportation System

2021

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Maglev transportation system is become a hot topic for researchers because of the distinctive advantages, such as frictionless motion, low power consumption, less noise, and being environmentally friendly. The maglev transportation system’s performance gets sufficiently influenced by the control method and the magnetic levitation system’s dynamic performance, which is a critical component of the maglev transportation system. The Magnetic Levitation System (MLS) is a group of unstable, nonlinear, uncertain, and electromagnetically coupled practical application. Control objective of this study is to design a position stabilizing control strategy for Magnetic Levitation system under extreme uncertain parametric conditions using a reference model governed by a reference stabilizer and nonlinear adaptive control structure. After successful tuning the reference stabilizer with and without time-varying payload disturbance, the tracking-error dynamics are obtained in the presence of both matched and mismatched types of parametric uncertainties. Next, the close-loop stability theorem is formulated for Lyapunov stability analysis to get the design constraints, parameter update laws, and adaptive control law. Numerical simulations performed for a high range of parametric violations check the control design’s efficacy. The performance robustness gets confirmed by comparing the results with the nonlinear control approach. The MLS gets performance recovery and settles within safe limits in few seconds using the proposed methodology. However, the nonlinear controller faces permanent failure in stabilizing the MLS.

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Section: Design Of Parameter Adaptation Mechanismmentioning

confidence: 97%

Section: Model-assisted Adaptive Control Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Reference Model Assisted Adaptive Control Structure for Maglev Transportation System

2021

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“…The DNM is a model that vests dendrite function to the existing single layer perceptron [38][39][40] and is composed of four layers. Inputs x 1 , x 2 , .…”

Section: Dendritic Neuron Modelmentioning

confidence: 99%

Validation of Large-Scale Classification Problem in Dendritic Neuron Model Using Particle Antagonism Mechanism

Jia

Fujishita²,

et al. 2020

Electronics

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With the characteristics of simple structure and low cost, the dendritic neuron model (DNM) is used as a neuron model to solve complex problems such as nonlinear problems for achieving high-precision models. Although the DNM obtains higher accuracy and effectiveness than the middle layer of the multilayer perceptron in small-scale classification problems, there are no examples that apply it to large-scale classification problems. To achieve better performance for solving practical problems, an approximate Newton-type method-neural network with random weights for the comparison; and three learning algorithms including back-propagation (BP), biogeography-based optimization (BBO), and a competitive swarm optimizer (CSO) are used in the DNM in this experiment. Moreover, three classification problems are solved by using the above learning algorithms to verify their precision and effectiveness in large-scale classification problems. As a consequence, in the case of execution time, DNM + BP is the optimum; DNM + CSO is the best in terms of both accuracy stability and execution time; and considering the stability of comprehensive performance and the convergence rate, DNM + BBO is a wise choice.

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“…The general approach to dealing with the stability analysis in the model-based fuzzy control, treated in the main woks [1][2][3], is to make use of Takagi-Sugeno-Kang fuzzy models of the process and express the stability analysis conditions as Linear Matrix Inequalities (LMIs) in terms of the parallel distributed compensation (PDC) approach, which states that the dynamics of each local subsystem in the rule consequents of the Takagi-Sugeno-Kang fuzzy models of the process is controlled using the eigenvalue analysis [2,3]. Recent results on LMI-based stability analysis include the relaxation of stability conditions [4][5][6][7][8][9][10][11], the negative absolute eigenvalue approach [12] and the use of Lyapunov-Krasovskii functionals [13].…”

Section: Introductionmentioning

confidence: 99%

A Center Manifold Theory-Based Approach to the Stability Analysis of State Feedback Takagi-Sugeno-Kang Fuzzy Control Systems

Precup

Preitl²,

Petriu³

et al. 2020

FU Mech Eng

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The aim of this paper is to propose a stability analysis approach based on the application of the center manifold theory and applied to state feedback Takagi-Sugeno-Kang fuzzy control systems. The approach is built upon a similar approach developed for Mamdani fuzzy controllers. It starts with a linearized mathematical model of the process that is accepted to belong to the family of single input second-order nonlinear systems which are linear with respect to the control signal. In addition, smooth right-hand terms of the state-space equations that model the processes are assumed. The paper includes the validation of the approach by application to stable state feedback Takagi-Sugeno-Kang fuzzy control system for the position control of an electro-hydraulic servo-system.

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Takagi-Sugeno fuzzy regulator design for nonlinear and unstable systems using negative absolute eigenvalue approach

Cited by 17 publications

References 44 publications

A Reference Model Assisted Adaptive Control Structure for Maglev Transportation System

A Reference Model Assisted Adaptive Control Structure for Maglev Transportation System

Validation of Large-Scale Classification Problem in Dendritic Neuron Model Using Particle Antagonism Mechanism

A Center Manifold Theory-Based Approach to the Stability Analysis of State Feedback Takagi-Sugeno-Kang Fuzzy Control Systems

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