Proportional PDC Design-Based Robust Stabilization and Tracking Control Strategies for Uncertain and Disturbed T-S Model

Ghorbel, Chekib; Tiga, Amira; Braïek, Naceur Benhadj

doi:10.1155/2020/8910132

Cited by 13 publications

(6 citation statements)

References 33 publications

(60 reference statements)

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“…Consequently, the following augmented system was built according to fuzzy system (4) and error dynamic system (14).…”

Section: Controller Rule Imentioning

confidence: 99%

“…With the expression of the T-SFM, the T-S fuzzy descriptor system (T-SFDS) can also be constructed for NDSs to avoid the non-trivial controller design process. According to references [13,14], the Parallel Distributed Compensation (PDC) concept is introduced for the fuzzy controller design of T-SFM. Note that each linear fuzzy controller shares the same premise part of the subsystem in T-SFM.…”

Section: Introductionmentioning

confidence: 99%

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Robust Observer-Based Proportional Derivative Fuzzy Control Approach for Discrete-Time Nonlinear Descriptor Systems with Transient Response Requirements

Lin,

Lee,

Chang

et al. 2024

Processes

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This paper proposes an observer-based proportional Derivative (O-BPD) fuzzy controller for uncertain discrete-time nonlinear descriptor systems (NDSs). Representing NDSs with the Takagi–Sugeno fuzzy model (T-SFM), the proportional derivative (PD) feedback method can be utilized in the fuzzy controller design via the Parallel Distributed Compensation (PDC) concept, such that the noncausal problem and impulse behavior are avoided. A fuzzy observer is proposed to obtain unmeasured states to fulfill the PD fuzzy controller. Moreover, uncertainties and transient response performances are taken into account for the NDSs. Then, a stability analysis process and corresponding stability conditions are derived from the Lyapunov theory with the robust control method and the pole constraint. Different from existing research, the Singular Value Decomposition (SVD) and the projection lemma are utilized to transfer the stability conditions into the Linear Matrix Inequation (LMI) form. Because of this reason, the conservatism of the analysis process can be reduced by eliminating the restriction on the positive definite matrix in the Lyapunov function. By giving the proper center and radius parameters of the pole constraint in the O-BPD fuzzy controller design process, the expected transient responses can be obtained for different designers and different practical applications. Finally, the effectiveness and applicability of the proposed O-BPD fuzzy controller are demonstrated by two examples of the simulation.

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“…Consequently, the following augmented system was built according to fuzzy system (4) and error dynamic system (14).…”

Section: Controller Rule Imentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust Observer-Based Proportional Derivative Fuzzy Control Approach for Discrete-Time Nonlinear Descriptor Systems with Transient Response Requirements

Lin,

Lee,

Chang

et al. 2024

Processes

View full text Add to dashboard Cite

show abstract

“…Notably, based on the sector nonlinearity approach Takagi and Sugeno (1985), the overall T-S model is achieved by interpolating local linear models through nonlinear fuzzy membership functions. In the controller design procedure, a parallel distributed compensation (PDC) concept has been employed to overcome different stability and stabilization problems of T-S fuzzy systems (Ghorbel et al, 2020; Tlili, 2019; Wei et al, 2016). In the PDC concept, each control rule is designed from the corresponding rule of a T-S fuzzy model.…”

Section: Introductionmentioning

confidence: 99%

Nonfragile H∞ tracking control strategies for classes of linear and bilinear uncertain Takagi-Sugeno fuzzy systems

Ghorbel

Braïek

2022

Transactions of the Institute of Measurement and Control

Self Cite

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This paper presents fuzzy tracking control strategies for classes of linear and bilinear Takagi-Sugeno Fuzzy System with Uncertainties and Disturbances (T-S FSUD). For both classes, the Lyapunov direct approach and the parallel distributed compensation concept are used to design nonfragile H∞ tracking controllers, which ensure the robust asymptotic stability of augmented systems despite the presence of parameter uncertainties, external disturbances, and controllers fragility. Besides that, based on the Schur complement, the separation lemma, and through some variable transformations, sufficient stability conditions of each augmented T-S FSUD are established and formulated in terms of linear matrix inequalities. Finally, numerical simulations are carried out to demonstrate the validity and the applicability of designed control schemes on tracking control of an inverted pendulum and a nonlinear mechanical system.

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“…Indeed, it is clear that relatively small perturbations in controller gain parameters can result in instability of the controlled system [32,33]. Hence, it is necessary that any controller should be able to tolerate some bounded uncertainty in its parameters [3,34,35]. For instance, a nonfragile controller for uncertain nonlinear networked control systems was proposed in [36].…”

Section: Introductionmentioning

confidence: 99%

Nonfragile $H_{\infty}$ Stabilizing Nonlinear Systems Described by Multivariable Hammerstein Models

2021

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This paper presents the problem of robust and nonfragile stabilization of nonlinear systems described by multivariable Hammerstein models. The objective is focused on the design of a nonfragile feedback controller such that the resulting closed-loop system is globally asymptotically stable with robust H ∞ disturbance attenuation in spite of controller gain variations. First, the parameters of linear and nonlinear blocks characterizing the multivariable Hammerstein model structure are separately estimated by using a subspace identification algorithm. Second, approximate inverse nonlinear functions of polynomial form are proposed to deal with nonbijective invertible nonlinearities. Thereafter, the Takagi–Sugeno model representation is used to decompose the composition of the static nonlinearities and their approximate inverses in series with the linear subspace dynamic submodel into linear fuzzy parts. Besides, sufficient stability conditions for the robust and nonfragile controller synthesis based on quadratic Lyapunov function, H ∞ criterion, and linear matrix inequality approach are provided. Finally, a numerical example based on twin rotor multi-input multi-output system is considered to demonstrate the effectiveness.

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Proportional PDC Design-Based Robust Stabilization and Tracking Control Strategies for Uncertain and Disturbed T-S Model

Cited by 13 publications

References 33 publications

Robust Observer-Based Proportional Derivative Fuzzy Control Approach for Discrete-Time Nonlinear Descriptor Systems with Transient Response Requirements

Robust Observer-Based Proportional Derivative Fuzzy Control Approach for Discrete-Time Nonlinear Descriptor Systems with Transient Response Requirements

Nonfragile H∞ tracking control strategies for classes of linear and bilinear uncertain Takagi-Sugeno fuzzy systems

Nonfragile $H_{\infty}$ Stabilizing Nonlinear Systems Described by Multivariable Hammerstein Models

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Proportional PDC Design-Based Robust Stabilization and Tracking Control Strategies for Uncertain and Disturbed T-S Model

Cited by 13 publications

References 33 publications

Robust Observer-Based Proportional Derivative Fuzzy Control Approach for Discrete-Time Nonlinear Descriptor Systems with Transient Response Requirements

Robust Observer-Based Proportional Derivative Fuzzy Control Approach for Discrete-Time Nonlinear Descriptor Systems with Transient Response Requirements

Nonfragile H∞ tracking control strategies for classes of linear and bilinear uncertain Takagi-Sugeno fuzzy systems

Nonfragile H ∞ Stabilizing Nonlinear Systems Described by Multivariable Hammerstein Models

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Nonfragile $H_{\infty}$ Stabilizing Nonlinear Systems Described by Multivariable Hammerstein Models