Proportional plus derivative state feedback controller design for a class of fuzzy descriptor systems

Asian Journal of Control

Varadarajan

2020

This paper applies the state derivative feedback method and proportional plus derivative state feedback method to design the fuzzy controllers for the nonlinear singular systems with external noises. The Takagi‐Sugeno fuzzy modeling technology is employed in this paper to represent the nonlinear singular systems with external noise. Considering the singular Takagi‐Sugeno fuzzy model, the passivity constraint is chosen to treat the external noises for the controlled systems. By using the parallel distributed compensation method, the fuzzy controller is designed to satisfy the Lyapunov stability conditions and passivity constraints simultaneously. These sufficient conditions can be effectively solved in terms of linear matrix inequalities, which can be solved via the convex optimization technique. At last, some numerical examples are provided to verify the applicability and effectivity of the proposed fuzzy controller design methods.

Section: Numerical Examplesmentioning

confidence: 99%

F_{d 1} = ([], \begin{array}{c} 0.0526 & 0.2796 & - 1.4453 \end{array}),

F_{p 1} = ([], \begin{array}{c} 183.3683 & 68.5245 & 10.6792 \end{array}),

F_{d 2} = ([], \begin{array}{c} 0.0526 & 0.2796 & - 1.4453 \end{array}),

F_{p 2} = ([], \begin{array}{c} 183.3683 & 68.5245 & 10.6792 \end{array}) .

…”

Section: Numerical Examplesmentioning

confidence: 99%

“…If x 1 ( t ) is about ξ 2 ( κ ( t )), then

u ((), t) = F_{p 2} x ((), t) - F_{d 2} \overset{x}{true} ((), t) .

Section: Numerical Examplesmentioning

confidence: 99%

See 1 more Smart Citation

Fuzzy controller design for nonlinear singular systems with external noises subject to passivity constraints

Asian Journal of Control

Varadarajan

2020

“…By incorporating the derivative action, the PDF control scheme can effectively dampen the impact of disturbances, minimizing their effect on the system's output and ensuring stability and accurate control in T-S DIS. In the past few years, many efforts have been made to study PDF control problems for descriptor systems [23,24]. In [25], a study on decentralized control with the PDF control method for the T-S DIS was proposed.…”

Section: Introductionmentioning

confidence: 99%

Constrained Cost Fuzzy Control via Decentralized Design Approach for Nonlinear Descriptor Interconnected Systems

et al. 2023

Machines

This paper proposes a decentralized robust constrained cost fuzzy controller (DRCCFC) design for nonlinear descriptor interconnected systems (DIS) with uncertainties. The considered nonlinear DIS is modeled using Takagi–Sugeno fuzzy model (T-S FM) with fuzzy rules and strong interconnections. To derive sufficient stability conditions, the quadratic Lyapunov function (QLF) and free-weighting function (FWF) are defined. In contrast to the existing control approaches, the proportional–derivative feedback (PDF) control is introduced in this paper. Using the PDF control techniques, the regular and causal problems of the system can be solved easily. Based on the PDF control technique and constrained cost control (CCC) function, a set of fuzzy controllers are designed to effectively control the Takagi–Sugeno descriptor interconnected systems (T-S DIS). Then, the proposed sufficient conditions for the T-S DIS are derived in the form of linear matrix inequalities using the Schur complement technique. Finally, two simulation examples are provided to demonstrate the validity of the proposed control scheme.

“…In recent years, the PD method has been proposed to control singular systems [15]. It can be known that the PD fuzzy controller is more realistic and convenient than the state-feedback or output feedback for the descriptor systems [16]. Recently, there are only a few results for the design of PD controllers for the linear large-scale interconnected singular systems [17] or large-scale interconnected nonlinear descriptor systems [18].…”

Section: Introductionmentioning

confidence: 99%

Robust Decentralized Fuzzy Controller Design for Nonlinear Large-Scale Interconnected Descriptor Systems

Pen

et al. 2022

J. Phys.: Conf. Ser.

This paper dealt with the robust control problem for fuzzy large-scale descriptor systems (FLSDS) with uncertainties. First, each nonlinear subsystem of the large-scale descriptor system was described as a FLSDS with interconnectivity and uncertainty. Based on the proportional-plus-derivative state feedback (PD) method, the decentralized fuzzy controller in each subsystem was designed to stabilize the whole system. In order to solve the uncertainties problem in the control system simply, a benefits robust approach has been proposed. The final stability conditions can be recast into the linear matrix inequality (LMI) problem by the Schur complement. At last, a numerical example was given to illustrate the control design procedure and its effectiveness.