Research Papers

Design of Robust Double-Fuzzy-Summation Nonparallel Distributed Compensation Controller for Chaotic Power Systems

[+] Author and Article Information
Navid Vafamand

School of Electrical and Computer Engineering,
Shiraz University,
Shiraz 71886-97476, Fars, Iran
e-mail: n.vafamand@shirazu.ac.ir

Mohammad Hassan Khooban

Department of Energy Technology,
Aalborg University,
Aalborg 71886-97476, Denmark
e-mail: mhk@et.aau.dk

Alireza Khayatian

School of Electrical and Computer Engineering,
Shiraz University,
Shiraz 71348-51154, Fars, Iran
e-mail: khayatia@shirazu.ac.ir

Frede Blabbjerg

Department of Energy Technology,
Aalborg University,
Aalborg 71886-97476, Denmark
e-mail: fbl@et.aau.dk

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received October 30, 2016; final manuscript received June 18, 2017; published online November 8, 2017. Assoc. Editor: Heikki Handroos.

J. Dyn. Sys., Meas., Control 140(3), 031004 (Nov 08, 2017) (8 pages) Paper No: DS-16-1523; doi: 10.1115/1.4037527 History: Received October 30, 2016; Revised June 18, 2017

This paper studies a systematic linear matrix inequality (LMI) approach for controller design of nonlinear chaotic power systems. The presented method is based on a Takagi–Sugeno (TS) fuzzy model, a double-fuzzy-summation nonparallel distributed compensation (non-PDC) controller, and a double-fuzzy-summation nonquadratic Lyapunov function (NQLF). Since time derivatives of fuzzy membership functions (MFs) appear in the NQLF-based controller design conditions, local controller design criteria is considered, and sufficient conditions are formulated in terms of LMIs. Compared with the existing works in hand, the proposed LMI conditions provide less conservative results due to the special structure of the NQLF and the non-PDC controller in which two fuzzy summations are employed. To evaluate the effectiveness of the presented approach, two practical benchmark power systems, which exhibit chaotic behavior, are considered. Simulation results and hardware-in-the-loop illustrate the advantages of the proposed method compared with the recently published works.

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Grahic Jump Location
Fig. 1

CODOPS system states (Theorem 2 “—,” Ref. [5] “····,” and Ref. [23] “-·-”): (a) The state x1 and (b) the state x2

Grahic Jump Location
Fig. 4

Liu system states (Theorem 2 “—” and Ref. [30] “····”): (a) The state x1, (b) the state x2, (c) the state x3, and (d) the statex4

Grahic Jump Location
Fig. 5

Liu system control input (Theorem 2 “—” and Ref. [33] “····”): (a) the state x1, (b) the state x2, (c) the state x3, and (d) the state x4

Grahic Jump Location
Fig. 2

PMSM system states (Theorem 2 “—” and Ref. [33] “····”): (a) The state x1, (b) the state x2, and (c) the state x3

Grahic Jump Location
Fig. 3

PMSM system control input (Theorem 2 “—” and Ref. [33] “····”)



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