Table 4 Optimal gain parameters of controllers optimized by FBI and QOFBI techniques.

From: A quasi-oppositional FBI algorithm driven fuzzy cascaded fractional-order controller for enhancing transient stability in hybrid power systems

Controllers

Optimal gain parameters

KP

KI

KD

λ

µ

KPP

KII

λs

QOFBI FFOPID(1 + FOPI)

 Area-1

1.9146

2.0000

2.0000

0.0010

0.3389

2.0000

2.0000

0.9023

 Area-2

0.7779

2.0000

1.1317

1.0910

0.0723

1.8705

0.1130

0.0010

FBI FFOPID(1 + FOPI)

 Area-1

1.6046

2

0.0010

0.8268

0.0010

1.9997

2

0.0012

 Area-2

1.2358

0.0010

1.6156

0.0013

0.0010

2

1.9879

0.8338

FBI FPID(1 + PI)

 Area-1

1.7515

1.9014

0.5149

  

1.6715

1.3872

 

 Area-2

1.1837

0.4349

1.0824

  

0.8652

0.3647

 

FBI FFOPID

 Area-1

2

1.9987

0.0011

0.8974

0.0010

   

 Area-2

0.2427

2

1.9897

0.6564

0.0010

   

FBI FPID

 Area-1

2.0000

2.0000

0.0010

     

 Area-2

0.0010

2.000

0.1756

     

FBI FOPID

 Area-1

1.9788

1.9454

1.0667

0.8269

1.2863

   

 Area-2

1.9998

1.0531

0.2333

0.9337

1.4223

   

FBI PID

 Area-1

1.9687

2.0000

0.4519

     

 Area-2

1.9998

2.0000

1.8268

     
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