0
Research Papers

Fractional Control With a Smith Predictor

[+] Author and Article Information
Isabel S. Jesus1

Department of Electrical Engineering, Institute of Engineering of Porto, Rua Dr. António Bernardino de Almeida, 4200-072 Porto, Portugalisj@isep.ipp.pt

J. Tenreiro Machado

Department of Electrical Engineering, Institute of Engineering of Porto, Rua Dr. António Bernardino de Almeida, 4200-072 Porto, Portugaljtm@isep.ipp.pt

1

Corresponding author.

J. Comput. Nonlinear Dynam 6(3), 031014 (Mar 02, 2011) (10 pages) doi:10.1115/1.4002834 History: Received June 08, 2009; Revised October 01, 2010; Published March 02, 2011; Online March 02, 2011

The advantageous use of fractional calculus (FC) in the modeling and control of many dynamical systems has been recognized. In this paper, we study the control of a heat diffusion system based on the application of the FC concepts. Several algorithms are investigated and compared, when integrated within a Smith predictor control structure. Simulations are presented assessing the performance of the proposed fractional algorithms.

Copyright © 2011 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Polar Diagrams of G(jω), G̃(jω), ĜInt(jω), and ĜFrac(jω), for x=3.0 m and kc=0.042 m2 s−1

Grahic Jump Location
Figure 2

Closed-loop system SP_PIDβ of the Smith predictor with a fractional PIDβ controller Gc(s)

Grahic Jump Location
Figure 3

The SP_PIDβ parameters (K,Ti,Td) versus β for the ISE and the ITSE criteria, x=3.0 m, kc=0.042 m2 s−1

Grahic Jump Location
Figure 4

Step responses of the closed-loop system for the SP_PIDβ[ĜInt], x=3.0 m, kc=0.042 m2 s−1, for the ISE and ITSE indices and for the optimal values of β

Grahic Jump Location
Figure 5

Parameters ts, tr, tp, and ov(%) for the step responses of the closed-loop system with a SP_PIDβ[ĜInt], for the ISE, x=3.0 m, and kc=0.042 m2 s−1

Grahic Jump Location
Figure 6

Parameters ts, tr, tp, ov(%) for the step responses of the closed-loop system with a SP_PIDβ[ĜInt], for the ITSE, x=3.0 m, and kc=0.042 m2 s−1

Grahic Jump Location
Figure 7

Energy Em versus the ISE and the ITSE indices for 0≤β≤1, x=3.0 m, and kc=0.042 m2 s−1

Grahic Jump Location
Figure 8

The SP_PIDβ parameters (K,Ti,Td) versus β for the ISE and the ITSE criteria, x=3.0 m, and kc=0.042 m2 s−1

Grahic Jump Location
Figure 9

Step responses of the closed-loop system for the SP_PIDβ[ĜFrac] and SP_PIDβ[ĜInt], x=3.0 m, and kc=0.042 m2 s−1, for the ISE and ITSE indices and for the optimal values of β

Grahic Jump Location
Figure 10

Parameters ts, tr, tp, ov(%) for the step responses of the closed-loop system with a SP_PIDβ[ĜFrac], for the ISE, x=3.0 m, and kc=0.042 m2 s−1

Grahic Jump Location
Figure 11

Parameters ts, tr, tp, ov(%) for the step responses of the closed-loop system with a SP_PIDβ[ĜFrac], for the ITSE, x=3.0 m, and kc=0.042 m2 s−1

Grahic Jump Location
Figure 12

Energy Em versus the ISE and the ITSE Indices for 0≤β≤1, x=3.0 m, and kc=0.042 m2 s−1

Grahic Jump Location
Figure 13

Step responses of the closed-loop system for the SP_PIDβ[ĜInt], for the ISE and the ITSE indices, kc={0.036,0.038,0.040,0.042,0.044,0.046,0.048}, x=3.0 m, βISE=0.4, and βITSE=0.55

Grahic Jump Location
Figure 14

Step responses of the closed-loop system for the SP_PIDβ[ĜFrac], for the ISE and the ITSE indices, kc={0.036,0.038,0.040,0.042,0.044,0.046,0.048}, x=3.0 m, βISE=0.9, and βITSE=0.9

Grahic Jump Location
Figure 15

Variation of the ISE and the ITSE indices versus kc for kc={0.036,0.038,0.040,0.042,0.044,0.046,0.048} and x=3.0 m

Grahic Jump Location
Figure 16

Variation of ov(%) versus kc for the step responses of the closed-loop system with a SP_PIDβ[ĜInt], {βISE,βITSE}={0.4,0.55}, and SP_PIDβ[ĜFrac], {βISE,βITSE}={0.9,0.9}, and x=3.0 m

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In