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Research Papers

Application of CRONE Control to a Sampled Time Varying System With Periodic Coefficients

[+] Author and Article Information
Jocelyn Sabatier

LAP-ENSEIRB, Université Bordeaux 1, Equipe CRONE, UMR 5131 CNRS 351, Cours de la Libération, 33405 Talence, Francejocelyn.sabatier@u-bordeaux1.fr

Aitor Garcia Iturricha, Mathieu Moze, Alain Oustaloup

LAP-ENSEIRB, Université Bordeaux 1, Equipe CRONE, UMR 5131 CNRS 351, Cours de la Libération, 33405 Talence, France

J. Dyn. Sys., Meas., Control 130(6), 061005 (Sep 25, 2008) (12 pages) doi:10.1115/1.2957629 History: Received September 26, 2006; Revised April 24, 2008; Published September 25, 2008

An application of CRONE robust control extended to discrete-time-varying systems with periodic coefficients is presented. The application is carried out in the frequency domain through the representation of considered systems using time varying z-transforms and time varying pseudofrequency responses.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 2

Nyquist path Γw in the w-plane

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Figure 3

Picture of the test bench

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Figure 4

Gain of transmittances P0(s), Pc1(s), and Ps1(s) for (a) the nominal parametric states of the plant and for (b) the parametric state characterized by A0=0.3, A1=0.11, and Jm=0.024 —, transmittances P0(s); - - -, transmittances, Psk(s); …, transmittances Pck(s).

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Figure 5

Representation of plant P

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Figure 6

Representation of sampled P system (with zero-order hold)

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Figure 7

Bode diagrams (in the w-plane) of (a) transmittances C0(w), Cck(w)k∊[1,10](…), andCsk(w)k∊[1,10](---)and (b) enlargement on C0(w) and Cc1(w)

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Figure 8

(a) Nyquist eigenvalue locus of matrix B̂ with w∊Γw for the seven considered parametric states of the plant and (b) Nichols eigenvalues locus of matrix B̂ with w=jν, ν∊[0,tan(π∕M)]: nominal (—) and perturbed parametric (---) states of the plant

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Figure 9

(a) Gain diagrams of T0(w) for the seven parametric states of the plant and (b) gain diagrams of Tk(w), k∊[1,10] for the six extreme parametric states of the plant

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Figure 10

Schematic representation of the implementation

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Figure 11

Closed loop time responses to (a) step inputs r(t)=15H(t)τ with τ=0, τ=T+T∕4, τ=2T+T∕2, and τ=3T+3T∕4 for the nominal parametric state of the plant and (b) the corresponding plant input

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Figure 12

Closed loop time responses to (a) step inputs r(t)=15H(t−τ) for τ=0, τ=2T, τ=4T, and for extreme parametric state of the plant and (b) the corresponding plant input

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Figure 13

Closed loop time responses with the PI controller to (a) step inputs r(t)=15H(t−τ) with τ=0, τ=T+T∕4, τ=2T+T∕2, and τ=3T+3T∕4, and for the nominal parametric state of the plant and (b) the corresponding plant input

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Figure 14

Closed loop time responses with the PI controller to (a) step inputs r(t)=15H(t−τ) for τ=0, τ=2T, and τ=4T, and for extreme parametric states of the plant (b) and the corresponding plant input

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