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M r Mmax (0 dB, -180°) b = 0 a ωcg M r M max (0 dB, -180°) b Mr ETTC2003 European Test and Telemetry Conference ω cg a M max (0 dB, -180°) (a) (b) (c) Figure 4 – Optimal open-loop Nichols locus to position the uncertainty domains In the example of the test-bench, figure 4 presents the optimal open-loop Nichols with the uncertainty domains computed the various operating points and the various parameters of the structure to be tested. Magnitude dB) 40 20 0 -20 -40 -60 -80 -100 -120 -140 -400 -350 -300 -250 -200 -150 -100 Phase (deg) Figure 4 – Optimal open-loop Nichols locus of the test-bench a optimal ω cg b optimal
Validation tests have been achieved with tested structures represented by different masses. These tests show that the control strategy permits to guarantee good dynamic performance in spite of uncertainties (Figure 5). Figure 5 – Test results: controlled position for three different structures 1.4 - Conclusion Robust control permits to take into account the uncertainty of the test bench. Thus tests can be achieved under better conditions and with good performance. The complexity of the control system is not much higher than with a classical PID and so robust control is benefic. Bibliography: [1] Oustaloup, A. & Mathieu, B. (1999) La commande CRONE du scalaire au multivariable. Hermès. Paris. [2] S.G. Samko, A.A. Kilbas and O.I. Marichev (1993), « Fractional integrals and derivatives », Gordon and Breach Science Publishers. [3] A.Oustaloup, & al, (2000), « The CRONE toolbox for Matlab», 11th IEEE International Symposium on Computer-Aided Control System Design, CACSD - Anchorage, Alaska, USA, September 25-27 [4] V. Pommier, (2002), « Commande non entière et commande robuste non linéaire d’un banc d’essais hydraulique », Thèse de l’Ecole Nationale Supérieure des Arts et Métiers. ETTC2003 European Test and Telemetry Conference
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Validation tests have been achieved with tested structures represented by<br />
different masses. These tests show that the control strategy permits to guarantee<br />
good dynamic performance in spite of uncertainties (Figure 5).<br />
Figure 5 – Test results: controlled position for three different structures<br />
1.4 - Conclusion<br />
Robust control permits to take into account the uncertainty of the test<br />
bench. Thus tests can be achieved under better conditions and with good<br />
performance. The complexity of the control system is not much higher than with a<br />
classical PID and so robust control is benefic.<br />
Bibliography:<br />
[1] Oustaloup, A. & Mathieu, B. (1999) La commande CRONE du scalaire au<br />
multivariable. Hermès. Paris.<br />
[2] S.G. Samko, A.A. Kilbas and O.I. Marichev (1993), « Fractional integrals<br />
and derivatives », Gordon and Breach Science Publishers.<br />
[3] A.Oustaloup, & al, (2000), « The CRONE toolbox for Matlab», 11th IEEE<br />
International Symposium on Computer-Aided Control System Design, CACSD -<br />
Anchorage, Alaska, USA, September 25-27<br />
[4] V. Pommier, (2002), « Commande non entière et commande robuste non<br />
linéaire d’un banc d’essais hydraulique », Thèse de l’Ecole Nationale Supérieure<br />
des Arts et Métiers.<br />
ETTC2003 European Test and Telemetry Conference