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Synchronised trajectory-tracking control of multiple 3 ... - IEEE Xplore

Synchronised trajectory-tracking control of multiple 3 ... - IEEE Xplore

Fig. 4Three 3-DOF

Fig. 4Three 3-DOF helicopters experimental setupTable 1: Parameters and control gains for three 3-DOF helicoptersParameters=gains Helicopter I Helicopter II Helicopter IIIMoment of inertia J ei ; kgm 2 1.044 1.030 1.017Moment of inertia J pi ; kgm 2 0.0455 0.0455 0.0455Mass m i ; kg 0.142 p 0.128 0.113K fi ; N=V 0.625 0.625 0.625l ai ; m 0.648 0.648 0.648l hi ; m 0.178 0.178 0.178ADS system yes no noFeedback gains for elevation, ½K P ; K D Š ½30:0 15:0 Š ½30:0 15:0 Š ½30:0 15:0 ŠSync. feedback gains, K si 1.0 1.0 1.0Sync. coupling gains, B i 1.0 1.0 1.0p Value measured when ADS is at farthest position from propellers, 0.170 for middle position in slide bar, 0.213 for nearest position from propellers.For comparison between different synchronisationerrors, two synchronisation strategies are considered:Strategy I: The synchronisation error and the coupledattitude error are chosen to be those in (18) and (23);Strategy II: The synchronisation error and the coupledattitude error are those in (19) and (24). The synchronisationerror in (18) is employed as the uniform synchronisationerror for performance evaluation in all experiments.Furthermore, the ADS on Helicopter I is activated by asquare wave command, see Fig. 5, for performingdisturbance to the control system. In this way the effectivemass of Helicopter I will vary between 0.142 and0.213 kg. The asymptotic convergences of both trajectorytracking and synchronisation errors can only be realisedwhen the exact system parameters are known. If there is aparametric disturbance, such as the mass disturbance inour case, the asymptotic convergence cannot be guaranteedalthough the system may still be stable. The aim ofintroducing the mass disturbance in our experiments is toverify the effectiveness of the proposed controller. We688ADS position, mFig. 50.30.250.20.150.10.050–0.050 10 20 30 40 50 60time, sADS position trajectory0 means ADS is at farthest position from propellers, 0.26 means ADS is atnearest position from propellersIEE Proc.-Control Theory Appl., Vol. 152, No. 6, November 2005

Fig. 6Experimental result of attitude trajectory tracking control without synchronisation strategya Trajectories of elevation angleb Trajectories of travel anglec Trajectory tracking errors of elevation angled Synchronisation errors of elevation anglee Control voltages for front motorsf Control voltages for back motorsinspect how these 3-DOF helicopters response without=with synchronisation strategies, and compare the synchronisationperformance using different synchronizationstrategies under the parametric disturbance.Figure 6 shows the experimental results of elevationtracking control of three 3-DOF helicopters withoutsynchronisation strategy (by setting K si ¼ 0 and B i ¼ 0Þ:Figures 7 and 8 are the experimental results usingsynchronisation strategy I and II, respectively. The maximalelevation tracking and synchronisation errors are measuredand listed in Table 2. For each experiment the three valuespresent the maximal elevation trajectory tracking errorsduring maneuver (from 0 to 20 s), after maneuver(maneuver completed, after 20 s in our experiments), andthe maximal synchronisation error during whole experiment,respectively.It can be seen from Fig. 6 that the elevation trajectorytracking error of Helicopter I is large because of the ADS.Table 2 shows that the maximal elevation trajectorytracking errors during and after the maneuver are 3.136IEE Proc.-Control Theory Appl., Vol. 152, No. 6, November 2005 689

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