Applications of Time Delay Systems by John Chiasson, Jean Jacques Loiseau

By John Chiasson, Jean Jacques Loiseau

This booklet offers an replace of the newest study accountable for time hold up platforms and functions by way of international major specialists. it's going to attract engineers, researchers and scholars up to speed.

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Additional resources for Applications of Time Delay Systems

Sample text

Consider the system described by (3) with a constant delay τ , controlled by (12). If the estimated delay τˆ is diﬀerent from the one experienced by the control input and Δ describes the deviation of this delay, then the characteristic-equation of the closed-loop system is det sIn − A + BK − eτˆA e−ˆτ s (1 − e−Δs )BK . Remark 6. This result shows the correlation between the choice of the controller gain K, the estimated delay and the maximum acceptable deviation of this delay. This illustrates the necessary compromise between a high gain control scheme (broad bandwidth) and the robustness with respect to the uncertainties on the delay (sensitivity of the closed-loop system).

From Figure 2 we see that the samples with time stamps from 20 to 200 msec arrived to the controller’s computer at tc = 200 msec. This problem however, did not manifest itself with UDP packets which arrived every 20 msec, as sampled. Figure 3 shows a plot of the time stamp arrivals, with a sampling time of 200 msec. Now the sampling time is equal to the lower bound in the broadcasting rate induced by TCP and the packets are not retained. The retention of packets generates a later bursting of those packets.

In the third experiment we used a sampling time ts = 200 msec, and the compensations for both time-delays were also applied at t = 0. 6 volts. Two disconnections occurred, the ﬁrst at t = 50 secs, and the second at t = 113 secs, but the system suffered a minimum level of disruption. 4 Teleoperation Experiment So far, we have exposed the various issues that arise in a NCS. In this section, we focus on the time-delay issue, in a teleoperation experiment. 1 Experimental Setup The teleoperation experiment was set up between a PHANToM T M Desktop haptic device as a master device, that was locally at the Coordinated Science Laboratory at the University of Illinois at Urbana Campaign, and a slave mobile robot located at the Network Control Systems Laboratory at the UNM.