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This paper studies control problems of sampled data systems which are subject to random sample rate variations and delays. Due to the rapid growth of the use of computers more and more systems are controlled digitally. Complex systems such as space telerobotic systems require the integration of a number of sub-systems at different hierarchical levels. While many sub-systems may run on a single processor, some sub-systems require their own processor or processors. The sub-systems are integrated into functioning systems through communications. Communication between processes sharing a single processor are also subject to random delays due to memory management and interrupt latency. Communications between processors involve random delays due to network access and to data collisions. Furthermore, all control processes involve delays due to causal factors in measuring devices and to signal processing.
Traditionally, sampling rates are chosen to meet the worst case communication delay. Such a strategy is wasteful as the processors are then idle a great proportion of the time; sample rates are not as high as possible resulting in poor performance or in the over specification of control processors; there is the possibility of missing data no matter how low the sample rate is picked.
Randomly sampled systems have been studied since later 1950's, however, results on this subject are very limited and they are not applicable to practical systems. This paper studies asymptotical stability with probability one for randomly sampled multi-dimensional linear systems. A sufficient condition for the stability is obtained. This condition is so simple that it can be applied to practical systems. A design procedure is also shown.
These results are applied to robot control systems using PD controllers with a feedforward term, computed torque controllers or simple computed torque controllers. The effectiveness of the method is demonstrated by simulations.
Hiroaki Kobayashi, Xiaoping Yun, and Richard P. Paul, "Control of Randomly Sampled Robotic Systems", . May 1989.
Date Posted: 05 November 2007