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[ pdf ] Real-Time Control Systems with Delays

Real-Time Control Systems with Delays Download
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Topic under  Control Engineering
Source: www.control.lth.se 
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Last download on: Sun Feb 18, 2018 01:53:05 PM
Short Desciption:
Control loops that are closed over a communication network get more and more common as the hardware devices for network and network nodes become cheaper. A control system communicating with sensors and actuators over a communication network will be called a distributed real-time control system.

Summary:
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Outline of the Thesis and Publications . . . . . . . . . . . . . . 9 2. Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . 13 2.1 Distributed Control . . . . . . . . . . . . . . . . . . . . . 13 2.2 Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3 Clock Synchronization . . . . . . . . . . . . . . . . . . . . 20 2.4 RelatedWork . . . . . . . . . . . . . . . . . . . . . . . . . 23 3. Modeling of Network Delays . . . . . . . . . . . . . . . . . . 29 3.1 Network Modeled as Constant Delay . . . . . . . . . . . 29 3.2 Network Modeled as Delays Being Independent . . . . . 30 3.3 Network Modeled Using Markov Chain . . . . . . . . . . 31 3.4 Sampling of Systems with Network Delays . . . . . . . . 31 4. Experimental Delay Measurements . . . . . . . . . . . . . . 35 4.1 CAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.2 Ethernet Network . . . . . . . . . . . . . . . . . . . . . . 50 4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5. Analysis and Control with Independent Delays . . . . . . 56 5.1 Closed Loop System . . . . . . . . . . . . . . . . . . . . . 56 5.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 5.3 Simulation of Systems with Network Delays . . . . . . . 62 5.4 Optimal Stochastic Control . . . . . . . . . . . . . . . . . 63 5.5 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5 Contents 6. Analysis and Control with Markov Delays . . . . . . . . . 76 6.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 6.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 6.3 Proof of Theorem 6.1 . . . . . . . . . . . . . . . . . . . . . 89 6.4 Optimal Stochastic Control . . . . . . . . . . . . . . . . . 92 6.5 Proof of Theorem 6.4 . . . . . . . . . . . . . . . . . . . . . 98 6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 7. Special Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 7.1 Markov Chain with Two Transitions Every Sample . . . 103 7.2 Sampling Interval Jitter . . . . . . . . . . . . . . . . . . . 106 7.3 Estimation of Markov State . . . . . . . . . . . . . . . . . 110 7.4 TheMIMO Problem . . . . . . . . . . . . . . . . . . . . . 111 7.5 Timeout . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 7.6 Timeout and Vacant Sampling . . . . . . . . . . . . . . . 120 7.7 Asynchronous Loops . . . . . . . . . . . . . . . . . . . . . 122 8. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 9. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 A. Kronecker Products . . . . . . . . . . . . . . . . . . . . . . . 133 A.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 A.2 Basic Rules of Calculation . . . . . . . . . . . . . . . . . 134 B. Some Results from Probability Theory . . . . . . . . . . . 135 B.1 Markov Chains . . . . . . . . . . . . . . . . . . . . . . . . 135 B.2 Conditional Independence . . . . . . . . . . . . . . . . . . 136
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