Time-Dependent Dynamics in Networked Sensing and Control

Time-Dependent Dynamics in Networked Sensing and Control

Time-Dependent Dynamics in Networked Sensing and Control Justin R. Hartman Michael S. Branicky Vincenzo Liberatore Outline Previous Work Network Properties and Difficulties Stability Regions and Traffic Locus

Co-Simulation Methodology and Results Conclusions 9 June 2005 American Control Conference 2005 2 Previous Work Nilssons Assumptions Walsh et al.: MATI

Zhang: hsuff Branicky, Liberatore, Phillips: Co-Simulation for Co-Design (ACC 03) 9 June 2005 American Control Conference 2005 3 NSCS Difficulties

Packet delays, dropped packets Delays related to: Computation and Propagationfixed delay per link Transmissionrelated to link speed Queuingrelated to link buffer size Dropped packets related to:

Collisions (but not in a switched network) Bandwidth and Queuingrelated to link speed and link buffer size 9 June 2005 American Control Conference 2005 4 NSCS Difficulties Illustrated 9 June 2005 American Control Conference 2005 5

Network Delays Delays are bounded by [min, max] 9 June 2005 American Control Conference 2005 6 Packet Loss Packet loss due to network congestion

Packet loss changes sampling period in discrete set: {h,2h,3h,...} Over a long time, calculate the effective sampling period: Si 8h iN hi ,h L { heff max 9 June 2005 }

American Control Conference 2005 7 Effective Sampling Period 9 June 2005 American Control Conference 2005 8 Outline

Previous Work Network Properties and Difficulties Stability Regions and Traffic Locus Co-Simulation Methodology and Results Conclusions 9 June 2005 American Control Conference 2005 9 Stability Region

Previous work has developed a Sampling Period and Delay Stability Region (SPDSR) Analytical bound on system stability assuming fixed sampling period and fixed delays 9 June 2005 American Control Conference 2005 10 SPDSR

9 June 2005 American Control Conference 2005 11 Traffic Locus Describes where (on average) in the SPDSR the system will perform given certain parameters Vary:

Number of plants Queue size Sampling period Packet size etc. 9 June 2005 American Control Conference 2005 12 Traffic Locus (Cont.) 9 June 2005

American Control Conference 2005 13 Outline Previous Work Network Properties and Difficulties Stability Regions and Traffic Locus Co-Simulation Methodology and Results

Conclusions 9 June 2005 American Control Conference 2005 14 Co-Simulation Methodology Simultaneously simulate both the dynamics of the control system and the network activity Achieved through ns-2 network simulator [http://vorlon.cwru.edu/~vxl11/NetBots/]

Vary parameters to achieve interesting results Number of plants Cross-traffic Sample scheduling Etc. 9 June 2005 American Control Conference 2005

15 Network Topology 10 Mbps link between plants (2-4) and router (1), with 0.1 ms fixed link delay 1.5 Mbps T1 line between router (1) and controller (0), with 1.0 ms fixed link delay First plant (2) under observation Delays are asymmetric 9 June 2005 American Control Conference 2005

16 Control System Assumes full-state feedback Non-linear equations linearized about the unstable equilibrium Sampled at 50 ms Feedback designed via discrete LQR Control signal is cart acceleration 9 June 2005

American Control Conference 2005 17 Baseline Simulation One plant on the network No cross-traffic No bandwidth contention Delays fixed at min No lost packets Slight performance degradation due to fixed delays 9 June 2005

American Control Conference 2005 18 Threshold Behavior 147 Plants on the network (just more than the network bottleneck) No cross-traffic Performance slightly worse than baseline 9 June 2005 American Control Conference 2005

19 Threshold Behavior (Cont.) Delays are asymmetric and variable Delay ranges from min to max 147 plants slightly exceeds network bandwidth Packet drops due to excessive queuing 9 June 2005 American Control Conference 2005

20 Cross-Traffic 130 Plants on network Bursty FTP crosstraffic at random intervals Performance similar to threshold case 9 June 2005 American Control Conference 2005 21 Cross-Traffic (Cont.)

Delays are asymmetric and variable Delay ranges in min to max, depending on traffic flow 130 plants below network bandwidth, but cross-traffic exceeds Packet drops due to queuing 9 June 2005 American Control Conference 2005 22

Over-Commissioned 175 Plants on network well above network bandwidth No cross-traffic Performance degrades substantially 9 June 2005 American Control Conference 2005 23 Over-Commissioned (Cont.) Delays

asymmetric sc quickly fixed at max ca still fixed at min 175 plants well above network bandwidth Many packet drops due to excessive queuing 9 June 2005 American Control Conference 2005 24

SPDSR from Simulations 9 June 2005 American Control Conference 2005 25 Conclusions Controlled physics depend on real-time communications properties Analytical stability criteria are interesting

and helpful, but they do not completely describe the stability of a dynamic NSCS "Average-case" analysis cannot explain poor system performance -- analysis must account for exact network dynamics 9 June 2005 American Control Conference 2005 26 Website NSCS Repository http://home.case.edu/ncs/ 9 June 2005 American Control Conference 2005

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