Antinomy between Schedulability and Quality of Control using a Feedback Scheduler RTNS’2014
EMP ISAE-ENSMA LSI-USTHB Antinomy between Schedulability and Quality of Control using a Feedback Scheduler RTNS’2014 Authors Zakaria Sahraoui Emmanuel Grolleau Mohamed Ahmed Nacer Dris Mehdi EMP LIAS ISAE-ENSMA LSI USTHB LIAS ISAE-ENSMA Algeria France Algeria France LIAS ISAE-ENSMA France Speaker Henri Bauer Outline Introduction Antinomy in co-design Scheduling artifacts characterization Conclusion Antinomy in codesign... RTNS’2014 2 Why should we care ? Traditional real-time scheduling models give poor support for scheduling/control co-design... Antinomy in codesign... RTNS’2014 3 Off-line optimization M peak E ss M peak = f M (period, latency) T rise Antinomy in codesign... T set RTNS’2014 E ss = f E (period, latency) T rise = f r (period, latency) T set = f s (period, latency) [Seto '96, Ryu '97] 4 Experimental settings RM scheduled periodic tasks with implicit deadlines shape factor = 3 scale = 0.15 localization = 2ms Maximal observed execution time Minimal observed execution time Best case WCET Execution times distribution following a Weibull law (given: best and WCET) Antinomy in codesign... RTNS’2014 5 The feedback scheduler processor utilization bound + Scheduler Manager estimated execution time plant ref. Scheduler Filter (aging factor) error + periods - Task i Regulator observed execution time sampling period control D/A measure Antinomy in codesign... RTNS’2014 Process G(s) A/D 6 Processor utilization bounds [Liu & Layland '73] 1 n ∑ U i⩽n (2 −1) [Bini '03] (hyperbolic condition) ∏ (U i +1)⩽2 Antinomy in codesign... RTNS’2014 7 Timings and delays Task period Next task period I/O latency Exec. time tk measure control next I/O latency Samp. latency t k+1 measure control t k+2 Control latency Sampling latency: higher priority task execution I/O latency: execution time + higher priority preemption Scheduling artifacts: latencies and jitters... Antinomy in codesign... RTNS’2014 8 Two study cases ● ● Three servo-motors with a PID regulator – Well known study case from [Åström & Hägglund] – Adaptive samples: backward difference for derivative – Controlled by a single processor computer Three inverted pendulums with cart – Another well studied benchmark [Åström & Furuta] – Strongly non linear three order coupled system – With cart: only horizontal moves Antinomy in codesign... RTNS’2014 9 Three servo-motors example 1000 G(s)= s (s +1) PID CONTROL FUNCTION Controller performance parameters: (ω 0, ξ)=(20, 0.707) ● Use of adaptive samples in the PID ● Antinomy in codesign... RTNS’2014 10 Simulation setup COST CONTROL OUTPUT Tsim SCHEDULING ERROR COST FUNCTION: ∫ |ref −output|dt 0 Antinomy in codesign... RTNS’2014 11 Assumption Minimizing tasks' period improves quality of control... Antinomy in codesign... RTNS’2014 12 Performance analysis ● ● ● Three periodic tasks: nominal period hinom → task priority (RM) Feedback scheduling: hik+1 = α hik → reach the utilization bound Execution time: 3 ≤ Ci ≤ 5 ms (Weibull distribution) Bound L&L test (U < 0.69) h inom = Hyperbolic test Threshold (U = 0.5) τ1 τ2 τ3 τ1 τ2 τ3 τ1 τ2 τ3 Error 0.063 0.065 0.64 0.060 0.062 1.35 0.088 768.7 >108 Sampling period (ms) 12.52 15.55 18.79 12.40 15.51 18.60 19.43 24.24 29.15 I/O latency (ms) 3.88 5.24 7.32 3.88 5.09 7.93 3.87 4.84 5.28 (4, 5, 6) Antinomy in codesign... RTNS’2014 13 The antinomy Scheduling artifacts (response time and jitter) increase when processor utilization increases (controller tasks periods decrease). The degradation caused by these phenomena on a PID controller can be greater than the gain generated by the increase in sampling rate. Antinomy in codesign... RTNS’2014 14 The antinomy illustrated ● Three servo-motors: periodic tasks τ1, τ2, ● Scheduled with RM Ci h inom τ1 8.85 17.7 τ2 8.85 17.7 τ3 8.85 17.7 Antinomy in codesign... τ3 (tie breaker: smallest task index) RTNS’2014 15 The antinomy illustrated Ci h inom τ1 4.6 17.7 Same Ui but... τ2-τ3 4.6 17.7 doubled pace for Antinomy in codesign... RTNS’2014 τ1 Ci h inom τ1 2.3 8.85 τ2-τ3 4.6 17.7 16 Artifact characterization ● Three servo-motors example Ci τ1 τ2 τ3 3.4 h inom Mode k µ λ 6 3.2 3.1 0.2 3 13 3.2 3.1 0.2 3 14 3.2 3.1 0.2 3 mean sample period Error cost function of mean sample periods for task τ3 Antinomy in codesign... RTNS’2014 17 Artifact characterization I/O latency sampling latency Error cost function of IO and control jitter Error cost function of sampling latencies for τ3 control jitter for τ3 Linear correlation (SRS): 0.95 (I/O) and -0.81 (Samp) Linear correlation (SRS): -0.88 Antinomy in codesign... RTNS’2014 18 Artifact characterization ● Three inverted pendulum example Ci τ1 τ2 3.4 τ3 h inom Mode k µ λ 6 3.2 3.1 0.2 3 13 3.2 3.1 0.2 3 14 3.2 3.1 0.2 3 I/O latency Antinomy in codesign... sampling latency RTNS’2014 mean sample period control jitter 19 Conclusion & perspectives ● Do not (always) trust intuitive assumptions ● Impact of scheduling artifacts on QoC – ● Contribution – ● Try to keep I/O latency low... Identify scheduling parameters that deteriorate a real-time control when the lower priority task's frequency tends toward the closed-loop system bandwidth Perspective: guidelines for better co-design... Antinomy in codesign... RTNS’2014 20 EMP ISAE-ENSMA LSI-USTHB Thank you for your attention
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