Integrated Control and
Scheduling
James Yang, Steve Sheng, Bill Li
Instructor: Prof. Insup Lee
Outline
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Motivation
Periodic scheduling
Control Concepts
Robust scheduling
Motivation
• Misunderstanding between control and
scheduling communities
– C: computer platforms provide deterministic,
fixed sampling period
– S: control tasks have:
• fixed periods
• hard deadlines
• known worst-case execution times (WCETs)
The Vision
• Dynamic, flexible, interactive integrated
control and scheduling environment
– Control performance vs. computing resource
– Relax known WCET
• On-line information exchange
– Desired period of control task
– Nominal execution time
– Desired deadline
Delete,Real-Time Scheduling
• Concept about task
– Periodic, sporadic, aperiodic
– Worst case CPU time C, deadline D
• Scheduling of CPU time for periodic tasks
– Static cyclic executive scheduling
• Off-line to generate execution table
– Priority-based scheduling
• Assumption: Di=Ti, no communication, ideal kernel
• Earliest deadline first(EDF)
• Rate-monotonic(RM)
Periodic Task Scheduling
• EDF
– If U<=1, then all deadlines will be met
– Processor fully utilized with deadlines met
• RM
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Tasks with shorter period get higher priority
If U<=n(2^1/n-1)
Iff Ri<Di for all tasks
Bad performance when Di<<Ti
Implementation and Scheduling
of Periodic Control Loops
• What is control loop?
– Three parts: data collection, algorithm
computation, output transmission
– Periodical in most cases
• Implementation
– Single-task approach
– Multiple-task approach
Loop Timing Constrains
sample control
period
sample
control
latency
• The period should be constant
• Input-output latency
– Decrease stability, limits performance
– Ignore if minimized, otherwise be considered
Single-task Implementation
LOOP
Await clock interrupt
Data collection
Algorithm calculation
Output transmission
END
CurrentTime(t)
LOOP
Data collection
Algorithm calculation
Output transmission
t = t+h
WaitUntil(t)
END
Control Delay
• Separate algorithm
calculation
– Calculate output: make
use of current sample
information
– Update state: update
controller states
CurrentTime(t)
LOOP
Data collection
calculate output
Output transmission
update state
t = t+h
WaitUntil(t)
END
Timing Requirement
• Data collection: same instant every period
• Calculate output: ASA sample available
• Output transmission: immediately after CO,
or at fixed instant after data collection
• Update state: before next period, or before
release of next “calculate output”
Scheduling of Control Tasks
• Fixed-priority scheduling
– Describe controller as period tasks
– Rate-monotonic is optimal if D=T
– Deadline-monotonic is optimal if D<=T, used
to improve important long period control tasks
Deadline Assignment
• Period T and execution time C are known
• Deadlines D must be assigned, optimal
deadline assignment is NP-hard
• Effective-deadline-monotonic assignment
– Later subtasks given just enough time
Dij=Di-Sum[j+1<=k<=ni]Cik
Scheduling Under Overload
Conditions
• Relaxation of known worst-case execution
time
– Treat longer-than-worst actual execution time
as overload conditions
– Algorithm: associate positive value with task
• Complete the most important tasks
• Avoid domino effect
Robust Aperiodic Scheduling
• Real-time systems should handle
– Periodic tasks
• Hard deadlines
– Aperiodic tasks—irregular arrival times
• Soft deadlines
– minimize average response time
• Firm deadlines
– Reject tasks going to be late
– Maximize completed tasks
– Maximize system value
Assumptions
• All periodic tasks have hard deadlines,
known constant period and WCET
• Arrival time of aperiodic tasks is unknown
• WCET of aperiodicities is known on arrival
• Aperiodicities have firm deadlines and can
be rejected
Terminology
• J: a set of aperiodic Ji
ordered by deadline
• ri:arrival time of Ji
• Ci:max computation
time of Ji
• Ci’:actual computation
time of Ji
• di:deadline of Ji
• mi:deadline tolerance
• vi:task value(relative
importance)
• fi:finishing time
• Ei:exceeding time
Total Bandwidth Algorithm
• Assign a suitable deadline
– dk=max(rk, dk-1)+Ck/Us
– d0=0
• Schedule it as periodic tasks
TB Algorithm: Example
Resource Reclaiming
• TB behavior depends on est. max time
– What if the value is overestimated?
• Correct the assigned deadlines
– di=ri’+Ci/Us
– ri’=max(ri, d’i-1, fi-1)
– At task completion, di’=ri’+Ci’/US
Resource Reclaiming: example
Schedulability
• Theorem: given a set n of periodic tasks
with Up and a TB server with Us, the whole
set is schedulable iff Up+Us<=1
• Lemma: in [t1,t2], if Cape is the total
execution time of aperiodic tasks, then
Cape<=(t2-t1)Us
Robust Scheduling
What if overload?
– Assign large bandwidth to server
– Introduce overload awareness
• RED algorithm