Transcript Networked Control Loops

Networked Control Loops An Overview
Karl-Erik Årzén
HRTC Wien 11-13 Sep 2002
Outline
• Overview
• Analysis and Design
– constant network delays
– varying network delays
• JitterBug
– analysis of networked control loops
• TrueTime
– simulation of networked control loops
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Intra-net
Control Builder
OPC Server
Data access
Control Network (TCP/IP)
Controllers
IO
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I/O Fieldbuses
Networked Operations
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Data presentation & recording
Event notification
Code distribution
Task downloading
Commands
Control loops
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Motivation
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Reduced cabling costs
Network hardware cheaper
Manufacturer independent nodes
Modularity and flexibility in system design
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Temporal Determinism
• The key issue in real-time systems
• However, temporal determinism is not a yes
or no thing.
• Levels of determinism rather than hard or soft
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Control - Hard or Soft?
• Both
• However, most feedback control loops can
manage deadline misses without any
problems.
• Probably easier to find hard r-t in discrete
(logic) control
• “Hard real-time” is a model
– often works well
– in many cases overly restrictive
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Control System Characteristics
• For many controllers a worst-case design
approach works well
– e.g., PI, PID, …
• However, a lot of exceptions:
– hybrid controllers that switch between different
modes with different characteristics
– model-predictive controllers (MPC)
• convex optimization problem solved every sample
• execution time can easily vary an order of magnitude
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Delays
• Networks induce delays:
– limited bandwidth
– overhead in network interface
– overhead in network
• Time delays in control loops:
– give rise to phase lag
– degenerate system stability and performance
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Control messages
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Small in size
Frequent, often periodic
“Best consumed before 2002-09-15”
Loosing occasional messages is often
acceptable
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Network Types
• Different networks give different levels of
determinism:
– constant delay (no jitter)
– stochastically varying delays
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CAN: Experimental Data
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Ethernet: Experimental data
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Two Points of View
• Computer Science
– Scheduling principles
– Resource allocation
– What can be guaranteed?
• Control
– Model the delays
– Design of controllers
– Robustness, stability, performance
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Two design approaches
• Maximize temporal determinism
– use protocols and scheduling techniques that maximize
determinism
– e.g. TTA/TTP
– well suited for formal analysis, safety critical systems
– matches sampled control theory well
– non-COTS, requires complete knowledge
• Compensate for temporal non-determinism
– inherent robustness of feedback
– temporally robust off-line design methods
– on-line compensation
• need to measure delays, e.g. “time-stamping”
• gain-scheduling, feedforward, ...
• Complementary
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Feedback Scheduling in Control
– Scheduling of computing resources (CPU time,
bandwidth, memory, power) with guaranteed
control performance
– Co-design of control and scheduling
– Control performance as a QoS parameter (QoC)
– Negotiation and contracts
– Examples:
• adjust sampling frequencies dynamically to control CPU
utilization
• adjust execution time quota for any-time controllers to
control CPU utilization
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Outline
 Overview
• Analysis and Design
– constant network delays
– varying network delays
• JitterBug
– analysis of networked control loops
• TrueTime
– simulation of networked control loops
HRTC Wien 11-13 Sep 2002
Delay Models
• Constant delay
• Random delay
– independent from transfer to transfer
• Random delay
– dependent
– e.g. probability distribution governed
by Markov chain
– “Low load”, “Medium load”,
“High load”
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Constant Delays
• Straightforward
• Continuous time
– e.g. Otto-Smith Controller
– e.g. Predictive PI
• Discrete Time
– sampling of a system with time delay
– time-invariant finite-dimensional system
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Robust vs Worst-Case
• Left: Robust design
taking the delay into
account
• Top Right: Design for
zero delay
• Bottom Right: Design
for worst-case delay
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Random Delays
• More tricky
• Time-varying system
• Examples can be found of systems that are
stable for all constant delays, but become
unstable when the delay varies
• It is important to be clear of what the available
results cover:
– constant delays within a certain range
– varying delays within a certain range
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Sampling of systems with varying delays
• Closed Loop System (plant + controller)
• Similar for sampling jitter
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Stability
• Delays that change according to a finite,
repeating cycle
• Delays that change randomly
– Lyapunov stability theory
– Stable if we can find a common quadratic
Lyapunov function for all delays
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Stability
• New stability criterion for systems with
varying time delays (Lincoln, 2002)
– simple & graphical
– Small gain theorem
– so far only for open-loop stable processes
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Frequency Domain Criterium
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left
right
• Bo Lincoln: “A simple stability criterion for digital control systems
with varying delays”, IFAC World Congress, 2002
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SISO Control - Basic Setup
• Computational Model:
– different possibilities
– our approach (Nilsson): time-driven sensor &
event-driven controller and actuator
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Alternative Approach
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Luck and Ray
Make invariant through max-delay buffers
Longer delays than necessary
Almost always worse than having shorter, varying
delays
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LQG Control - Independent delays
• Johan Nilsson - PhD
– “Real-Time Control Systems with Delays”
• Time stamping
• Old delays known when calculating uk
– sensor-controller delay up to k
– controller-actuator delay up to k-1
• Independent random delays with known
distributions
• State feedback
– full state information
– all states from the same node in the same frame
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LQG Control
• Stochastic Riccati equation
• Updating of S not always possible in real-time
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Simplifications
• Off-line calculation of stationary Riccati
– tabular for L
– interpolation
– linear approximation
• Suboptimal scheme
– delay-free feedback
vector
– predict from time k over
average delay
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Extensions
• Optimal state estimator
• Optimal output feedback controller
– separation principle holds
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LQG Control - Dependent delays
• Delay distributions governed by Markov chain
• Optimal state feedback
– requires knowledge of the delay mode (Markov
chain state)
• Optimal state estimate & output feedback
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LQG Control: Extensions
• Markov chain with two transitions every
sample
– different delay distributions for sender-controller
message and controller-actuator message
• Sampling interval jitter in sensor node
– optimal state feedback, estimator & output
feedback
– requires the solution of the Riccati in every sample
• Estimation of the Markov state
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LQG Control: Extensions
• MIMO Control
– multiple sensor and actuator nodes
– time-driven sampling (synchronized clocks)
– optimal state feedback and estimator results has
been derived
– based on the delay of the latest received sensor
measurement
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Timeout
• Can control performance be improved by
having a timeout on sensor values?
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Timeout Control
• Prediction-Based Controller
• Two versions:
– Lost samples: The delayed samples will eventually arrive
and can be used for updating the filters
– Vacant samples: The delayed samples are lost
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Timeout Control
• 2nd order process, uniform delay on [0,h]
• LQG optimal control
Why wait for a noisy measurement?
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Multi-rate Periodic Control
• Asynchronous periodic loops
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Interesting Delay Patterns
Small change in timing patterns
Björn Wittenmark, Lund
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MIMO Controllers - Other approaches
• Strobe connection
– time-driven controller multicasts a message telling
the sensors to sample
• Poll connection
– time-driven controller sends individual messages
to each sensor node in turn, requesting them to
sample
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Dynamic Delay-Jitter Compensation
• New approach by Bo Lincoln
• Assumptions:
– time-stamping
– full process model not required (only at high frequencies)
– delay statistics not needed
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linear compensator as an add-on to an existing controller
frequency domain conditions for stability and performance
loop shaping design
stability compensation and performance compensation
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Dynamic Jitter Compensation
• Bo Lincoln: “Jitter Compensation in Digital Control Systems”,
ACC 02
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Collision Detection
• Opens up interesting possibilities
• Sensor nodes that detect collisions:
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re-send old sample
discard sample
resample and send new sample …
increase sampling interval to reduce
communication load - tradeoff
• Layered model inadequate
HRTC Wien 11-13 Sep 2002
Outline
 Overview
 Analysis and Design
– constant network delays
– varying network delays
• JitterBug
– analysis of networked control loops
• TrueTime
– simulation of networked control loops
HRTC Wien 11-13 Sep 2002
JITTERBUG
• Matlab-based toolbox for
analysis of real-time control
performance
• Developed by Bo Lincoln and
Anton Cervin
• Calculation of a quadratic
performance criterion function
• Linear process, linear controller
• Stochastic timing description
• Theory for jump-linear systems
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JITTERBUG Analysis
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Example of a JITTERBUG model
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Example of analysis
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Matlab Commands
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More complicated cases
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Example: Mechanical Servo
• Second order system
• PD controller
Case 1: Constant delay
0-100% of h
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Example: Mechanical Servo
Case 2: Random delay
uniform [0-a] where
a is 0-100% of h
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Example: Mechanical Servo
Constant delay ([a]) uniform delay [0-a]
Always > 0
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Example: Mechanical Servo
Constant delay +
delay comp.
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Example: Mechanical Servo
Uniform delay +
dynamic delay comp.
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Outline
 Overview
 Analysis and Design
– constant network delays
– varying network delays
 JitterBug
– analysis of networked control loops
• TrueTime
– simulation of networked control loops
HRTC Wien 11-13 Sep 2002
TrueTime
• Simulation of control loops under shared
computing resources
• Developed by Anton Cervin, Dan Henriksson,
Johan Eker
• Simulink-based
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Main Idea
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Computer Block
• Fixed priority
• EDF
• (static schedule)
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Network Block
• MAC layer
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Execution Model
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Controller Realization
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Example of a Code Function
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Initialization
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Screen Dump
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Example: Networked Control Loop
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Example: Networked Control Loop
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Results, without interference
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Results, with interference
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Other actors
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Greg Walsh, Maryland
Michael Branicky, Case Western
Dawn Tilbury, Univ Michigan
Linda Bushnell, Univ Washington
KTH/DAMEK
...
• Good overview in IEEE Control Systems Special
Issue on Networked Control Systems, February 2001
HRTC Wien 11-13 Sep 2002
Example: Mechanical Servo
Uniform delay ([0,a]) constant average delay
Almost always > 0
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