EECE 396-1 Hybrid and Embedded Systems: Computation T. John Koo Institute for Software Integrated Systems Department of Electrical Engineering and Computer Science Vanderbilt University 300 Featheringill Hall January 14, 2004 [email protected]http://www.vuse.vanderbilt.edu/~kootj
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EECE 396-1 Hybrid and Embedded Systems: Computation T. John Koo Institute for Software Integrated Systems Department of Electrical Engineering and Computer.
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EECE 396-1Hybrid and Embedded Systems: Computation
T. John Koo
Institute for Software Integrated Systems
Department of Electrical Engineering and Computer Science
Discrete Event• operations on events• continuous time• discrete events
7
The Hierarchical View of Systems
controller
I C
H
car model
enginepowertrain
E
8
Embedded Systems
Embedded systems composed of hardware and software components are designed to interact with a physical environment in real-time in order to fulfill control objectives and design specifications.
Environment
Embedded Hardware
Board Support Packages
Operating System
Embedded Software
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Embedded Systems
Embedded software refers to application software to process information to and fro between the information and physical worlds.
Environment
Embedded Hardware
Board Support Packages
Operating System
Embedded Software
q1q2
q3
u
xç = f (x) + g(x)u
xD/A A/D
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High-ConfidenceEmbedded Software
From Design to Implementation
q1q2
q3
u(t)
xç = f (x) + g(x)u
x(t)
GPS Card INSServos
q1q2
q3
x(t)u(t)
x[k]u[k]
How?
1. Guaranteed closed-loop performance
2. Interaction between asynchronous and synchronous components
RX valuesRX valuesYamaha Receiver(using HW INT & proxy)
Ground computerWin 98
Processesrunning on QNX
4±1Hz10Hz
ANYTIME
APERIODIC
PERIODIC
PERIODIC
PERIODIC
High-Confidence Embedded Software
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Why Hybrid Systems?
Modeling abstraction of Continuous systems with phased operation (e.g. walking robots,
mechanical systems with collisions, circuits with diodes) Continuous systems controlled by discrete inputs (e.g. switches, valves,
digital computers) Coordinating processes (multi-agent systems)
Important in applications Hardware verification/CAD, real time software Manufacturing, communication networks, multimedia
Large scale, multi-agent systems Automated Highway Systems (AHS) Air Traffic Management Systems (ATM) Uninhabited Aerial Vehicles (UAV) Power Networks
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Different Approaches
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H ig h -C o n fid e n c e E m b e d d e d S y s te m s• C o rre c tn e ss b y c o n s tru c tio n
• F a u lt- to le ra n ce
• R e s is ta n ce to a tta c k
200 Hz 400
Hz
200 Hz
1 kHz
F lig h t C o n tro l S o ftw a re
Embedded Software• Embedded software refers to application software to process
information to and fro between the information and physical worlds.
Environment
Embedded Hardware
Board Support Packages
Operating System
Embedded Software
N e tw o r k - C e n t r ic D is t r ib u te d S y s te m s• C o o p e r a t iv e C o n tro l o f M u lt ip le U A V s
• P o w e r E le c t ro n ic s C ir c u i ts
• S e n s o r N e tw o rk s
H y b r i d S y s t e m sC o n t r o l T h e o r y
C o n t r o l o f i n d i v i d u a l a g e n t sC o n t i n u o u s m o d e l sD i f f e r e n t i a l e q u a t i o n s
C o m p u t e r S c i e n c eM o d e l s o f c o m p u t a t i o nC o m m u n i c a t i o n m o d e l sD i s c r e t e e v e n t s y s t e m s
H y b r i d S y s t e m s
Research Directions
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What Are Hybrid Systems?
Dynamical systems with interacting continuous and discrete dynamics
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Proposed Framework
Control TheoryControl of individual agentsContinuous modelsDifferential equations
Computer ScienceModels of computationCommunication modelsDiscrete event systems
Hybrid Systems
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ENNA GmbH
Power Electronics Power electronics found in:
DC-DC converters Power supplies Electric machine drives
Circuits can be defined as networks of: Voltage and current sources (DC or AC) Linear elements (R, L, C) Semiconductors used as switches (diodes, transistors)
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ENNA GmbH
Power Electronics Discrete dynamics
N switches, (up to) 2N discrete states Only discrete inputs (switching): some
discrete transitions under control, others not
Continuous dynamics Linear or affine dynamics at each discrete
state
+ +
23=8 possible configurations
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Power Electronics : DC-DC Converters
Have a DC supply (e.g. battery), but need a different DC voltage
Different configurations depending on whether Vin<Vout or Vin>Vout
Control switching to maintain Vout with changes in load (R), and Vin
Vin
L C Rsw1
sw2+
-
+
-
Vout
iL
iL
Vout
2 1 2
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Two Output DC-DC Converter
Want two DC output voltages Inductors are big and heavy, so
only want to use one Similar to “two tank” problem
Vin
L
C2 R2sw1
sw2+
-
+
-
VoutA
iL+
-
VoutB
sw3
C3 R3
iL
VoutA
VoutB
1 2 3 1 2 3
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Circuit Operation
One and only one switch closed at any time
Each switch state has a continuous dynamics
sw1: iL, VoutA, VoutB
sw2: iL , VoutA , VoutB sw3: iL , VoutA, VoutB
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Design Objective
Objective: Regulate two output voltages and limit current by switching between three discrete states with continuous dynamics.
iL, VoutA, VoutB
iL , VoutA , VoutB
iL , VoutA, VoutB
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Typical Circuit Analysis/Control
Governing equations Time domain, steady state Energy balance
System dynamics Discretization in time
Switched quantity only sampled at discrete instants
Assumes a fixed clock Averaging
Switched quantity approximated by a moving average
Assumes switching is much faster than system time constants
Control Linearize with duty () as input Use classical control techniques
T
T (1- )T
i0
i1
i2
match!
iL(t)iL(t)
iL[k]
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Outline
Background on Power Electronics Hybrid Modeling of DC-DC Converters Controlled Invariant Balls Conclusions
Vin
L C Rsw1
sw2+
-
+
-Vout
iL
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Problem Formulation
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q1
xç(t) = f q1(x(t))x(t) 2 I q1
q2
xç(t) = f q2(x(t))x(t) 2 I q2
û = û2
û = û1
q1
û = û1
q2
û = û2
x 2 G12
x 2 G21
û 2 Î
x 2 X
H1
H2
Problem Formulation Parallel Composition of Hybrid
Automata
Given a collection of Modes and Edges, design Guards
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Research Issues Modeling & Simulation
Control: classify discrete phenomena, existence and uniqueness of execution, Zeno [Branicky, Brockett, van der Schaft, Astrom]
Computer Science: composition and abstraction operations [Alur-Henzinger, Lynch, Sifakis, Varaiya]
Sastry] or deductive methods [Lynch, Manna, Pnuelli], Abstraction [Pappas-Tabuada, Koo-Sastry]
Controller Synthesis Control: optimal control [Branicky-Mitter, Bensoussan-Menaldi],
hierarchical control [Caines, Pappas-Sastry], supervisory control [Lemmon-Antsaklis], safety specifications [Lygeros-Sastry, Tomlin-Lygeros-Sastry], control mode switching [Koo-Pappas-Sastry]
Computer Science: algorithmic synthesis [Maler et.al., Wong-Toi], synthesis based on HJB [Mitchell-Tomlin]
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Hybrid Systems
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Hybrid Systems
Hybrid Automata (Lygeros-Tomlin-Sastry, 2001)
Ref: J. Lygeros, C. Tomlin, and S. Sastry, The Art of Hybrid Systems, July 2001.
Post(P) = fx 2 Xj9x0 2 P 9t õ 0 s:t: x = þ(t;ri;x0)g
Check if Post(X S) \ X F = ; ?
Forward Reachable Set
Reachability Problem
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Computational Tools – Hybrid Systems
Reach Sets ComputationFiniteAutomata
TimedAutomata
LinearAutomata
LinearHybrid Systems
NonlinearHybrid Systems
d/dtCheckMate
Timed COSPANKRONOSTimed HSISVERITIUPPAAL
HYTECHCOSPANSMVVIS…
Requiem
xç= 1 Axçô b xç= Ax xç= f (x)
Si(r i)Sj(r j)
Prei(Sj(r j);r i)
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Research Directions
Hybrid Systems Embedded Software High-Confidence Embedded Systems Network-Centric Distributed Systems
Development of formal methods for the design of high-confidence embedded software based on hybrid system theory with applications to distributed, network-centric, embedded systems such as sensor networks, power electronics circuits, and cooperative UAV systems
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Research Collaboration
Institutions Center for Hybrid and Embedded Systems and Software (CHESS),
University of California at Berkeley GRASP Laboratory, University of Pennsylvania Hybrid Systems Laboratory, Stanford University Control Group, Cambridge University INRIA, France KTH, Sweden Honeywell Laboratories Cadence Berkeley Laboratory
Conferences Workshop on Hybrid Systems: Computation and Control (HSCC) Workshop on Embedded Software (EMSOFT) IEEE Conference on Decision and Control (CDC) IEEE Conference on Robotics and Automation (ICRA) …
International Workshop on Hybrid Systems: Computation and Control