Controller Design Using Multiple
Models of Computation
Edward Lee
Johan Eker
with thanks to Paul Griffiths, Jie Liu, Xiaojun Liu,
Steve Neuendorffer, and Yuhong Xiong
MoBIES PI-Meeting, 16-18 July 2001, Jackson Hole
Overview
 Mixed signal control systems
 The throttle control system by Paul Griffith
 Modal controllers
 Extended throttle controller by Johan Eker
 Design patterns
 The use of domains and hierarchy
 Mixed signal models
 Modal models
 Code generation
 co-compilation
Eker & Lee, UC Berkeley 2
A Throttle Control System
discrete-time controller
throttle model
Input: desired throttle angle (and derivatives)
Throttle controller by Paul Griffiths
(Mobies Phase II, UC Berkeley)
Top-level model
Continuous-time (CT) domain in Ptolemy II
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A Throttle Control System
Result of
executing the
model shows
intial convergence
phase followed by
tracking with a
slight phase lag.
The control signal
chatters to
overcome friction.
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Design Pattern:
Discrete Time in Continuous Time
Synchronous dataflow director
indicates a new model of
computation.
No director indicates no
new model of computation.
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Control Engineer View
 plant dynamics in continuous time
 controller in discrete time
 focus on stability, phase margins, rise time...
 assume ideal sampling with no or little latency
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Embedded System Engineer View
 dynamics modeled with RK-4, variable-step solver
 controller modeled in synthesizable SDF, FRP, …
 focus on scheduling, memory, communication...
 assume fixed controller design
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A More Integrated Approach
 controller design informed by software issues
 domain-oriented modeling language
 modeling = implementation
 latency and jitter are part of the model
 software design informed by controller issues
 expressing timing constraints
 correct-by-construction synthesis
 heterogeneous modeling
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Elaborated Throttle Control System
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Design Pattern: Modal Discrete-Time
Controller in Continuous Time
continuous time
finite-state machine
discrete time
Hierarchical, heterogeneous model
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This is Still An Idealized Model
No jitter, no delays
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Extend the ideal model
 Influence from implementation:
 Jitter
 Control delay
 Execution:
 Multitasking environment
 Incorporate the behavior of the RTOS
 Communication:
 Shared communication links
 Behavior of the network
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A more accurate model
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Software Realism
 Express timing constraints
 sample rates
 latency
 jitter tolerances
 Build models in appropriate abstractions
 Giotto: time-triggered
 HPM: hierarhical preemptive multitasking
 FRP: functional-reactive programming
 …

These facilitate correct-by-construction implementation
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The Next Problem:
Synthesizing an Implementation
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Outline of our Approach
Jeff Tsay, Christopher
Hylands, Steve
Neuendorffer
Model of Computation semantics defines communication, flow of control
parser
Ptolemy II model
scheduler
Schedule:
- fire Gaussian0
- fire Ramp1
- fire Sine2
- fire AddSubtract5
- fire SequenceScope10
method call
All actors are
given in Java,
then translated
to embedded
Java, C, VHDL,
etc.
if
block
method call
block
abstract syntax tree
…
for (int i = 0; i < plus.getWidth(); i++) {
if (plus.hasToken(i)) {
if (sum == null) {
sum = plus.get(i);
} else {
sum = sum.add(plus.get(i));
}
}
}
…
target code
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Division of Responsibility
 MoC semantics defines

flow of control across actors
 communication protocols between actors
 Actors define:

functionality of components
 Actors are compiled by a MoC-aware compiler

generate specialized code for actors in context
 Hierarchy:

Code generation at a level of the hierarchy produces a new
actor definition
We call this co-compilation.
Multiple domains may be used in the same model
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Software Progress
Build on:
 First version on Titanium (UC Berkeley)
 Second version on Soot (McGill)
Targeting:
 Simulation acceleration
 Embedded software synthesis

Maryland subcontract
 Configurable hardware synthesis

delegated to Brigham Young
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Our Generator Approach
 Actor libraries are built and maintained in Java
 more maintainable, easier to write
 polymorphic libraries are rich and small
 Java + MoC translates to target language
 concurrent and imperative semantics
 Efficiency gotten through code transformations
 specialization of polymorphic types
 code substitution using MoC semantics
 removal of unnecessary code
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Code transformations (data types)
// Original actor source
Token t1 = in.get(0);
Token t2 = in.get(1);
out.send(0, t1.multiply(t2));
specialization of Token declarations
// With specialized types
IntMatrixToken t1 = in.get(0);
IntMatrixToken t2 = in.get(1);
out.send(0, t1.multiply(t2));
The Ptolemy II type system
supports polymorphic actors with
propagating type constraints and
static type resolution. The
resolved types can be used in
optimized generated code.
See Jeff Tsay, A Code Generation Framework for Ptolemy II
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Type system by Yuhong Xiong
Type System
Input of general type
- anything will do
Output of type
general - pure event
with no value
general
double
Polymorphic output
- type depends on
the parameters
double
general
double
int
Opaque port - types
propagated from
inside
Lossless runtime
type conversion
Polymorphic actor
uses late binding in
Java to determine
implementation of
addition.
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Type System
 Extensible type lattice
 Knowledgeable users can add full-featured types
 Unification infrastructure
 Finds a least fixed point
 Composite types
 records, arrays, matrices
 Higher-order types planned
 model = data
 Experiments with dependent types
 encoding MoC constraints
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Code transformations (MoC-informed)
// With specialized types
IntMatrixToken t1 = in.get(0);
IntMatrixToken t2 = in.get(1);
out.send(0, t1.multiply(t2));
MoC-polymorphic code is
replaced with specialized code.
transformation using MoC semantics
// Extended Java with specialized communication
int[][] t1 = _inbuf[0][_inOffset = (_inOffset+1)%5];
int[][] t2 = _inbuf[1][_inOffset = (_inOffset+1)%5];
_outbuf[_outOffset = (_outOffset+1)%8] = t1 * t2;
See Jeff Tsay, A Code Generation Framework for Ptolemy II
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Synchronous Dataflow (SDF) Domain



Balance equations (one for each channel):
FAN = FBM
Scheduled statically
Decidable resource requirements
get(0)
send(0,t)
B
A
N
M
token t
Available optimizations:
 eliminate checks for input data
 statically allocate communication buffers
 statically sequence actor invocations (and inline?)
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Synchronous/Reactive Domain
 A discrete model of time progresses as a
sequence of “ticks.” At a tick, the signals are
defined by a fixed point equation:
x OLf (1) O
L
M
P
M
P
y

f
(
z
)
M
P
M
P
P
M
f
(
x
,
y
)
Nz P
QM
N Q
A ,t
B ,t
C ,t
A
x
C
B
Available optimizations:
• Statically sequence fixed-point iteration
• Communication via registers
y
z
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Other Domains with Useful Properties
for Code Generation
 Strong static analyzability
 Giotto (time triggered)
 HPM (hierarchical preemptive multitasking)
 FRP (functional reactive programming – Yale)
 Finite state machines
 Discrete time
 Good for hardware descriptions
 Discrete events
 Process networks
 Continuous time (analog hardware)
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Hierarchical Heterogeneity
Ptolemy II composes domains hierarchically,
where components in a model can be refined into
subcomponents where the component
interactions follow distinct semantics.
M: Manager
E0
Transparent
Composite
Actor
Opaque
Composite
Actor
D1: local director
E2
D2: local director
E1
P1
P2
E4
P5
P6
E3
P3
P4
E5
P7
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Conclusions
 Hierarchically heterogenous modeling matches
the applications well…
 Hierarchically heterogenous modeling appears to
be suited to high-quality sythesis
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