Slide 1John Milios CEO
• Focused initially on technologies for battery system design and management, expanding into other markets
• Fabless semiconductor and technology company
• Privately held, founded in 2010, headquartered in NYC
• Award winning products
Core Converging Technologies
Sendyne in the Internet of Things
“Model Based” is key concept in control apps • Used in a majority of existing multivariable control applications
• Technology of choice for new complex control systems
• Success of the technology rides on MCU computing power increase
• Technology has become multidisciplinary
methods • Easier to maintain
• Changing model or specs does not require a complete redesign
• MCU advances open the field for embedded applications
“PDEs, ODEs & DAE
• Physics based models are described generally with a set of non-linear Differential Algebraic Equations
• In the general case an analytical solution is either not known or does not exist
• For systems described by a set of Partial Differential Equations (PDEs) spatial discretization schemes are employed to transform them into a set of DAEs
• Real-time control methods require such models to be ported into an embedded processor and solved in “real time” relative to the time constants of the controlled process
• These DAEs need to be solved using modern numerical techniques
“There is only one precise way of presenting the (..physics) laws, and that is by means of differential equations. They have the advantage of being fundamental and, so far as we know, precise.” The Feynman lectures on Physics
Model Concepts – ODEs & DAEs
• In order to advance the model in time, the solver requires information related to the derivatives of the model equations with respect to the state variables. This is the so- called Jacobian matrix of the model
• The Jacobian can be calculated automatically with the AD module
Explicit ODE ( , ; )t= ∂

γ


t i e t t
y y p
• Two step process • Model is developed and tested in
Computer Aided Engineering environment (CAE)
• Code is generated for the embedded environment
• This code does not contain useful features of the CAE environment
• Model changes require a high-cost repetition of the process
The Sendyne dtSolve™ paradigm
the embedded controller
• You only need to enter the DAEs of the model
• You solve the model with all the essential capabilities of the CAE environment
dtSolve™ structure
• Solve all model equations concurrently
• Solver obtains values of state variables for different values of independent variables
• The process is iterative • User obtains new values by advancing
the model in time • One step process
Explicit ODE ( , ; )t=y F y p
DAE or implicit ODE ( , , ; ) 0t =G y y p
- independent variable ( . ., time or position) ( ) - state variables ( ) - state variables derivatives - parameters
t i e t t
y y p
• A collection of tools provides model optimization
• Gradient-based, derivative free and global optimizers can be coupled with AD and sensitivity analysis
• Optimizers can be used for online optimization in control applications, such as Model Reference Adaptive Control
Automatic Differentiation
• Automatic differentiation (AD) makes it possible to exactly evaluate the derivatives of any numerical function
• Removes the need for the user to deal with the tedious and error-prone task of implementing such computations
• AD is built on C++ operator overloading features and introduces only a minimal overhead in terms of performance (memory and speed of execution)
• Reliability Accurate to machine precision
• Computational Cost Forward mode: 2 ~3n x cost(f)
• Human Effort No time spent in preparing code for differentiation
Automatic Differentiation concept 1 2 1 2 1
1 2
1 1
2 2
like:
s
m
in( )
f x x x x x f x x
= +
= = = = = +
4 1 1
) 0( 0 x
w w w w w w w w w w w w
x w
x x
x x
w w wf f x w w w x
∂ ∂ ∂∂ ∂ =
∂ ∂ ∂ ∂ ∂
Chain rule
• A set of techniques to numerically evaluate the derivative of a function specified by a computer program
• AD exploits the fact that every computer program, no matter how complicated, executes a sequence of elementary arithmetic operations (addition, subtraction, multiplication, division, etc.) and elementary functions (exp, log, sin, cos, etc.)
• dtSolve™ implements operator overloading in C++
• No changes in original code • Flexible when changing code or
platform
dtSolve™ base • dtSolve™ Base is the foundation of
dtSolve™ and contains all the essential features for the model optimizer and the model solver
• The implementation details of each components are encapsulated so that the user benefits transparently of those features
• Memory management unit provides predictable and conflict free memory pools
Memory management • Memory management unit provides
predictable and conflict free memory poolsMemory allocated at initialization and instantiation phase
• No conflicts or unbounded delays among contending solver processes
• Different types of memory pools to accommodate most requirements of embedded software
• C++ STL allocators based on those memory pools are also provided to make it possible to use efficient high level algorithms
Memory management
Dynamic memory allocation dtSolve™ memory handling
Memory management • Current interface implemented in
C++
Sensitivities • Sensitivities can be used to assess the
effect of selected parameters to the model output
• Useful in control problems or model optimization
• dtSolve™ can automatically update the sensitivity matrix
Sensitivity matrix ∂
yy p
initial time
final time
change in a given parameter induces changes in the state variables values.
Van der Pol Oscillator Example • Hallmark example of nonlinear self-
oscillation
• ODE model
2
(1 ) 0
ydot_vector[Y2]=sens_parameters[MU]*
y_vector[Y1];
code
• A second board is loaded with Matlab™ Embedded Coder (ode 23)
• Both boards solve the Van der Pol model equations
• Solver outputs are collected in real time through a serial port
Sendyne test platform NXP ARM Cortex-M4 MK64FN1M0VLL12: 120MHz, 256KB RAM, 1MB Flash GCC ARM 5.3 Compiler
Performance benchmark dtSolve™
• Simple Equivalent Circuit Models Phenomenological modeling of time constants
Dependence of element values on T, SOC, ILoad
“Pseudo” multi-scale (P2D)
M. Doyle, T. F. Fuller, and J. Newman, “Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell,” Journal of the Electrochemical Society, vol. 140, p. 1526, 1993.
( ) ( )pC T T q
Materials balance
2 2
1 s
t r rr ∂ ∂∂ = ∂ ∂ ∂
exp expa n SEI cs e s n SEe n
Ia F U i R a F U i R i
RT R i
Reaction kinetics
Charge balance
Representative Elementary Volume
0 0ln1
D t F
Internal cell views
Dynamic simulation-reaction zone
MCMB/LiCoO2 Li-ion, parameters given at: J. Mao, W. Tiedemann, and J. Newman, “Simulation of temperature rise in Li-ion cells at very high currents,” Journal of Power Sources, vol. 271, pp. 444–454, 2014.
Enhanced control capabilities
0 < cs(x,t) Sudden power loss Power prediction
0 < ce(x,t) Sudden power loss Power prediction
USEI < φs-e(x,t) Fade prevention
φs-e(x,t) < USEI SEI formation
• Heat sources • “Copper” losses in the windings
• Joule effect (DC-resistance) • Skin and proximity effect (AC-resistance)
• “Iron” losses due to magnetic flux • Hysteresis and eddy current losses • Stator & rotor losses
• Permanent magnet losses • Negligible in most cases
• Joint project with Engineering Dept. Columbia University
Robotic systems
+ + = =
∂ =
∂
B q q H q q q E q τ y K q
Ky q q


F. Casella, F. Donida, and J. Åkesson, “An XML representation of DAE systems obtained from Modelica models,” in Proceedings of the 7th International Modelica Conference, 2009.
Index-3 DAE -> index-1 DAE
• Memory requirements dependent on size of model and activated features
• Memory allocations are handled by dtSolve™ within the environment created during model initialization
• After initialization no more dynamic allocation is performed
• dtSolve™ can be used within an RTOS environment to perform real time model simulations with deterministic response time
Size
About Sendyne
“Model Based” is key concept in control apps
“PDEs, ODEs & DAE
The Sendyne dtSolve™ paradigm
Memory management
Embedding the code
“Pseudo” multi-scale (P2D)
Internal cell views
Dynamic simulation-reaction zone
Enhanced control capabilities
Robotic systems
Hardware requirements