US20170045880A1 - Model numerical solver for system control - Google Patents
Model numerical solver for system control Download PDFInfo
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- US20170045880A1 US20170045880A1 US15/110,408 US201615110408A US2017045880A1 US 20170045880 A1 US20170045880 A1 US 20170045880A1 US 201615110408 A US201615110408 A US 201615110408A US 2017045880 A1 US2017045880 A1 US 2017045880A1
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/4155—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by programme execution, i.e. part programme or machine function execution, e.g. selection of a programme
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
- G06F17/13—Differential equations
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/30—Circuit design
- G06F30/32—Circuit design at the digital level
- G06F30/33—Design verification, e.g. functional simulation or model checking
- G06F30/3323—Design verification, e.g. functional simulation or model checking using formal methods, e.g. equivalence checking or property checking
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/30—Circuit design
- G06F30/36—Circuit design at the analogue level
- G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N5/00—Computing arrangements using knowledge-based models
- G06N5/01—Dynamic search techniques; Heuristics; Dynamic trees; Branch-and-bound
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/39—Robotics, robotics to robotics hand
- G05B2219/39077—Solve inverse geometric model by iteration, no matrixes inversion
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/06—Power analysis or power optimisation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F8/00—Arrangements for software engineering
- G06F8/40—Transformation of program code
- G06F8/41—Compilation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06G—ANALOGUE COMPUTERS
- G06G7/00—Devices in which the computing operation is performed by varying electric or magnetic quantities
- G06G7/48—Analogue computers for specific processes, systems or devices, e.g. simulators
- G06G7/64—Analogue computers for specific processes, systems or devices, e.g. simulators for non-electric machines, e.g. turbine
Definitions
- the present invention relates to adaptive control of an embedded system. More specifically, the invention relates to a model numerical solver program for use with a model description in an embedded processor of a control system.
- a mathematical model refers to a set of mathematical equations relating dependent variables and independent variables. That is, those equations define explicitly or implicitly a set of dependent variables as functions, in the mathematical sense, of independent variables.
- the equations of a model can either be differential (the derivative of at least one dependent variable with respect to an independent variable appears in the equation) or algebraic (no derivative appears in the equation), and for the present invention at least one of the model equations is differential.
- the number of model equations is always equal to the number of dependent variables.
- Those equations can involve numerical quantities referred to as parameters which do not depend on any of the model variables, and whose values lie between fixed upper and lower bounds.
- model equations include functions of the independent variables referred to as input sources, whose values can be arbitrarily controlled and defined.
- a model description therefore consists of a list of differential and algebraic equations together with a list of dependent and independent variables, the values and bounds of the parameters, and the definition of the input sources in terms of the independent variables.
- the purpose of a model numerical solver software is to perform the computational tasks required to obtain the values of the dependent variables as numerical functions of the independent variables, parameters and input sources. This task is achieved by computing numerical approximations of the model equations using finite differences techniques of arbitrary order, which are implemented in the solver numerical routines.
- Model Reference Adaptive Control require the capability of updating the model parameters to achieve a pre-defined goal while operating the controlled system, such as minimizing the error between the model prediction and the actual response of the controlled system.
- This can be achieved by the model numerical solver through the use of a numerical optimizer which computes the optimal values of the model parameters with respect to a pre-defined goal.
- the numerical optimizer should guarantee that the computed optimal values of the parameters lie within the lower and upper bounds defined in the model description.
- Mathematical models are used in various control applications ranging from mechatronics to industrial systems controls. These models are typically described by a set of non-linear Differential Algebraic Equations (DAE) for which an analytical solution either is not known or does not exist. Modern numerical techniques are extremely efficient for obtaining numerical solutions of such equations. For systems described by a set of Partial Differential Equations (PDE) spatial discretization schemes are employed to transform them into a set of DAEs.
- DAE non-linear Differential Algebraic Equations
- PDE Partial Differential Equations
- 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.
- Some advanced control methods such as Model Reference Adaptive Control (MRAC) also involve updating the parameters of the model in real time in order to minimize error or adapt to changes in the controlled system.
- MRAC Model Reference Adaptive Control
- model development/optimization and its embedded implementation has been a two-step process.
- CAE Computer Aided Engineering
- the two-step process has the following drawbacks:
- the present invention discloses a complete model numerical solver that is small enough to reside on an embedded processor. It contains all the features of a State-of-the-Art solver including Automatic Differentiation (AD), complete DAE solver like IDAS or DASSL, sparse linear algebra techniques, sensitivity analysis, numerical optimization routines and adaptive step size. It accomplishes all these functions in a few hundred KB of code space (depending on enabled features) without requiring creation of custom embedded code. All an operator needs to input is the model description (as explained above), as one would input them in a general purpose CAE package.
- AD Automatic Differentiation
- complete DAE solver like IDAS or DASSL
- sparse linear algebra techniques sparse linear algebra techniques
- sensitivity analysis sensitivity analysis
- numerical optimization routines numerical optimization routines
- adaptive step size a few hundred KB of code space (depending on enabled features) without requiring creation of custom embedded code. All an operator needs to input is the model description (as explained above), as one would input them in a general purpose CA
- the complex computational steps associated with solving a set of algebraic differential equations describing a model require memory allocations (for example, allocating memory to an array in order to perform a linear algebra operation).
- Those memory allocations are traditionally dynamic allocations, i.e. memory is allocated “on the fly” during run time without knowledge of the exact amount of space needed at compile time.
- Dynamic allocation is by nature non-deterministic. The time required to “find” the requested memory space will depend both on the size of memory requested as well as the memory used by other processes executed on the embedded processor. Any task associated with dynamic memory allocation can thus take an arbitrarily long time or even fail. This is not the case with “static memory allocation” where the exact memory size requirement must be known at compile time.
- Prior art model solvers designed for environments with much higher computing and memory resources than those of an embedded processor, use dynamic memory allocation.
- SUNDIALS Suite of Nonlinear and Differential/Algebraic equation solvers
- the code examples shipped with the SUNDIALS software package e.g., cvsDiurnal_FSA_kry.c
- dynamic memory allocations are performed at each solving step.
- the present invention model numerical solver implements a specific memory layout and memory allocation strategy to address those issues.
- the numerical solver of the present invention automatically estimates an upper bound on the total memory requirements of the various components of the solver (i.e., model variables, solver data structures and solver internal memory requirements, additional memory pools; see FIG. 6 ).
- the present invention solver then proceeds with the allocation of all the required memory during the instantiation and initialization phase.
- this allocation of the model data includes allocating memory pools, i.e. memory segments that can be shared among the solver tasks. Those memory pools are used to perform memory allocation during the solving steps, the advantage being that those allocations are equivalent to static allocations since the memory has already been allocated for the pool and its size cannot be exceeded by any solver process.
- the present invention eliminates the need for custom model code by solving the model equations directly; speeds up the model deployment effort; is more reliable and cost effective as it eliminates one step in the model deployment process; makes available to the control application sophisticated solver features such as Automatic Differentiation, sensitivity analysis, sparse linear algebra techniques, numerical optimization routines, and adaptive step size.
- the model numerical solver of the present invention is suitable for stiff problems such as the battery modeling problem.
- the model solver program is written in C/C++ and provides a clean, stable and well-documented API (Application Programming Interface) making possible convenient interfacing with external software and use of the model numerical solver's features in a wide range of applications.
- API Application Programming Interface
- the description of the model can be input into the program using one of the following methods:
- FIG. 1 is a prior art illustration of model based adaptive control as implemented in a Battery Management System.
- FIG. 2 is a prior art illustration of a typical two-step process for model development and deployment in an embedded environment.
- FIG. 3 is an illustration of model equations solved directly in an embedded processor according to the present invention.
- FIG. 4 is an illustration of the model numerical solver structure as implemented in the invention.
- FIG. 5 is an example of an arrangement of the present invention in a physical battery system.
- FIG. 6 is an exemplary memory allocation of the present invention.
- FIG. 7 is a comparison between the memory strategy of the model solver in the present invention and a traditional memory strategy.
- FIG. 8 shows the model/simulator performance in a single cell simulation in real time under random current load.
- FIG. 1 A model based adaptive control system as implemented in a Battery Management System is shown in FIG. 1 .
- the battery model 10 and state estimator 12 receive information as input sources from the battery 16 indicating a present state of the battery.
- the battery model 10 and state estimator 12 use this information to calculate an estimation of a future state of the battery. This estimation is communicated to control algorithms 18 which control operation of the battery 16 according to their own performance standards.
- FIG. 2 A typical two-step process for model development and deployment in an embedded environment is shown in FIG. 2 .
- a developer enters the model description 20 into a general purpose CAE environment 22 which optimizes and generates custom code either automatically or manually. After this initial step, the generated code 26 is then provided to the embedded environment 28 of the specific system.
- FIG. 3 is an illustration of the model numerical solver operation according to the invention.
- Model description 30 is entered directly into the embedded environment 38 .
- the embedded environment 38 contains the model numerical solver, which solves the model equations 30 directly and concurrently.
- Model equations 40 and model parameters 45 are defined and provided to a model 48 . Refinement of the model is possible through user-controlled solver parameters 42 and optimizer parameters 43 . Model solving is performed in the solver 44 and model optimization is performed in the model optimizer 41 .
- FIG. 5 is an example of an arrangement of the invention in a physical battery system.
- a physical battery system 50 includes a battery 52 driving a load 54 .
- the battery 52 and the load 54 provide information values to an embedded processor 56 related to the present state of the battery and the load requirements.
- the model numerical solver 51 of the present invention resides within a memory of the embedded processor 56 and, after solving the model equations for the provided values, estimates a future state of the battery and communicates this future state to a control application 53 .
- the control application 53 determines the operation of a battery management system 58 , which optimizes characteristics of the battery 52 .
- FIG. 6 An exemplary memory allocation of the present invention is shown in FIG. 6 .
- FIG. 7 provides a comparison between the memory strategy 70 of the model solver in the present invention and a traditional memory strategy 72 .
- FIG. 8 shows the model/simulator performance in real time under random load.
- the average computational time was 12 ms, which is 4.1 times faster than the simulation step used of ⁇ 50 ms.
- the model used includes: 13 dependent variables and 24 scalar parameters.
- a method for performing numerical model computations within an embedded processor which involves loading a model numerical solver software program into a memory of the embedded processor and defining a model description which itself includes a list of independent and dependent variables, parameters values and bounds, input sources, and model differential and algebraic equations, then inputting the model description into the model solver, estimating an upper bound on the total memory requirement of the model numerical solver computational tasks for the particular model description, allocating required amounts of memory during instantiation and initialization of the model numerical solver as determined by the estimation of the upper bound on the total memory requirement of the model numerical solver computational tasks for the particular model description prior to commencement of solver steps, receiving at the model solver at least one value for at least one independent variable of the model equations, solving the model equations directly and concurrently with the solver numerical routines and outputting at least one value of one of the dependent variables.
- inputting the model description may involve a Functional Mock-up Interface (FMI) description of the model, a C++ source file containing at least the definition of a numerical routine to evaluate the dependent variables of the model as numerical functions for the independent variables, parameters and input sources, or an XML/MathML file describing the model description as a list of independent and dependent variables, parameters values and bounds, input sources and differential and algebraic equations.
- the model numerical solver software program of the method may include Automatic Differentiation (AD), a complete Differential Algebraic Equation solver, sparse linear algebra techniques, sensitivity analysis, numerical optimization routines, and adaptive step-size.
- the method may also provide user-controllable solver parameters and optimizer parameters.
- Also disclosed herein is a method for controlling a system which involves embedding a processor into an electronic device, loading a model solver software program into a memory of the embedded processor, defining a model description which itself includes a list of independent and dependent variables, parameters values and bounds, input sources, and model differential and algebraic equations, then inputting the model description into the model solver, estimating an upper bound on the total memory requirement for the numerical solver computational tasks for the particular model description, allocating required amounts of memory during instantiation and initialization of the model numerical solver as determined by the estimation of the upper bound on the total memory requirement of the model numerical solver computational tasks for the particular model description and prior to commencement of solver steps, receiving at the model solver at least one value for at least one variable of the model equations, solving the model equations directly and concurrently with the solver numerical routines, outputting at least one value of one dependent variable of the model equations and receiving the at least one value of one dependent variable at a controller, wherein the controller effects changes to the state of the system in response to
- inputting the model description may involve a Functional Mock-up Interface (FMI) description of the model, a C++ source file containing at least the definition of a numerical routine to evaluate the dependent variables of the model as numerical functions for the independent variables, parameters and input sources, or an XML/MathML file describing the model description as a list of independent and dependent variables, parameters values and bounds, input sources and differential and algebraic equations.
- the model numerical solver software program of the method may include Automatic Differentiation (AD), a complete Differential Algebraic Equation solver, sparse linear algebra techniques, sensitivity analysis, numerical model optimization and adaptive step-size.
- the method may also provide user-controllable solver parameters and optimizer parameters.
- a model numerical solver software program in a memory of an embedded processor as herein disclosed may include a list of independent and dependent variables, parameters values and bounds, input sources, and model differential and algebraic equations, a memory structure wherein the model solver estimates an upper bound on the total memory requirement for the model numerical solver computational tasks for the particular model description and wherein required amounts of memory are allocated during instantiation and initialization of the model simulation as determined by the upper bound estimation on the total memory requirement of the model numerical solver computational tasks for this particular model description and prior to commencement of solver steps, means for receiving at least one input signal from at least one source and computational means for solving at least two equations concurrently.
- This model solver software program may receive input signals from a Functional Mock-up Interface (FMI) description of the model, a C++ source file containing at least the definition of a numerical routine to evaluate the dependent variables of the model as numerical functions for the independent variables, parameters and input sources, or an XML/MathML file describing the model as a list of independent and dependent variables, parameters values and bounds, input sources and differential and algebraic equations.
- the model solver program of the method may include an Automatic Differentiation (AD) feature, a complete Differential Algebraic Equation solver, sparse matrix techniques, sensitivities computation, AC small signal analysis and adaptive step-size.
- the model numerical solver software program may include Automatic Differentiation (AD), a complete Differential Algebraic Equation solver, sparse linear algebra techniques, sensitivity analysis, numerical model optimization and adaptive step-size.
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Abstract
Description
- This application claims the benefit of provisional application No. 62/147,312 filed Apr. 14, 2015 and incorporated herein by reference for all purposes.
- The present invention relates to adaptive control of an embedded system. More specifically, the invention relates to a model numerical solver program for use with a model description in an embedded processor of a control system.
- In various control applications and for the present invention, a mathematical model refers to a set of mathematical equations relating dependent variables and independent variables. That is, those equations define explicitly or implicitly a set of dependent variables as functions, in the mathematical sense, of independent variables. The equations of a model can either be differential (the derivative of at least one dependent variable with respect to an independent variable appears in the equation) or algebraic (no derivative appears in the equation), and for the present invention at least one of the model equations is differential. The number of model equations is always equal to the number of dependent variables. Those equations can involve numerical quantities referred to as parameters which do not depend on any of the model variables, and whose values lie between fixed upper and lower bounds. In addition, the model equations include functions of the independent variables referred to as input sources, whose values can be arbitrarily controlled and defined. A model description therefore consists of a list of differential and algebraic equations together with a list of dependent and independent variables, the values and bounds of the parameters, and the definition of the input sources in terms of the independent variables. The purpose of a model numerical solver software is to perform the computational tasks required to obtain the values of the dependent variables as numerical functions of the independent variables, parameters and input sources. This task is achieved by computing numerical approximations of the model equations using finite differences techniques of arbitrary order, which are implemented in the solver numerical routines. Those approximations are used iteratively to numerically solve the model equations, and the sequence of those iterative approximations is referred to as the solving steps. It is important to note that, the numerical routines used to numerically solve the model equations are independent from the precise form of the model equations.
- Control methods referred to as Model Reference Adaptive Control require the capability of updating the model parameters to achieve a pre-defined goal while operating the controlled system, such as minimizing the error between the model prediction and the actual response of the controlled system. This can be achieved by the model numerical solver through the use of a numerical optimizer which computes the optimal values of the model parameters with respect to a pre-defined goal. The numerical optimizer should guarantee that the computed optimal values of the parameters lie within the lower and upper bounds defined in the model description.
- Mathematical models are used in various control applications ranging from mechatronics to industrial systems controls. These models are typically described by a set of non-linear Differential Algebraic Equations (DAE) for which an analytical solution either is not known or does not exist. Modern numerical techniques are extremely efficient for obtaining numerical solutions of such equations. For systems described by a set of Partial Differential Equations (PDE) 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. Some advanced control methods such as Model Reference Adaptive Control (MRAC) also involve updating the parameters of the model in real time in order to minimize error or adapt to changes in the controlled system.
- So far the process of model development/optimization and its embedded implementation has been a two-step process. First the model is developed and optimized in a general purpose Computer Aided Engineering (CAE) environment. After the model has been verified and optimized custom model code is generated either automatically or manually.
- The two-step process has the following drawbacks:
-
- 1. The code produced does not contain all the functionality available in the CAE environment. For example the Embedded Coder of MATLAB™ does not provide essential numerical routines such as the DAE solver itself. The resulting software is compromised as it cannot benefit from features such as an efficient DAE solver or runtime sensitivity analysis which may be required in certain adaptive control applications. Other features that affect computational performance such as adaptive step-size are also not included.
- 2. Any change in the model itself requires repetition of the two-step process. If the code is produced manually it adds significantly to the cost of the system.
- Accordingly, a solution which minimizes or eliminates these current drawbacks for model development and its embedded implementation would be beneficial.
- The present invention discloses a complete model numerical solver that is small enough to reside on an embedded processor. It contains all the features of a State-of-the-Art solver including Automatic Differentiation (AD), complete DAE solver like IDAS or DASSL, sparse linear algebra techniques, sensitivity analysis, numerical optimization routines and adaptive step size. It accomplishes all these functions in a few hundred KB of code space (depending on enabled features) without requiring creation of custom embedded code. All an operator needs to input is the model description (as explained above), as one would input them in a general purpose CAE package.
- It should be appreciated that for porting a model numerical solver into an embedded processor the designer has to work within the constraints of a finite memory size.
- The complex computational steps associated with solving a set of algebraic differential equations describing a model require memory allocations (for example, allocating memory to an array in order to perform a linear algebra operation). Those memory allocations are traditionally dynamic allocations, i.e. memory is allocated “on the fly” during run time without knowledge of the exact amount of space needed at compile time. Dynamic allocation is by nature non-deterministic. The time required to “find” the requested memory space will depend both on the size of memory requested as well as the memory used by other processes executed on the embedded processor. Any task associated with dynamic memory allocation can thus take an arbitrarily long time or even fail. This is not the case with “static memory allocation” where the exact memory size requirement must be known at compile time.
- Prior art model solvers, designed for environments with much higher computing and memory resources than those of an embedded processor, use dynamic memory allocation. For example, the SUNDIALS (Suite of Nonlinear and Differential/Algebraic equation solvers) software package developed by Lawrence Livermore National Laboratory is considered to represent the state of the art for numerical solvers for ordinary and algebraic differential equations. In the code examples shipped with the SUNDIALS software package (e.g., cvsDiurnal_FSA_kry.c) it is shown that dynamic memory allocations are performed at each solving step.
- It is obvious that for a task that must be executed in real time, the memory requirements of prior art and resulting unpredictable execution times are unacceptable in a safety critical application such as battery management, which requires continuous monitoring and control in real time.
- The present invention model numerical solver implements a specific memory layout and memory allocation strategy to address those issues.
- Once a model is defined, the numerical solver of the present invention automatically estimates an upper bound on the total memory requirements of the various components of the solver (i.e., model variables, solver data structures and solver internal memory requirements, additional memory pools; see
FIG. 6 ). The present invention solver then proceeds with the allocation of all the required memory during the instantiation and initialization phase. In particular, this allocation of the model data includes allocating memory pools, i.e. memory segments that can be shared among the solver tasks. Those memory pools are used to perform memory allocation during the solving steps, the advantage being that those allocations are equivalent to static allocations since the memory has already been allocated for the pool and its size cannot be exceeded by any solver process. This implies that the model numerical solver of the present invention guarantees that after the instantiation and initialization phase no dynamic memory allocation will be performed. This is a difference compared to the prior art. - These methods make possible performance of the computational tasks associated with solving differential equations within the microprocessor of an embedded device and are thus able to guarantee a deterministic response time.
- The present invention eliminates the need for custom model code by solving the model equations directly; speeds up the model deployment effort; is more reliable and cost effective as it eliminates one step in the model deployment process; makes available to the control application sophisticated solver features such as Automatic Differentiation, sensitivity analysis, sparse linear algebra techniques, numerical optimization routines, and adaptive step size. The model numerical solver of the present invention is suitable for stiff problems such as the battery modeling problem.
- According to the present invention, the model solver program is written in C/C++ and provides a clean, stable and well-documented API (Application Programming Interface) making possible convenient interfacing with external software and use of the model numerical solver's features in a wide range of applications.
- The description of the model can be input into the program using one of the following methods:
-
- A Functional Mock-up Interface (FMI) description of the model (FMI is a standardized interface for the description of complex physical systems).
- A C++ source file that will be evaluated at compile time containing at least the definition of a numerical routine to evaluate the dependent variables of the model as numerical functions for the independent variables, parameters and input sources.
- A XML/MathML file describing the model as a list of independent and dependent variables, parameters values and bounds, input sources and differential and algebraic equations, which makes it possible to use available parsers to convert the description of the model in other formats (for example, LaTeX or HTML).
- The invention will be described with respect to a drawing in several figures, of which:
-
FIG. 1 is a prior art illustration of model based adaptive control as implemented in a Battery Management System. -
FIG. 2 is a prior art illustration of a typical two-step process for model development and deployment in an embedded environment. -
FIG. 3 is an illustration of model equations solved directly in an embedded processor according to the present invention. -
FIG. 4 is an illustration of the model numerical solver structure as implemented in the invention. -
FIG. 5 is an example of an arrangement of the present invention in a physical battery system. -
FIG. 6 is an exemplary memory allocation of the present invention. -
FIG. 7 is a comparison between the memory strategy of the model solver in the present invention and a traditional memory strategy. -
FIG. 8 shows the model/simulator performance in a single cell simulation in real time under random current load. - A model based adaptive control system as implemented in a Battery Management System is shown in
FIG. 1 . Thebattery model 10 andstate estimator 12 receive information as input sources from thebattery 16 indicating a present state of the battery. Thebattery model 10 andstate estimator 12 use this information to calculate an estimation of a future state of the battery. This estimation is communicated to controlalgorithms 18 which control operation of thebattery 16 according to their own performance standards. - A typical two-step process for model development and deployment in an embedded environment is shown in
FIG. 2 . A developer enters themodel description 20 into a generalpurpose CAE environment 22 which optimizes and generates custom code either automatically or manually. After this initial step, the generatedcode 26 is then provided to the embeddedenvironment 28 of the specific system. -
FIG. 3 is an illustration of the model numerical solver operation according to the invention.Model description 30 is entered directly into the embeddedenvironment 38. The embeddedenvironment 38 contains the model numerical solver, which solves the model equations 30 directly and concurrently. - The structure and operation of the model numerical solver is illustrated in
FIG. 4 .Model equations 40 andmodel parameters 45 are defined and provided to amodel 48. Refinement of the model is possible through user-controlledsolver parameters 42 andoptimizer parameters 43. Model solving is performed in thesolver 44 and model optimization is performed in themodel optimizer 41. -
FIG. 5 is an example of an arrangement of the invention in a physical battery system. Aphysical battery system 50 includes abattery 52 driving aload 54. Thebattery 52 and theload 54 provide information values to an embeddedprocessor 56 related to the present state of the battery and the load requirements. The modelnumerical solver 51 of the present invention resides within a memory of the embeddedprocessor 56 and, after solving the model equations for the provided values, estimates a future state of the battery and communicates this future state to acontrol application 53. Thecontrol application 53 determines the operation of abattery management system 58, which optimizes characteristics of thebattery 52. - An exemplary memory allocation of the present invention is shown in
FIG. 6 . -
FIG. 7 provides a comparison between thememory strategy 70 of the model solver in the present invention and atraditional memory strategy 72. - To evaluate the real-time capabilities and portability of the solver, a single cell simulation on a commercial development board was performed. The board used was the PandaBoard [25] with a Dual-core ARM® Cortex™-A9 MPCore™ at 1 GHz and 1 GB of memory. A physical cell was exercised under random current loads. The varying current values were read and presented to the solver along with the environment temperature. The cell voltage and temperature predicted by the simulation was then compared to the actual voltage and temperature produced by the physical cell.
FIG. 8 shows the model/simulator performance in real time under random load. The average computational time was 12 ms, which is 4.1 times faster than the simulation step used of ˜50 ms. The model used includes: 13 dependent variables and 24 scalar parameters. - Disclosed herein is a method for performing numerical model computations within an embedded processor, which involves loading a model numerical solver software program into a memory of the embedded processor and defining a model description which itself includes a list of independent and dependent variables, parameters values and bounds, input sources, and model differential and algebraic equations, then inputting the model description into the model solver, estimating an upper bound on the total memory requirement of the model numerical solver computational tasks for the particular model description, allocating required amounts of memory during instantiation and initialization of the model numerical solver as determined by the estimation of the upper bound on the total memory requirement of the model numerical solver computational tasks for the particular model description prior to commencement of solver steps, receiving at the model solver at least one value for at least one independent variable of the model equations, solving the model equations directly and concurrently with the solver numerical routines and outputting at least one value of one of the dependent variables. With this method, inputting the model description may involve a Functional Mock-up Interface (FMI) description of the model, a C++ source file containing at least the definition of a numerical routine to evaluate the dependent variables of the model as numerical functions for the independent variables, parameters and input sources, or an XML/MathML file describing the model description as a list of independent and dependent variables, parameters values and bounds, input sources and differential and algebraic equations. The model numerical solver software program of the method may include Automatic Differentiation (AD), a complete Differential Algebraic Equation solver, sparse linear algebra techniques, sensitivity analysis, numerical optimization routines, and adaptive step-size. The method may also provide user-controllable solver parameters and optimizer parameters.
- Also disclosed herein is a method for controlling a system which involves embedding a processor into an electronic device, loading a model solver software program into a memory of the embedded processor, defining a model description which itself includes a list of independent and dependent variables, parameters values and bounds, input sources, and model differential and algebraic equations, then inputting the model description into the model solver, estimating an upper bound on the total memory requirement for the numerical solver computational tasks for the particular model description, allocating required amounts of memory during instantiation and initialization of the model numerical solver as determined by the estimation of the upper bound on the total memory requirement of the model numerical solver computational tasks for the particular model description and prior to commencement of solver steps, receiving at the model solver at least one value for at least one variable of the model equations, solving the model equations directly and concurrently with the solver numerical routines, outputting at least one value of one dependent variable of the model equations and receiving the at least one value of one dependent variable at a controller, wherein the controller effects changes to the state of the system in response to receiving the at least one value of one dependent variable. With this method, inputting the model description may involve a Functional Mock-up Interface (FMI) description of the model, a C++ source file containing at least the definition of a numerical routine to evaluate the dependent variables of the model as numerical functions for the independent variables, parameters and input sources, or an XML/MathML file describing the model description as a list of independent and dependent variables, parameters values and bounds, input sources and differential and algebraic equations. The model numerical solver software program of the method may include Automatic Differentiation (AD), a complete Differential Algebraic Equation solver, sparse linear algebra techniques, sensitivity analysis, numerical model optimization and adaptive step-size. The method may also provide user-controllable solver parameters and optimizer parameters.
- A model numerical solver software program in a memory of an embedded processor as herein disclosed may include a list of independent and dependent variables, parameters values and bounds, input sources, and model differential and algebraic equations, a memory structure wherein the model solver estimates an upper bound on the total memory requirement for the model numerical solver computational tasks for the particular model description and wherein required amounts of memory are allocated during instantiation and initialization of the model simulation as determined by the upper bound estimation on the total memory requirement of the model numerical solver computational tasks for this particular model description and prior to commencement of solver steps, means for receiving at least one input signal from at least one source and computational means for solving at least two equations concurrently. This model solver software program may receive input signals from a Functional Mock-up Interface (FMI) description of the model, a C++ source file containing at least the definition of a numerical routine to evaluate the dependent variables of the model as numerical functions for the independent variables, parameters and input sources, or an XML/MathML file describing the model as a list of independent and dependent variables, parameters values and bounds, input sources and differential and algebraic equations. The model solver program of the method may include an Automatic Differentiation (AD) feature, a complete Differential Algebraic Equation solver, sparse matrix techniques, sensitivities computation, AC small signal analysis and adaptive step-size. The model numerical solver software program may include Automatic Differentiation (AD), a complete Differential Algebraic Equation solver, sparse linear algebra techniques, sensitivity analysis, numerical model optimization and adaptive step-size.
- An alert and thoughtful reader will have no difficulty devising myriad variations, improvements and applications of the solver and methods disclosed herein. All such variations, improvements and applications are intended to be encompassed within the claims that follow.
Claims (17)
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US20180067479A1 (en) | 2018-03-08 |
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