http://www.modelon.com/news/news-display/artikel/modelica-conference/ Authors: - Maria Henningsson, Modelon AB - Johan Åkesson, Modelon AB - Hubertus Tummescheit, Modelon Inc. Concepts from quality sciences, such as robust design, six-sigma, and design-of-experiments have had a large impact on product development in industry. These concepts are increasingly used in a model-based engineering context where data is gathered from simulation models rather than laboratory setups or prototypes. This work presents a framework to apply such ideas to analysis of dynamical systems. A set of tools that can be used for uncertainty analysis of dynamical Modelica models is presented. These tools are made available in the FMI Toolbox for MATLAB. The workflow and tools are demonstrated on a cooling loop design problem. Check full text paper at: https://www.modelica.org/events/modelica2014/proceedings/html/submissions/ECP1409635_HenningssonAkessonTummescheit.pdf

1. AN FMI-BASED TOOL FOR ROBUST DESIGN OF
DYNAMICAL SYSTEMS
Maria Henningsson, Johan Åkesson, Hubertus Tummescheit
Modelon AB / Modelon Inc.
2014-04-28 © Modelon 1

2. WHY SIMULATION MODELS?
To answer questions:
• Hardware optimization
 What’s the best nominal design for our
process?
• Verification
 Will performance be OK over entire operating
envelope?
• Quality
 Will performance be OK considering tolerances
on components?
• Controls
 How can we tune our controllers? Will they
work robustly?
Modelica




2014-04-28 © Modelon 2

3. WHY SIMULATION MODELS?
To answer questions:
• Hardware optimization
 What’s the best nominal design for our
process?
• Verification
 Will performance be OK over entire operating
envelope?
• Quality
 Will performance be OK considering tolerances
on components?
• Controls
 How can we tune our controllers? Will they
work robustly?
Modelica




2014-04-28 © Modelon 3

4. HOW TO GET THE ANSWERS?
Example: control design
2014-04-28 © Modelon 4
Modelica models
• Complex models
• Nonlinear
• Many parameters
Design and implementation of controllers in
Matlab / Simulink
• Prefer simpler models
• Linearizations
• Understanding dominating parameter
effects
• Understanding system variability
• Identify worst cases

5. THE POWER OF FMI
• Can separate modeling and
answering questions to
different tools
• Use the best tool for each
purpose
• Take advantage of engineers’
skills in specific tools
• Facilitate cross-team use of
the same model portfolio
2014-04-28 © Modelon 5
Model
Modeling
tool
Sizing
Tool 1
Quality
Tool 2
Control
design
Tool 3
Formal
verification
Tool 4

6. TWO ACADEMIC PARADIGMS
 Large potential in combining approaches
 Modelica and FMI is a suitable platform
2014-04-28 © Modelon 6
• Static models
• Many parameters
• Data-driven models
• Focus on workflows, processes and tools
Quality science/ Robust design / Six-sigma / Design-of-experiments
• Dynamic models
• Few parameters
• Physics-based or data-driven models
• Focus on mathematical rigor
Control engineering

7. DESIGN-OF-EXPERIMENTS (DOE)
• Run a limited set of experiments (or simulations)
• Identify crude models for how variables affect the behavior of a
system in order to:
 Optimize hardware design
 Calibrate
 Understand system variability
2014-04-28 © Modelon 7

8. DOE: SIMPLISTIC APPROACHES
• One-factor-at-a-time (OFAT)
• Full-factorial design (gridding)
2014-04-28 © Modelon 8
x1
x2
x1
x2

9. DOE DESIGNS
2014-04-28 © Modelon 9
Common ad-hoc
approach
Space-filling
algorithms
Good coverage, also
in higher
dimensions
100 test points, two factors
Scales poorly with
nbr of factors
Corner cases
poorly covered in
higher dimensions

10. A DOE TOOL FOR DYNAMIC SYSTEMS: REQUIREMENTS
User input
• FMU model
• DoE factors from model
• Ranges and distributions of factors
• Type of DoE design
• Response variables to analyze or
visualize
Tool tasks
• Construct test matrix
• Set FMU parameters
• Simulate at all points, find steady-
state
• Find inputs to match specified
outputs
• Catch and manage simulation errors
• Linearize system at test matrix points
• Provide support for visualizing results
• Construct meta-models for analysis
2014-04-28 © Modelon 10

11. DOE IN THE FMI TOOLBOX FOR MATLAB
2014-04-28 © Modelon 11
FMU
DoE
variable
spec
Test matrix
Run
experiments
Visualize
result
Excel /
Matlab
Modeling
tool
FMI Toolbox for
Matlab
from version 1.6
FMUDoESetup class
constructor input:
• FMU file name
• Excel file name
• [Excel sheet]
• [options]
methods:
• qmc
• mc
• fullfact
• custom
FMUDoEResult class
properties:
• generation_date
• model_data
• doe
• constants
• experiment_status
• steady_state
• linsys
• options
• comp_time
visualization methods:
• main_effects
• bode
• step

12. EXAMPLE: ENGINE COOLING SYSTEM
• Demo model from Modelon’s
Liquid Cooling Library
• Design variables:
 Maximum pump speed
 Radiator efficiency
 Minimum air mass flow
• Requirements:
 Engine-out coolant temp < 100 oC
 Handle heat load of 100 kW
 Ambient temperature operating
range [-20oC, 45oC]
2014-04-28 © Modelon 12

13. SIZING: SCREENING DESIGN SPACE
2014-04-28 © Modelon 13
>> doe_setup = FMUDoESetup('CoolingLoop.fmu', 'DesignParameters.xlsx', 'Screening');
>> nbr_of_experiments = 100;
>> result = doe_setup.qmc(nbr_of_experiments);
>> T_engine_out = result.steady_state.y( : , 3)
>> result.main_effects(result, ’T_liquid_ae’, T_engine_out > 100);

14. SIZING: DETERMINING A DESIGN
Zooming in to a smaller region of
the design space:
2014-04-28 © Modelon 14
>> doe_setup = FMUDoESetup('CoolingLoop.fmu', 'DesignParameters.xlsx', 'Sizing');
>> nbr_of_experiments = 100;
>> result = doe_setup.qmc(nbr_of_experiments);
>> T_engine_out = result.steady_state.y( : , 3)
>> result.main_effects(result, ’T_liquid_ae’, T_engine_out > 100);
Design

15. EVALUATING THE DESIGN
• Finding representative operating points
 Let input heat load be a free variable
 Let output T_engine_out be a DoE factor
2014-04-28 © Modelon 15

16. DYNAMICS
 input = pump speed
 output = engine-out coolant temperature
Bode plot for ensemble of linear systems
2014-04-28 © Modelon 16
>> doe_setup = FMUDoESetup('CoolingLoop.fmu', 'DesignParameters.xlsx', ‘Dynamics’');
>> nbr_of_experiments = 100;
>> result = doe_setup.qmc(nbr_of_experiments);
>> result.bode(1, 1)

17. DYNAMICS: WHERE IS THE NONLINEARITY?
• Correlate feature of Bode plot with DoE factors
2014-04-28 © Modelon 17
>> N = result.doe.nbr_of_experiments;
>> ss_gain = zeros(N,1);
>> for k = 1:1:N
>> ss_gain(k) = dcgain(result.linsys.sys{k} (1, 1));
>> end
>> result.main_effects(ss_gain, ’gain’);

18. CONTROLLER EVALUATION
• Loop-shaping: PI-controller with K = -50, Ti = 100
• Closed-loop step response
2014-04-28 © Modelon 18
>> s = tf(‘s’);
>> Gc = -50*(1+1/(100*s));
>> cl_sys = cell(N,1);
>> for k = 1:1:N
>> Gp = result.linsys.sys{k}(1, 1);
>> cl_sys{k} = minreal(Gp*Gc/(1+Gp*Gc));
>> end
>> batch_step(cl_sys);

19. CONCLUSIONS
• Modelica and FMI is a powerful platform for analysis of parametric
uncertainty in dynamical systems
• Need for tools to that manage multi-factor uncertainty in a better
way than ad-hoc one-factor-at-a-time trial-and-error
2014-04-28 © Modelon 19