design of a control system model in simulationx … bosch, e.on, nokia, siemens, bmw are supported...

1

Design of a control system model in

SimulationX using calibration and

optimization

Dynardo GmbH

2Design of a control system model in SimulationX

using calibration and optimization

© Dynardo GmbH

Notes

• Please let your microphone muted

• Use the chat window to ask questions

• During short breaks we will answer your questions

• From version 4.1 optiSLang supports SimulationX since version 3.5

Supported versions



1. Introduction 2. Process integration

4. Optimization3. Sensitivity analysis

5. Trainings & Contact

© Dynardo GmbH



© Dynardo GmbH

Dynardo

• Founded: 2001 (Will, Bucher,

CADFEM International)

• More than 60 employees,

offices at Weimar and Vienna

• Leading technology companies

Daimler, Bosch, E.ON, Nokia,

Siemens, BMW are supported

Software Development

Dynardo is engineering specialist for

CAE-based sensitivity analysis,

optimization, robustness evaluation

and robust design optimization

• Mechanical engineering

• Civil engineering &

Geomechanics

• Automotive industry

• Consumer goods industry

• Power generation

CAE-Consulting



© Dynardo GmbH

Application of Multi-disciplinary Optimization

• Virtual prototyping is an interdisciplinary process

• Multidisciplinary approach requires to run different solvers in parallel

and to handle different types of constraints and objectives

• Arbitrary engineering software with complex non-linear analysis have

to be connected

• The resulting optimization problem may become very noisy, very

sensitive to design changes or ill conditioned for mathematical function

analysis (e.g. non-differentiable, non-convex, non-smooth)



Excellence of optiSLang

• algorithmic toolbox for

• sensitivity analysis,

• optimization,

• robustness evaluation,

• reliability analysis

• robust design optimization (RDO)

• complete functionality of stochastic analysis

to run real world industrial applications

• optiSLang advantages:

• easy and reliable application,

• predefined workflows,

• algorithmic wizards and

• robust default settings

© Dynardo GmbH



Example: design of a control system

© Dynardo GmbH

• control loop consisting of a dynamic system and a controller

• system transfer function should fit with a measured one from a real

system

• consequence is a difference between input and output signal

• controller has to minimize the difference between both signals

dynamic system



Design parameters

• System gain

• Delay time

• 2 time constants

© Dynardo GmbH

Step 1: calibration of the dynamic system

Responses

• Output signal

measured reference signal

SimulationX model

Task

• Minimize the difference

between output signal

and measured

reference signal



© Dynardo GmbH

Process Integration

Parametric model as base for

• User defined optimization (design) space

• Naturally given robustness (random) space

Design variablesEntities that define the design space

Response variablesOutputs from the system

The CAE processGenerates the results according to the inputs

Scattering variablesEntities that define the robustness space



© Dynardo GmbH

Input and Response Variables

• Scalar design variables with continuous, discrete and binary resolution

and real, integer or string type

• Scattering variables with continuous resolution

• Scalar responses with continuous resolution

• Vector responses with continuous resolution having variable length

• Signal responses having variable length and several channels



optiSLang Integrations

Connection of arbitraryASCII file based solvers

Direct integrations Ansys Workbench Matlab Python Excel SimulationX

Supported connections Ansys Abaqus Adams

© Dynardo GmbH



• The input parameters and its properties can be defined directly in the

SimulationX integration node

© Dynardo GmbH

Step 1: calibration of the dynamic system Definition of the Input Parameters



© Dynardo GmbH

• The reference signal

is given in an

ASCII text file

Step 1: calibration of the dynamic system Definition of the Reference Signal



© Dynardo GmbH

Step 1: calibration of the dynamic system Definition of the Error Measure and Responses

• The SimulationX and the reference signal are compared in an ETK node

• The resulting error measure is used as scalar response within the

objective function



• The objective function is defined as a minimization criterion

• Constraints are not necessary

© Dynardo GmbH

Step 1: calibration of the dynamic system Definition of the Objective and Constraint



© Dynardo GmbH

The Integration Flow

Parametric System• SimulationX node with loaded model system.isx• Text ETK node to read the reference signal from text file and to

compute the signal difference



© Dynardo GmbH

The Sensitivity Flow



© Dynardo GmbH

Scanning the Design Space

Inputs Design of Experiments Model evaluation Outputs

• Uniform distribution of inputs is represented by Latin Hypercube Sampling

• Minimum number of samples (variants) should represent statistical properties, cover the input space optimally and avoid clustering

• For each design all responses are calculated



Metamodel of Optimal Prognosis (MOP)

• Approximation of model output by fast surrogate model

• Reduction of input space to get best compromise between available

information (variants) and model representation (number of inputs)

• Determination of optimal approximation model

• Assessment of approximation quality

• Evaluation of variable sensitivities

© Dynardo GmbH



• The signal difference is mainly influenced by two parameters

• Moving Least Squares approximation is a sufficient meta-model

• Small values of the system gain

results in strong signal deviations

© Dynardo GmbH

Step 1: calibration of the dynamic system Sensitivity with Respect to the Objective



© Dynardo GmbH

The Optimization Flow

• Flow contains the existing sensitivity and an additional optimization• Due to the small number of design parameters, the simplex algorithm

is a good choice

• As start design automatically the best design of the sensitivity analysis is

considered



© Dynardo GmbH

optiSLang Optimization Algorithms

Gradient-based Methods

• Most efficient method if gradients are accurate enough

• Consider its restrictions like local optima, only continuous variablesand noise

Gradient-free Methods

• Attractive methods for a small set of continuous variables

• Method of choice if gradient-based fails

Nature inspired Optimization

• GA/EA/PSO imitate mechanisms of nature to improve individuals

• Method of choice if gradient-based or gradient-free fails

• Very robust against numerical noise, non-linearity, number of variables,…Start



Decision Tree for Optimizer Selection

• optiSLang automatically suggests an optimizer depending on the

parameter properties, the defined criteria and user specified settings

© Dynardo GmbH



© Dynardo GmbH

Step 1: calibration of the dynamic system Optimization

Downhill Simplex Method

• Convergence criteria fulfilled after 160 variants

• Small improvement after 81 variants



• The signal difference is reduced from 0.96 to 0.2

• System transfer function fits well with the measured one from the real

system

• The optimal parameter set is obtained

© Dynardo GmbH

Step 1: calibration of the dynamic system Final variant



Design parameters

• Controller gain

• Integration time

© Dynardo GmbH

Step 2: controller designSimulationX model

Responses

• Control time

• System output

• Overshoot

Input and output signal without

using a controller

Task

• Minimize the control time

having a maximum

overshoot of 5 %

SimulationX model



© Dynardo GmbH

Step 2: controller designSensitivity results

• During „Sensitivity Analysis“ only 7 variants (black) fulfill the constraint condition having control times between 3.5 s and 20 s

• A subsequent optimization using “Simplex” algorithm is performed

3.5 s



© Dynardo GmbH

Step 2: controller designOptimization results

• The control time is reduced from 3.5

to 2.55 s using 61 simulation runs

• The final overshoot of 0.12 % is inside

the given range of maximum 5 %

• The optimal parameter set is obtained

and a fast controller is constructed

2.55 s



© Dynardo GmbH

optiSLang Training

optiSLang and SimulationX 1 day introduction to the integration of SimulationX

models in a optiSLang solver chain, signal extraction, sensitivity analysis,

optimization and calibration

optiSLang 4 Basics 3 day introduction to process integration, sensitivity,

optimization, calibration and robustness analysis

Parameter Identification 1 day seminar on basics of model calibration,

application of sensitivity analysis and optimization to calibration problems

Robust Design and Reliability Analysis 1 day seminar on basics of probability,

robustness and reliability analysis, robust design optimization

See our website: http://www.dynardo.de/en/trainings.html

http://www.dynardo.de/en/trainings.html

design of a control system model in simulationx … bosch, e.on, nokia, siemens, bmw are supported...

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