1. TETRACOM: Technology Transfer in Computing Systems
FP7 Coordination and support action to fund 50 technology transfer projects (TTP) in computing systems.
This project has received funding from the European Union’s Seventh Framework Programme for research,
technological development and demonstration under grant agreement n⁰ 609491.
TETRACOM coordinator: Prof. Rainer Leupers, leupers@ice.rwth-aachen.de http://www.tetracom.eu | @TetracomProject
TETRACOM: Technology Transfer in Computing Systems
FP7 Coordination and Support Action to fund 50 technology transfer projects (TTP) in computing systems.
This project has received funding from the European Union’s Seventh Framework Programme for research,
technological development and demonstration under grant agreement n⁰ 609491.
TETRACOM coordinator: Prof. Rainer Leupers, leupers@ice.rwth-aachen.de http://www.tetracom.eu | @TetracomProject
TTP Facts
TTP Impact
TTP Solution
TTP Problem
Contact: Igor Škrjanc
E-mail: igor.skrjanc@fe.uni-lj.si
TETRACOM contribution: 30,131 EUR
Duration: 01/9/2014-30/06/2015
Nonlinear System Identification with advanced local linear models
Dejan Dovžan, Andrej Zdešar, Igor Škrjanc, Faculty of electrical engineering, University of Ljubljana, Slovenia
Martin Mayer, Evon GmbH, Austria
Implementation of fuzzy model Implementation of fuzzy model learning / identification
algorithm (SUHICLUST)
ri…local regions - clusters
μi…membership functions on
input space defining the local
regions - clusters
yi…local linear models
Is an advance process
control environment in C#
for the design of model-
based and other control
concepts for plant
optimization. Has its own
engine for data gathering.
Tools for simple model
generation based on
historical data.
LINEAR PLANT
Historic data
Linear model
identification
MPC control,
optimization, other
control design
NONLINEAR
PLANT
Historic data
MPC control,
optimization, other
control design
Linear model
identification
FUZZY MODEL PRINCIPLE
Input-output space is partitioned into
smaller regions
On each region linear one model is valid
Merging the outputs of local models
=
Nonlinear system approximation
FUZZY MODEL FEATURES
Simple to understand
EffectiveTransparent
Locally linear models
Simple transition from
existing MPC algorithms
in XAMControl to MPC for
nonlinear systems based
on fuzzy model
XAMControl Developmental Environment
Example of simulation model running in XAMControl (EAF simulator)
Initial step: create first cluster and identify local model using least squares method.
Identifcation of local regions - using hierarhical partitioning
Check the model error. If error higher than
threshold continue with splitting else stop.
Find the cluster with
the highest error
Split cluster in the direction
of the highest variance
Refining local positions of new clusters with
Gustaffson-Kessel clustering on local data
Refining global positions of all clusters with
Gustaffson-Kessel clustering on all data
Identification of local model parameters:
𝑦 𝑘 = 𝑎1 𝑦 𝑘 − 1 + ⋯ + 𝑎 𝑛 𝑦 𝑘 − 𝑛 + 𝑏1 𝑢 𝑘 − 1 + ⋯ + 𝑏 𝑚 𝑢 𝑘 − 𝑚 + 𝑟
Calculate membership degrees for all
data samples (on input space)
Use weighted least squares method for estimation of the local
models‘ parameters (membership degrees are weights)
Error reached.
Return the
generated fuzzy
model.
FUZZY MODEL
SUHICLUST – method for
fuzzy model identification
Implementation of fuzzy
model into XAMControl
Implementation of
SUHICLUST into
XAMControl
More powerfull XAMControl
More optimal MPC control of
proceses
Better approximation of
nonlinear plants
Better prediction models for
timeseries problems
More modelling options