Sted: Lunchrommet (NB! Lunchrommet ved kjemiteknikk.)
Tid: Onsdag 12/3 kl. 13.00. Foredraget starter kl. 13.30.
Bevertning: Pizza/brus.
Frode Martinsen
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Abstract
The theory of subspace identification (SID)
methods will be presented in general.
The theory and application of one particular SID method will
be presented in some detail.
A SID method can be viewed as a realization based approach to
estimating state space models from input and output data.
This is a most effective and useful method,
in particular for multivariable input and output
(combined deterministic and stochastic) systems.
A lower Left Q-orthogonal (LQ) decomposition is often used in
subspace identification methods in order to compute certain projection matrices
and subspaces of the known data matrices
and to estimate the system order and the extended observability matrix
of the dynamic system.
The dynamics of the system can be extracted from
the column space R(Z) of one particular projected matrix Z which is
computed from the input and output data matrices Y, U and
a method for computing subspaces, e.g., LQ decomposition,
singular value decomposition.
An alternative method (to compute the projection matrices,
subspaces and the column space R(Z))
which is based on the Partial Least Squares (PLS) method (decomposition)
is also presented.
Two examples are presented in order to compare different SID methods.
First: a Monte Carlo simulation experiment of a MIMO system
is presented in order to compare the numerically reliability
of one particular subspace method with two other subspace methods
presented in the literature.
Second: a real world example from the pulp and paper industry is presented
in order to compare the quality of the methods.
For this example there are three input variables in the U data matrix
and two output variables in the Y data matrix.
The data was collected from an experiment design.
The quality of the different models and validation aspects are addressed.
The estimated state space model is then used in a model predictive
control strategy. Simulation results are presented.