718 research outputs found
Moment Matching Based Model Reduction for LPV State-Space Models
We present a novel algorithm for reducing the state dimension, i.e. order, of
linear parameter varying (LPV) discrete-time state-space (SS) models with
affine dependence on the scheduling variable. The input-output behavior of the
reduced order model approximates that of the original model. In fact, for input
and scheduling sequences of a certain length, the input-output behaviors of the
reduced and original model coincide. The proposed method can also be
interpreted as a reachability and observability reduction (minimization)
procedure for LPV-SS representations with affine dependence
Realization Theory for LPV State-Space Representations with Affine Dependence
In this paper we present a Kalman-style realization theory for linear
parameter-varying state-space representations whose matrices depend on the
scheduling variables in an affine way (abbreviated as LPV-SSA representations).
We deal both with the discrete-time and the continuous-time cases. We show that
such a LPV-SSA representation is a minimal (in the sense of having the least
number of state-variables) representation of its input-output function, if and
only if it is observable and span-reachable. We show that any two minimal
LPV-SSA representations of the same input-output function are related by a
linear isomorphism, and the isomorphism does not depend on the scheduling
variable.We show that an input-output function can be represented by a LPV-SSA
representation if and only if the Hankel-matrix of the input-output function
has a finite rank. In fact, the rank of the Hankel-matrix gives the dimension
of a minimal LPV-SSA representation. Moreover, we can formulate a counterpart
of partial realization theory for LPV-SSA representation and prove correctness
of the Kalman-Ho algorithm. These results thus represent the basis of systems
theory for LPV-SSA representation.Comment: The main difference with respect to the previous version is as
follows: typos have been fixe
Model Reduction by Moment Matching for Linear Switched Systems
Two moment-matching methods for model reduction of linear switched systems
(LSSs) are presented. The methods are similar to the Krylov subspace methods
used for moment matching for linear systems. The more general one of the two
methods, is based on the so called "nice selection" of some vectors in the
reachability or observability space of the LSS. The underlying theory is
closely related to the (partial) realization theory of LSSs. In this paper, the
connection of the methods to the realization theory of LSSs is provided, and
algorithms are developed for the purpose of model reduction. Conditions for
applicability of the methods for model reduction are stated and finally the
results are illustrated on numerical examples.Comment: Sent for publication in IEEE TAC, on October 201
Model Reduction for Aperiodically Sampled Data Systems
Two approaches to moment matching based model reduction of aperiodically
sampled data systems are given. The term "aperiodic sampling" is used in the
paper to indicate that the time between two consecutive sampling instants can
take its value from a pre-specified finite set of allowed sampling intervals.
Such systems can be represented by discrete-time linear switched (LS) state
space (SS) models. One of the approaches investigated in the paper is to apply
model reduction by moment matching on the linear time-invariant (LTI) plant
model, then compare the responses of the LS SS models acquired from the
original and reduced order LTI plants. The second approach is to apply a moment
matching based model reduction method on the LS SS model acquired from the
original LTI plant, and then compare the responses of the original and reduced
LS SS models. It is proven that for both methods, as long as the original LTI
plant is stable, the resulting reduced order LS SS model of the sampled data
system is quadratically stable. The results from two approaches are compared
with numerical examples
Model reduction for linear parameter-varying systems through parameter projection
For affine linear parameter-varying (LPV) systems, this paper develops two
parameter reduction methods for reducing the dimension of the parameter space.
The first method achieves the complexity reduction by transforming the affine
LPV system into a parameter-ordered form and establishing an affine upper bound
of the system Gramians, which is extended to time-varying rate-bounded
parameters. The second method is based on considering the sensitivity function
of the transfer function and time evolution equations. Both methods are applied
to an academic example and a thermal model. Simulation results together with
some analysis are given.Comment: This paper has been accepted by 58th IEEE Conference on Decision and
Control (CDC 2019, Nice, France
Reducing the Mast Vibration of Single-Mast Stacker Cranes by Gain-Scheduled Control
In the frame structure of stacker cranes harmful mast vibrations may appear due to the inertial forces of acceleration or the braking movement phase. This effect may reduce the stability and positioning accuracy of these machines. Unfortunately, their dynamic properties also vary with the lifted load magnitude and position. The purpose of the paper is to present a controller design method which can handle the effect of a varying lifted load magnitude and position in a dynamic model and at the same time reveals good reference signal tracking and mast vibration reducing properties. A controller design case study is presented step by step from dynamic modeling through to the validation of the resulting controller. In the paper the dynamic modeling possibilities of single-mast stacker cranes are summarized. The handling of varying dynamical behavior is realized via the polytopic LPV modeling approach. Based on this modeling technique, a gain-scheduled controller design method is proposed, which is suitable for achieving the goals set. Finally, controller validation is presented by means of time domain simulations
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