Influence of the optimization methods on neural state estimation quality of the drive system with elasticity
Teresa Orlowska-Kowalska
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Marcin Kaminski
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Electrical Bayesian
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T. Orlowska-Kowalska (&) M. Kaminski Institute of Electrical Machines
, Drives and Measurements,
Wroclaw University of Technology
, Wroclaw,
Poland
The paper deals with the implementation of optimized neural networks (NNs) for state variable estimation of the drive system with an elastic joint. The signals estimated by NNs are used in the control structure with a state-space controller and additional feedbacks from the shaft torque and the load speed. High estimation quality is very important for the correct operation of a closed-loop system. The precision of state variables estimation depends on the generalization properties of NNs. A short review of optimization methods of the NN is presented. Two techniques typical for regularization and pruning methods are described and tested in detail: the Bayesian regularization and the Optimal Brain Damage methods. Simulation results show good precision of both optimized neural estimators for a wide range of changes of the load speed and the load torque, not only for nominal but also changed parameters of the drive system. The simulation results are verified in a laboratory setup. In most electrical drives, the elasticity of the shaft between a driving motor and a load machine must be taken into
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account. In order to obtain drive response to a reference
signal with high dynamics, and to minimize torsional
vibrations, different control methods of the drive system
with elastic joint, based on control theory, like PI/PID
methods, state controller-based methods, sliding-mode, and
adaptive or predictive control methods [16] are used. All
these control methods require feedbacks from different
mechanical state variables of the system (load side speed,
torsional torque, load torque). These mechanical variables
can be measured, but only in laboratory environments. In
the real drive systems, in industry, torsional or load torque
can not be measured, as the torque transducer is never
mounted between the driven motor and the loading
machine because lack of space and generation of additional
(high) cost. Similarly, the load side speed is hardly
measured because lack of place for additional speed transducer
and additional cabling, which is troublesome. In such a
case, only estimation of those state variables is the solution
for the industry conditions. This is the reason why we have
to estimate the torsional torque and the load side speed of a
two-mass system.
In many applications connected with electrical drives,
algorithmic methods are applied for the non-measurable
state variables estimation, for example, the Kalman filters
[4, 5] and the Luenberger observers [6]. However, the
algorithmic estimators require the mathematical model and
parameter knowledge of the system, which could change
during the system operationso to obtain the good
estimation quality the parameters of the state estimators must
be tuned on-line (by on-line plant parameters
identification or estimation). Alternative ways of solving this
problem are estimators based on neural networks (NNs). Such
estimators do not need a mathematical model and
parameters of the system, only the training data are required [79]
for the estimator design. Moreover, the generalization
ability causes that neural estimators are less sensitive to
parameters or measurement signals uncertainties.
However, in the case of NN applications in state
variable estimation, the determination of NN structure
for a specific task is one of the most important problems.
This structure should be carefully chosen to obtain good
estimation quality also in the case of NN input data
different than those used in the training procedure. It
means that a suitable generalization ability is required.
Data generalization is one of the main advantages of the
NN and consists in the possibility of solving a given task
by a trained network in case the elements of the input
vector are not taken into account in the NNs training
process. In the technical literature, many methods for
the improvement of the NN generalization properties
are presented. It is possible to distinguish three main
trends [7]:
impact on the length of the learning process (early
stopping) [10],
application of regularisation method [11],
modification of neural networks topology (growing or
pruning) [12, 13].
Many methods for NN structure optimization are
presented in the literature. Most of them require the initial
choice of NN structure, and then, selected neural
connections are eliminated. One of the simplest ways to choose a
specific inter-node connection for elimination is the
analysis of absolute values of NNs weights. Another method
consists in checking the influence of each connection on
the generalization error. In this case, the generalization
errors before and after the elimination each weight factor
are compared [7, 14].
Very good results are obtained with the sensitivity
methods. These algorithms are base (...truncated)