Abstract: The saltatory conduction is the way the action potential
is transmitted along a myelinated axon. The potential diffuses along
the myelinated compartments and it is regenerated in the Ranvier
nodes due to the ion channels allowing the flow across the membrane.
For an efficient simulation of populations of neurons, it is important
to use reduced order models both for myelinated compartments
and for Ranvier nodes and to have control over their accuracy and
inner parameters. The paper presents a reduced order model of this
neural system which allows an efficient simulation method for the
saltatory conduction in myelinated axons. This model is obtained
by concatenating reduced order linear models of 1D myelinated
compartments and nonlinear 0D models of Ranvier nodes. The
models for the myelinated compartments are selected from a series of
spatially distributed models developed and hierarchized according to
their modeling errors. The extracted model described by a nonlinear
PDE of hyperbolic type is able to reproduce the saltatory conduction
with acceptable accuracy and takes into account the finite propagation
speed of potential. Finally, this model is again reduced in order to
make it suitable for the inclusion in large-scale neural circuits.
Abstract: In this paper, longitudinal vibration of a micro-beam in micro-scale fluid media has been investigated. The proposed mathematical model for this study is made up of a micro-beam and a micro-plate at its free end. An AC voltage is applied to the pair of piezoelectric layers on the upper and lower surfaces of the micro-beam in order to actuate it longitudinally. The whole structure is bounded between two fixed plates on its upper and lower surfaces. The micro-gap between the structure and the fixed plates is filled with fluid. Fluids behave differently in micro-scale than macro, so the fluid field in the gap has been modeled based on micro-polar theory. The coupled governing equations of motion of the micro-beam and the micro-scale fluid field have been derived. Due to having non-homogenous boundary conditions, derived equations have been transformed to an enhanced form with homogenous boundary conditions. Using Galerkin-based reduced order model, the enhanced equations have been discretized over the beam and fluid domains and solve simultaneously in order to obtain force response of the micro-beam. Effects of micro-polar parameters of the fluid as characteristic length scale, coupling parameter and surface parameter on the response of the micro-beam have been studied.
Abstract: An algorithm is proposed for the order reduction of large scale linear dynamic multi variable systems where the reduced order model denominator is obtained by using Stability equation method and numerator coefficients are obtained by using SRAM. The proposed algorithm produces a lower order model for an original stable high order multivariable system. The reduction procedure is easy to understand, efficient and computer oriented. To highlight the advantages of the approach, the algorithm is illustrated with the help of a numerical example and the results are compared with the other existing techniques in literature.
Abstract: Designing a controller for stochastic decentralized interconnected large scale systems usually involves a high degree of complexity and computation ability. Noise, observability, and controllability of all system states, connectivity, and channel bandwidth are other constraints to design procedures for distributed large scale systems. The quasi-steady state model investigated in this paper is a reduced order model of the original system using singular perturbation techniques. This paper results in an optimal control synthesis to design an observer based feedback controller by standard stochastic control theory techniques using Linear Quadratic Gaussian (LQG) approach and Kalman filter design with less complexity and computation requirements. Numerical example is given at the end to demonstrate the efficiency of the proposed method.
Abstract: A mixed method by combining modified pole
clustering technique and modified cauer continued fraction is
proposed for reducing the order of the large-scale dynamic systems.
The denominator polynomial of the reduced order model is obtained
by using modified pole clustering technique while the coefficients of
the numerator are obtained by modified cauer continued fraction.
This method generated 'k' number of reduced order models for kth
order reduction. The superiority of the proposed method has been
elaborated through numerical example taken from the literature and
compared with few existing order reduction methods.
Abstract: The author presented a method for model order reduction of large-scale time-invariant systems in time domain. In this approach, two modified Hankel matrices are suggested for getting reduced order models. The proposed method is simple, efficient and retains stability feature of the original high order system. The viability of the method is illustrated through the examples taken from literature.
Abstract: This paper features the modeling and design of a
Robust Decentralized Fast Output Sampling (RDFOS) Feedback
control technique for the active vibration control of a smart flexible
multimodel Euler-Bernoulli cantilever beams for a multivariable
(MIMO) case by retaining the first 6 vibratory modes. The beam
structure is modeled in state space form using the concept of
piezoelectric theory, the Euler-Bernoulli beam theory and the Finite
Element Method (FEM) technique by dividing the beam into 4 finite
elements and placing the piezoelectric sensor / actuator at two finite
element locations (positions 2 and 4) as collocated pairs, i.e., as
surface mounted sensor / actuator, thus giving rise to a multivariable
model of the smart structure plant with two inputs and two outputs.
Five such multivariable models are obtained by varying the
dimensions (aspect ratios) of the aluminium beam. Using model
order reduction technique, the reduced order model of the higher
order system is obtained based on dominant Eigen value retention
and the Davison technique. RDFOS feedback controllers are
designed for the above 5 multivariable-multimodel plant. The closed
loop responses with the RDFOS feedback gain and the magnitudes of
the control input are obtained and the performance of the proposed
multimodel smart structure system is evaluated for vibration control.
Abstract: The authors present an algorithm for order reduction of linear time invariant dynamic systems using the combined advantages of the eigen spectrum analysis and the error minimization by particle swarm optimization technique. Pole centroid and system stiffness of both original and reduced order systems remain same in this method to determine the poles, whereas zeros are synthesized by minimizing the integral square error in between the transient responses of original and reduced order models using particle swarm optimization technique, pertaining to a unit step input. It is shown that the algorithm has several advantages, e.g. the reduced order models retain the steady-state value and stability of the original system. The algorithm is illustrated with the help of two numerical examples and the results are compared with the other existing techniques.
Abstract: In this paper static and dynamic response of a
varactor of a micro-phase shifter to DC, step DC and AC
voltages have been studied. By presenting a mathematical
modeling Galerkin-based step by step linearization method
(SSLM) and Galerkin-based reduced order model have been
used to solve the governing static and dynamic equations,
respectively. The calculated static and dynamic pull-in
voltages have been validated by previous experimental and
theoretical results and a good agreement has been achieved.
Then the frequency response and phase diagram of the system
has been studied. It has been shown that applying the DC
voltage shifts down the phase diagram and frequency
response. Also increasing the damping ratio shifts up the
phase diagram.
Abstract: Order reduction of linear-time invariant systems employing two methods; one using the advantages of Routh approximation and other by an evolutionary technique is presented in this paper. In Routh approximation method the denominator of the reduced order model is obtained using Routh approximation while the numerator of the reduced order model is determined using the indirect approach of retaining the time moments and/or Markov parameters of original system. By this method the reduced order model guarantees stability if the original high order model is stable. In the second method Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical examples.
Abstract: This paper proposes a new version of the Particle
Swarm Optimization (PSO) namely, Modified PSO (MPSO) for
model order formulation of Single Input Single Output (SISO) linear
time invariant continuous systems. In the General PSO, the
movement of a particle is governed by three behaviors namely
inertia, cognitive and social. The cognitive behavior helps the
particle to remember its previous visited best position. In Modified
PSO technique split the cognitive behavior into two sections like
previous visited best position and also previous visited worst
position. This modification helps the particle to search the target very
effectively. MPSO approach is proposed to formulate the higher
order model. The method based on the minimization of error
between the transient responses of original higher order model and
the reduced order model pertaining to the unit step input. The results
obtained are compared with the earlier techniques utilized, to validate
its ease of computation. The proposed method is illustrated through
numerical example from literature.
Abstract: In this paper presents a technique for developing the
computational efficiency in simulating double output induction
generators (DOIG) with two rotor circuits where stator transients are
to be included. Iterative decomposition is used to separate the flux–
Linkage equations into decoupled fast and slow subsystems, after
which the model order of the fast subsystems is reduced by
neglecting the heavily damped fast transients caused by the second
rotor circuit using integral manifolds theory. The two decoupled
subsystems along with the equation for the very slowly changing slip
constitute a three time-scale model for the machine which resulted in
increasing computational speed. Finally, the proposed method of
reduced order in this paper is compared with the other conventional
methods in linear and nonlinear modes and it is shown that this
method is better than the other methods regarding simulation
accuracy and speed.
Abstract: The concept of order reduction by least-squares moment matching and generalised least-squares methods has been extended about a general point ?a?, to obtain the reduced order models for linear, time-invariant dynamic systems. Some heuristic criteria have been employed for selecting the linear shift point ?a?, based upon the means (arithmetic, harmonic and geometric) of real parts of the poles of high order system. It is shown that the resultant model depends critically on the choice of linear shift point ?a?. The validity of the criteria is illustrated by solving a numerical example and the results are compared with the other existing techniques.
Abstract: A reduced order modeling approach for natural
gas transient flow in pipelines is presented. The Euler
equations are considered as the governing equations and
solved numerically using the implicit Steger-Warming flux
vector splitting method. Next, the linearized form of the
equations is derived and the corresponding eigensystem is
obtained. Then, a few dominant flow eigenmodes are used to
construct an efficient reduced-order model. A well-known test
case is presented to demonstrate the accuracy and the
computational efficiency of the proposed method. The results
obtained are in good agreement with those of the direct
numerical method and field data. Moreover, it is shown that
the present reduced-order model is more efficient than the
conventional numerical techniques for transient flow analysis
of natural gas in pipelines.
Abstract: In this paper a mixed method by combining an evolutionary and a conventional technique is proposed for reduction of Single Input Single Output (SISO) continuous systems into Reduced Order Model (ROM). In the conventional technique, the mixed advantages of Mihailov stability criterion and continued Fraction Expansions (CFE) technique is employed where the reduced denominator polynomial is derived using Mihailov stability criterion and the numerator is obtained by matching the quotients of the Cauer second form of Continued fraction expansions. Then, retaining the numerator polynomial, the denominator polynomial is recalculated by an evolutionary technique. In the evolutionary method, the recently proposed Differential Evolution (DE) optimization technique is employed. DE method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. The proposed method is illustrated through a numerical example and compared with ROM where both numerator and denominator polynomials are obtained by conventional method to show its superiority.
Abstract: The authors present an optimization algorithm for order reduction and its application for the determination of the relative mapping errors of linear time invariant dynamic systems by the simplified models. These relative mapping errors are expressed by means of the relative integral square error criterion, which are determined for both unit step and impulse inputs. The reduction algorithm is based on minimization of the integral square error by particle swarm optimization technique pertaining to a unit step input. The algorithm is simple and computer oriented. It is shown that the algorithm has several advantages, e.g. the reduced order models retain the steady-state value and stability of the original system. Two numerical examples are solved to illustrate the superiority of the algorithm over some existing methods.
Abstract: Reduction of Single Input Single Output (SISO) continuous systems into Reduced Order Model (ROM), using a conventional and an evolutionary technique is presented in this paper. In the conventional technique, the mixed advantages of Mihailov stability criterion and continued fraction expansions (CFE) technique is employed where the reduced denominator polynomial is derived using Mihailov stability criterion and the numerator is obtained by matching the quotients of the Cauer second form of Continued fraction expansions. In the evolutionary technique method Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical example.
Abstract: A new method identifies coupled fluid-structure system with a reduced set of state variables is presented. Assuming that the structural model is known a priori either from an analysis or a test and using linear transformations between structural and aeroelastic states, it is possible to deduce aerodynamic information from sampled time histories of the aeroelastic system. More specifically given a finite set of structural modes the method extracts generalized aerodynamic force matrix corresponding to these mode shapes. Once the aerodynamic forces are known, an aeroelastic reduced-order model can be constructed in discrete-time, state-space format by coupling the structural model and the aerodynamic system. The resulting reduced-order model is suitable for constant Mach, varying density analysis.
Abstract: This paper features the proposed modeling and design
of a Robust Decentralized Periodic Output Feedback (RDPOF)
control technique for the active vibration control of smart flexible
multimodel Euler-Bernoulli cantilever beams for a multivariable
(MIMO) case by retaining the first 6 vibratory modes. The beam
structure is modeled in state space form using the concept of
piezoelectric theory, the Euler-Bernoulli beam theory and the Finite
Element Method (FEM) technique by dividing the beam into 4 finite
elements and placing the piezoelectric sensor / actuator at two finite
element locations (positions 2 and 4) as collocated pairs, i.e., as
surface mounted sensor / actuator, thus giving rise to a multivariable
model of the smart structure plant with two inputs and two outputs.
Five such multivariable models are obtained by varying the
dimensions (aspect ratios) of the aluminum beam, thus giving rise to
a multimodel of the smart structure system. Using model order
reduction technique, the reduced order model of the higher order
system is obtained based on dominant eigen value retention and the
method of Davison. RDPOF controllers are designed for the above 5
multivariable-multimodel plant. The closed loop responses with the
RDPOF feedback gain and the magnitudes of the control input are
observed and the performance of the proposed multimodel smart
structure system with the controller is evaluated for vibration control.
Abstract: Induction machine models used for steady-state and
transient analysis require machine parameters that are usually
considered design parameters or data. The knowledge of induction
machine parameters is very important for Indirect Field Oriented
Control (IFOC). A mismatched set of parameters will degrade the
response of speed and torque control. This paper presents an
improvement approach on rotor time constant adaptation in IFOC for
Induction Machines (IM). Our approach tends to improve the
estimation accuracy of the fundamental model for flux estimation.
Based on the reduced order of the IM model, the rotor fluxes and
rotor time constant are estimated using only the stator currents and
voltages. This reduced order model offers many advantages for real
time identification parameters of the IM.