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: Pull-in instability is a nonlinear and crucial effect that is important for the design of microelectromechanical system devices. In this paper, the appropriate electrostatic voltage range is determined by measuring fluid flow pressure via micro pressure sensor based microbeam. The microbeam deflection contains two parts, the static and perturbation deflection of static. The second order equation regarding the equivalent stiffness, mass and damping matrices based on Galerkin method is introduced to predict pull-in instability due to the external voltage. Also the reduced order method is used for solving the second order nonlinear equation of motion. Furthermore, in the present study, the micro capacitive pressure sensor is designed for measuring special fluid flow pressure range. The results show that the measurable pressure range can be optimized, regarding damping field and external voltage.
Abstract: For the synchronous generator simulation and analysis and for the power system stabilizer design and synthesis a mathematical model of synchronous generator is needed. The model has to accurately describe dynamics of oscillations, while at the same time has to be transparent enough for an analysis and sufficiently simplified for design of control system. To study the oscillations of the synchronous generator against to the rest of the power system, the model of the synchronous machine connected to an infinite bus through a transmission line having resistance and inductance is needed. In this paper, the linearized reduced order dynamic model of the synchronous generator connected to the infinite bus is presented and analysed in details. This model accurately describes dynamics of the synchronous generator only in a small vicinity of an equilibrium state. With the digression from the selected equilibrium point the accuracy of this model is decreasing considerably. In this paper, the equations’ descriptions and the parameters’ determinations for the linearized reduced order mathematical model of the synchronous generator are explained and summarized and represent the useful origin for works in the areas of synchronous generators’ dynamic behaviour analysis and synchronous generator’s control systems design and synthesis. The main contribution of this paper represents the detailed analysis of the accuracy of the linearized reduced order dynamic model in the entire synchronous generator’s operating range. Borders of the areas where the linearized reduced order mathematical model represents accurate description of the synchronous generator’s dynamics are determined with the systemic numerical analysis. The thorough eigenvalue analysis of the linearized models in the entire operating range is performed. In the paper, the parameters of the linearized reduced order dynamic model of the laboratory salient poles synchronous generator were determined and used for the analysis. The theoretical conclusions were confirmed with the agreement of experimental and simulation results.
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 for model order reduction is
presented in this paper. The denominator polynomial is derived by
matching both Markov parameters and time moments, whereas
numerator polynomial derivation and error minimization is done
using Genetic Algorithm. The efficiency of the proposed method can
be investigated in terms of closeness of the response of reduced order
model with respect to that of higher order original model and a
comparison of the integral square error as well.
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: In this paper an optimal convex controller is designed to control the angle of attack of a FOXTROT aircraft. Then the order of the system model is reduced to a low-dimensional state space by using Balanced Truncation Model Reduction Technique and finally the robust stability of the reduced model of the system is tested graphically by using Kharitonov rectangle and Zero Exclusion Principle for a particular range of perturbation value. The same robust stability is tested theoretically by using Frequency Sweeping Function for robust stability.
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: A mixed method by combining a Eigen algorithm and improved pade approximations is proposed for reducing the order of the large-scale dynamic systems. The most dominant Eigen value of both original and reduced order systems remain same in this method. The proposed method guarantees stability of the reduced model if the original high-order system is stable and is comparable in quality with the other well known existing order reduction methods. The superiority of the proposed method is shown through examples taken from the literature.
Abstract: Large rotating systems, especially gear drives and gearboxes, occur as parts of many mechanical devices transmitting the torque with relatively small loss of power. With the increased demand for high speed machinery, mathematical modeling and
dynamic analysis of gear drives gained importance. Mathematical description of such mechanical systems is a complex task evolving for several decades. In gear drive dynamic models, which include flexible shafts, bearings and gearing and use the finite elements, nonlinear effects due to gear mesh and bearings are usually ignored, for such models have large number of degrees of freedom (DOF) and it is computationally expensive to analyze nonlinear systems with large number of DOF. Therefore, these models are not suitable for simulation of nonlinear behavior with amplitude jumps in frequency response. The contribution uses a methodology of nonlinear large rotating system modeling which is based on degrees of freedom (DOF) number reduction using modal synthesis method (MSM).
The MSM enables significant DOF number reduction while keeping
the nonlinear behavior of the system in a specific frequency range.
Further, the MSM with DOF number reduction is suitable for
including detail models of nonlinear couplings (mainly gear and
bearing couplings) into the complete gear drive models. Since each
subsystem is modeled separately using different FEM systems, it
is advantageous to parameterize models of subsystems and to use
the parameterization for optimization of chosen design parameters.
Final complex model of gear drive is assembled in MATLAB and
MATLAB tools are used for dynamical analysis of the nonlinear
system. The contribution is further focused on developing of a
methodology for investigation of behavior of the system by Nonlinear
Normal Modes with combination of the MSM using numerical
continuation method. The proposed methodology will be tested using
a two-stage gearbox including its housing.
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: Rounding of coefficients is a common practice in
hardware implementation of digital filters. Where some coefficients
are very close to zero or one, as assumed in this paper, this rounding
action also leads to some computation reduction. Furthermore, if the
discarded coefficient is of high order, a reduced order filter is
obtained, otherwise the order does not change but computation is
reduced. In this paper, the Least Squares approximation to rounded
(or discarded) coefficient FIR filter is investigated. The result also
succinctly extended to general type of FIR filters.
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, a new model order reduction
phenomenon is introduced at the design stage of linear phase digital
IIR filter. The complexity of a system can be reduced by adopting the
model order reduction method in their design. In this paper a mixed
method of model order reduction is proposed for linear IIR filter. The
proposed method employs the advantages of factor division technique
to derive the reduced order denominator polynomial and the reduced
order numerator is obtained based on the resultant denominator
polynomial. The order reduction technique is used to reduce the delay
units at the design stage of IIR filter. The validity of the proposed
method is illustrated with design example in frequency domain and
stability is also examined with help of nyquist plot.
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.