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: In this paper, we show that the association of the PI
regulators for the speed and stator currents with a control strategy
using the linearization by state feedback for an induction machine
without speed sensor, and with an adaptation of the rotor resistance.
The rotor speed is estimated by using the model reference adaptive
system approach (MRAS). This method consists of using two
models: The first is the reference model and the second is an
adjustable one in which two components of the stator flux, obtained
from the measurement of the currents and stator voltages are
estimated. The estimated rotor speed is then obtained by canceling
the difference between stator-flux of the reference model and those
of the adjustable one. Satisfactory results of simulation are obtained
and discussed in this paper to highlight the proposed approach.
Abstract: A cart-ball system is a challenging system from the
control engineering point of view. This is due to the nonlinearities,
multivariable, and non-minimum phase behavior present in this
system. This paper is concerned with the problem of modeling and
control of such system. The objective of control strategy is to place
the cart at a desired position while balancing the ball on the top of the
arc-shaped track fixed on the cart. A State-Feedback Controller
(SFC) with a pole-placement method will be designed in order to
control the system. At first, the mathematical model of a cart-ball
system in the state-space form is developed. Then, the linearization of
a model will be established in order to design a SFC. The integral
control strategy will be performed as to control the cart position of a
system. Simulation work is then performed using
MATLAB/SIMULINK software in order to study the performance of
SFC when applied to the system.
Abstract: Linearization of graph embedding has been emerged
as an effective dimensionality reduction technique in pattern
recognition. However, it may not be optimal for nonlinearly
distributed real world data, such as face, due to its linear nature. So, a
kernelization of graph embedding is proposed as a dimensionality
reduction technique in face recognition. In order to further boost the
recognition capability of the proposed technique, the Fisher-s
criterion is opted in the objective function for better data
discrimination. The proposed technique is able to characterize the
underlying intra-class structure as well as the inter-class separability.
Experimental results on FRGC database validate the effectiveness of
the proposed technique as a feature descriptor.
Abstract: In this paper we consider a nonlinear feedback control
called augmented automatic choosing control (AACC) for nonlinear
systems with constrained input using weighted gradient optimization
automatic choosing functions. Constant term which arises from
linearization of a given nonlinear system is treated as a coefficient of
a stable zero dynamics. Parameters of the control are suboptimally
selected by maximizing the stable region in the sense of Lyapunov
with the aid of a genetic algorithm. This approach is applied to a
field excitation control problem of power system to demonstrate the
splendidness of the AACC. Simulation results show that the new
controller can improve performance remarkably well.
Abstract: In this paper we consider a nonlinear control design for
nonlinear systems by using two-stage formal linearization and twotype
LQ controls. The ordinary LQ control is designed on almost
linear region around the steady state point. On the other region,
another control is derived as follows. This derivation is based on
coordinate transformation twice with respect to linearization functions
which are defined by polynomials. The linearized systems can be
made up by using Taylor expansion considered up to the higher order.
To the resulting formal linear system, the LQ control theory is applied
to obtain another LQ control. Finally these two-type LQ controls
are smoothly united to form a single nonlinear control. Numerical
experiments indicate that this control show remarkable performances
for a nonlinear system.
Abstract: In this work, we treat the problems related to chemical and petrochemical plants of a certain complex process taking the centrifugal compressor as an example, a system being very complex by its physical structure as well as its behaviour (surge phenomenon). We propose to study the application possibilities of the recent control approaches to the compressor behaviour, and consequently evaluate their contribution in the practical and theoretical fields. Facing the studied industrial process complexity, we choose to make recourse to fuzzy logic for analysis and treatment of its control problem owing to the fact that these techniques constitute the only framework in which the types of imperfect knowledge can jointly be treated (uncertainties, inaccuracies, etc..) offering suitable tools to characterise them. In the particular case of the centrifugal compressor, these imperfections are interpreted by modelling errors, the neglected dynamics, no modelisable dynamics and the parametric variations. The purpose of this paper is to produce a total robust nonlinear controller design method to stabilize the compression process at its optimum steady state by manipulating the gas rate flow. In order to cope with both the parameter uncertainty and the structured non linearity of the plant, the proposed method consists of a linear steady state regulation that ensures robust optimal control and of a nonlinear compensation that achieves the exact input/output linearization.
Abstract: A method based on the power series solution is proposed to solve the natural frequency of flapping vibration for the rotating inclined Euler beam with constant angular velocity. The vibration of the rotating beam is measured from the position of the corresponding steady state axial deformation. In this paper the governing equations for linear vibration of a rotating Euler beam are derived by the d'Alembert principle, the virtual work principle and the consistent linearization of the fully geometrically nonlinear beam theory in a rotating coordinate system. The governing equation for flapping vibration of the rotating inclined Euler beam is linear ordinary differential equation with variable coefficients and is solved by a power series with four independent coefficients. Substituting the power series solution into the corresponding boundary conditions at two end nodes of the rotating beam, a set of homogeneous equations can be obtained. The natural frequencies may be determined by solving the homogeneous equations using the bisection method. Numerical examples are studied to investigate the effect of inclination angle on the natural frequency of flapping vibration for rotating inclined Euler beams with different angular velocity and slenderness ratio.
Abstract: In the present analysis an unsteady laminar
forced convection water boundary layer flow is considered.
The fluid properties such as viscosity and Prandtl number are
taken as variables such that those are inversely proportional to
temperature. By using quasi-linearization technique the nonlinear
coupled partial differential equations are linearized and
the numerical solutions are obtained by using implicit finite
difference scheme with the appropriate selection of step sizes.
Non-similar solutions have been obtained from the starting
point of the stream-wise coordinate to the point where skin
friction value vanishes. The effect non-uniform mass transfer
along the surface of the cylinder through slot is studied on the
skin friction and heat transfer coefficients.
Abstract: One of the most attractive and important field of chaos theory is control of chaos. In this paper, we try to present a simple framework for chaotic motion control using the feedback linearization method. Using this approach, we derive a strategy, which can be easily applied to the other chaotic systems. This task presents two novel results: the desired periodic orbit need not be a solution of the original dynamics and the other is the robustness of response against parameter variations. The illustrated simulations show the ability of these. In addition, by a comparison between a conventional state feedback and our proposed method it is demonstrated that the introduced technique is more efficient.
Abstract: This paper examines the forced convection flow of
incompressible, electrically conducting viscous fluid past a sharp
wedge in the presence of heat generation or absorption with an
applied magnetic field. The system of partial differential equations
governing Falkner - Skan wedge flow and heat transfer is first
transformed into a system of ordinary differential equations using
similarity transformations which is later solved using an implicit
finite - difference scheme, along with quasilinearization technique.
Numerical computations are performed for air (Pr = 0.7) and
displayed graphically to illustrate the influence of pertinent physical
parameters on local skin friction and heat transfer coefficients and,
also on, velocity and temperature fields. It is observed that the
magnetic field increases both the coefficients of skin friction and heat
transfer. The effect of heat generation or absorption is found to be
very significant on heat transfer, but its effect on the skin friction is
negligible. Indeed, the occurrence of overshoot is noticed in the
temperature profiles during heat generation process, causing the
reversal in the direction of heat transfer.
Abstract: Minimization methods for training feed-forward networks with Backpropagation are compared. Feedforward network training is a special case of functional minimization, where no explicit model of the data is assumed. Therefore due to the high dimensionality of the data, linearization of the training problem through use of orthogonal basis functions is not desirable. The focus is functional minimization on any basis. A number of methods based on local gradient and Hessian matrices are discussed. Modifications of many methods of first and second order training methods are considered. Using share rates data, experimentally it is proved that Conjugate gradient and Quasi Newton?s methods outperformed the Gradient Descent methods. In case of the Levenberg-Marquardt algorithm is of special interest in financial forecasting.
Abstract: We propose a control design scheme that aims to
prevent undesirable liquid outpouring and suppress sloshing during
the forward and backward tilting phases of the pouring process, for
the case of liquid containers carried by manipulators. The proposed
scheme combines a partial inverse dynamics controller with a PID
controller, tuned with the use of a “metaheuristic" search algorithm.
The “metaheuristic" search algorithm tunes the PID controller based
on simulation results of the plant-s linearization around the operating
point corresponding to the critical tilting angle, where outpouring
initiates. Liquid motion is modeled using the well-known pendulumtype
model. However, the proposed controller does not require
measurements of the liquid-s motion within the tank.
Abstract: This paper presents an adaptive feedback linearization approach to derive helicopter. Ideal feedback linearization is defined for the cases when the system model is known. Adaptive feedback linearization is employed to get asymptotically exact cancellation for the inherent uncertainty in the knowledge of the given parameters of system. The control algorithm is implemented using the feedback linearization technique and adaptive method. The controller parameters are unknown where an adaptive control law aims to drive them towards their ideal values for providing perfect model matching between the reference model and the closed-loop plant model. The converged parameters of controller would then provide good estimates for the unknown plant parameters.
Abstract: Extended Kalman Filter (EKF) is probably the most
widely used estimation algorithm for nonlinear systems. However,
not only it has difficulties arising from linearization but also many
times it becomes numerically unstable because of computer round off
errors that occur in the process of its implementation. To overcome
linearization limitations, the unscented transformation (UT) was
developed as a method to propagate mean and covariance
information through nonlinear transformations. Kalman filter that
uses UT for calculation of the first two statistical moments is called
Unscented Kalman Filter (UKF). Square-root form of UKF (SRUKF)
developed by Rudolph van der Merwe and Eric Wan to
achieve numerical stability and guarantee positive semi-definiteness
of the Kalman filter covariances. This paper develops another
implementation of SR-UKF for sequential update measurement
equation, and also derives a new UD covariance factorization filter
for the implementation of UKF. This filter is equivalent to UKF but
is computationally more efficient.
Abstract: In this paper, we will implement three-dimensional pursuit guidance law with feedback linearization control method and study the effects of parameters. First, we introduce guidance laws and equations of motion of a missile. Pursuit guidance law is our highlight. We apply feedback linearization control method to obtain the accelerations to implement pursuit guidance law. The solution makes warhead direction follow with line-of-sight. Final, the simulation results show that the exact solution derived in this paper is correct and some factors e.g. control gain, time delay, are important to implement pursuit guidance law.
Abstract: In this paper we consider a nonlinear feedback control
called augmented automatic choosing control (AACC) using the
gradient optimization automatic choosing functions for nonlinear
systems. Constant terms which arise from sectionwise linearization
of a given nonlinear system are treated as coefficients of a stable
zero dynamics. Parameters included in the control are suboptimally
selected by expanding a stable region in the sense of Lyapunov
with the aid of the genetic algorithm. This approach is applied to
a field excitation control problem of power system to demonstrate
the splendidness of the AACC. Simulation results show that the new
controller can improve performance remarkably well.
Abstract: In this paper we improve the quasilinearization method by barycentric Lagrange interpolation because of its numerical stability and computation speed to achieve a stable semi analytical solution. Then we applied the improved method for solving the Fin problem which is a nonlinear equation that occurs in the heat transferring. In the quasilinearization approach the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The modified QLM is iterative but not perturbative and gives stable semi analytical solutions to nonlinear problems without depending on the existence of a smallness parameter. Comparison with some numerical solutions shows that the present solution is applicable.
Abstract: The permanent magnet synchronous motor (PMSM) is
very useful in many applications. Vector control of PMSM is popular
kind of its control. In this paper, at first an optimal vector control for
PMSM is designed and then results are compared with conventional
vector control. Then, it is assumed that the measurements are noisy
and linear quadratic Gaussian (LQG) methodology is used to filter
the noises. The results of noisy optimal vector control and filtered
optimal vector control are compared to each other. Nonlinearity of
PMSM and existence of inverter in its control circuit caused that the
system is nonlinear and time-variant. With deriving average model,
the system is changed to nonlinear time-invariant and then the
nonlinear system is converted to linear system by linearization of
model around average values. This model is used to optimize vector
control then two optimal vector controls are compared to each other.
Simulation results show that the performance and robustness to noise
of the control system has been highly improved.
Abstract: This paper presents an investigation into the design of a flight control system, using a robust sliding mode control structure, designed using the exact feedback linearization procedure of the dynamic of a small-size autonomous helicopter in hover. The robustness of the controller in the context of stabilization and trajectory tracking with respect to small body forces and air resistance on the main and tail rotor, is analytically proved using Lyapunov approach. Some simulation results are presented to illustrate the performance and robustness of such controller in the presence of small body forces and air resistance.