International Science Index
Attitude Stabilization of Satellites Using Random Dither Quantization
Recently, the effectiveness of random dither
quantization method for linear feedback control systems has
been shown in several papers. However, the random dither
quantization method has not yet been applied to nonlinear feedback
control systems. The objective of this paper is to verify the
effectiveness of random dither quantization method for nonlinear
feedback control systems. For this purpose, we consider the attitude
stabilization problem of satellites using discrete-level actuators.
Namely, this paper provides a control method based on the random
dither quantization method for stabilizing the attitude of satellites
using discrete-level actuators.
Feedback Stabilization Based on Observer and Guaranteed Cost Control for Lipschitz Nonlinear Systems
This paper presents a design of dynamic feedback
control based on observer for a class of large scale Lipschitz nonlinear
systems. The use of Differential Mean Value Theorem (DMVT) is to
introduce a general condition on the nonlinear functions. To ensure
asymptotic stability, sufficient conditions are expressed in terms of
linear matrix inequalities (LMIs). High performances are shown
through real time implementation with ARDUINO Duemilanove
board to the one-link flexible joint robot.
A Qualitative Description of the Dynamics in the Interactions between Three Populations: Pollinators, Plants, and Herbivores
In population dynamics the study of both, the
abundance and the spatial distribution of the populations in a
given habitat, is a fundamental issue a From ecological point of
view, the determination of the factors influencing such changes
involves important problems. In this paper a mathematical model to
describe the temporal dynamic and the spatiotemporal dynamic of the
interaction of three populations (pollinators, plants and herbivores) is
presented. The study we present is carried out by stages: 1. The
temporal dynamics and 2. The spatio-temporal dynamics. In turn,
each of these stages is developed by considering three cases which
correspond to the dynamics of each type of interaction. For instance,
for stage 1, we consider three ODE nonlinear systems describing
the pollinator-plant, plant-herbivore and plant-pollinator-herbivore,
interactions, respectively. In each of these systems different types of
dynamical behaviors are reported. Namely, transcritical and pitchfork
bifurcations, existence of a limit cycle, existence of a heteroclinic
orbit, etc. For the spatiotemporal dynamics of the two mathematical
models a novel factor are introduced. This consists in considering
that both, the pollinators and the herbivores, move towards those
places of the habitat where the plant population density is high.
In mathematical terms, this means that the diffusive part of the
pollinators and herbivores equations depend on the plant population
density. The analysis of this part is presented by considering pairs of
populations, i. e., the pollinator-plant and plant-herbivore interactions
and at the end the two mathematical model is presented, these models
consist of two coupled nonlinear partial differential equations of
reaction-diffusion type. These are defined on a rectangular domain
with the homogeneous Neumann boundary conditions. We focused
in the role played by the density dependent diffusion term into
the coexistence of the populations. For both, the temporal and
spatio-temporal dynamics, a several of numerical simulations are
Unconventional Calculus Spreadsheet Functions
The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.
Fault Diagnosis of Nonlinear Systems Using Dynamic Neural Networks
This paper presents a novel integrated hybrid
approach for fault diagnosis (FD) of nonlinear systems. Unlike most
FD techniques, the proposed solution simultaneously accomplishes
fault detection, isolation, and identification (FDII) within a unified
diagnostic module. At the core of this solution is a bank of adaptive
neural parameter estimators (NPE) associated with a set of singleparameter
fault models. The NPEs continuously estimate unknown
fault parameters (FP) that are indicators of faults in the system. Two
NPE structures including series-parallel and parallel are developed
with their exclusive set of desirable attributes. The parallel scheme is
extremely robust to measurement noise and possesses a simpler, yet
more solid, fault isolation logic. On the contrary, the series-parallel
scheme displays short FD delays and is robust to closed-loop system
transients due to changes in control commands. Finally, a fault
tolerant observer (FTO) is designed to extend the capability of the
NPEs to systems with partial-state measurement.
Identification of Nonlinear Systems Using Radial Basis Function Neural Network
This paper uses the radial basis function neural
network (RBFNN) for system identification of nonlinear systems.
Five nonlinear systems are used to examine the activity of RBFNN in
system modeling of nonlinear systems; the five nonlinear systems are
dual tank system, single tank system, DC motor system, and two
academic models. The feed forward method is considered in this
work for modelling the non-linear dynamic models, where the KMeans
clustering algorithm used in this paper to select the centers of
radial basis function network, because it is reliable, offers fast
convergence and can handle large data sets. The least mean square
method is used to adjust the weights to the output layer, and
Euclidean distance method used to measure the width of the Gaussian
Design of an Augmented Automatic Choosing Control with Constrained Input by Lyapunov Functions Using Gradient Optimization Automatic Choosing Functions
In this paper a nonlinear feedback control called augmented automatic choosing control (AACC) for a class of
nonlinear systems with constrained input is presented. When designed
the control, a 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.
Identification of Nonlinear Systems Structured by Hammerstein-Wiener Model
Standard Hammerstein-Wiener models consist of a linear subsystem sandwiched by two memoryless nonlinearities. The problem of identifying Hammerstein-Wiener systems is addressed in the presence of linear subsystem of structure totally unknown and polynomial input and output nonlinearities. Presently, the system nonlinearities are allowed to be noninvertible. The system identification problem is dealt by developing a two-stage frequency identification method. First, the parameters of system nonlinearities are identified. In the second stage, a frequency approach is designed to estimate the linear subsystem frequency gain. All involved estimators are proved to be consistent.
Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion
In this paper, the stability analysis of a GA-Based adaptive fuzzy sliding model controller for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving FLC rules. Then, FLC rules and the consequent parameter are decided on via an Evolved Bat Algorithm (EBA). After this, we guarantee a new tracking performance inequality for the control system. The tracking problem is characterized to solve an eigenvalue problem (EVP). Next, an adaptive fuzzy sliding model controller (AFSMC) is proposed to stabilize the system so as to achieve good control performance. Lyapunov’s direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality (LMI) problem. Finally, a numerical simulation is provided to demonstrate the control methodology.
Half-Circle Fuzzy Number Threshold Determination via Swarm Intelligence Method
In recent years, many researchers are involved in the
field of fuzzy theory. However, there are still a lot of issues to be
resolved. Especially on topics related to controller design such as the
field of robot, artificial intelligence, and nonlinear systems etc.
Besides fuzzy theory, algorithms in swarm intelligence are also a
popular field for the researchers. In this paper, a concept of utilizing
one of the swarm intelligence method, which is called Bacterial-GA
Foraging, to find the stabilized common P matrix for the fuzzy
controller system is proposed. An example is given in in the paper, as
Performances Assessment of Direct Torque Controlled IM Drives Using Fuzzy Logic Control and Space Vector Modulation Strategy
This paper deals with the direct torque control (DTC) of the induction motor. This type of control allows decoupling control between the flux and the torque without the need for a transformation of coordinates. However, as with other hysteresis-based systems, the classical DTC scheme represents a high ripple, in both the electromagnetic torque and the stator flux and a distortion in the stator current. As well, it suffers from variable switching frequency. To solve these problems various modifications, in conventional DTC scheme, have been made during the last decade. Indeed the DTC based on space vector modulation (SVM) has proved to generate very low ripples in torque and flux with constant switching frequency. It also shows almost the same dynamic performances as the classical DTC system. On the other hand, fuzzy logic is considered as an interesting alternative approach for its advantages: Analysis close to the exigencies of user, ability of nonlinear systems control, best dynamic performances and inherent quality of robustness.
Therefore, two fuzzy direct torque control approaches, for the induction motor fed by SVM-voltage source inverter, are proposed in this paper. By using these two approaches of DTC, the advantages of fuzzy logic control, space vector modulation, and direct torque control method are combined. The performances of these DTC schemes are evaluated through digital simulation using Matlab/Simulink platform and fuzzy logic tools. Simulation results illustrate the effectiveness and the superiority of the proposed Fuzzy DTC-SVM schemes in comparison to the classical DTC.
Gaussian Process Model Identification Using Artificial Bee Colony Algorithm and Its Application to Modeling of Power Systems
This paper presents a nonparametric identification of
continuous-time nonlinear systems by using a Gaussian process
(GP) model. The GP prior model is trained by artificial bee colony
algorithm. The nonlinear function of the objective system is estimated
as the predictive mean function of the GP, and the confidence
measure of the estimated nonlinear function is given by the predictive
covariance of the GP. The proposed identification method is applied
to modeling of a simplified electric power system. Simulation results
are shown to demonstrate the effectiveness of the proposed method.
Dynamic Analysis of Reduced Order Large Rotating Vibro-Impact Systems
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.
Positive Solutions of Initial Value Problem for the Systems of Second Order Integro-Differential Equations in Banach Space
In this paper, by establishing a new comparison result, we investigate the existence of positive solutions for initial value problems of nonlinear systems of second order integro-differential equations in Banach space.We improve and generalize some results (see[5,6]), and the results is new even in finite dimensional spaces.
On the Modeling and State Estimation for Dynamic Power System
This paper investigates a method for the state estimation of nonlinear systems described by a class of differential-algebraic equation (DAE) models using the extended Kalman filter. The method involves the use of a transformation from a DAE to ordinary differential equation (ODE). A relevant dynamic power system model using decoupled techniques will be proposed. The estimation technique consists of a state estimator based on the EKF technique as well as the local stability analysis. High performances are illustrated through a simulation study applied on IEEE 13 buses test system.
Identification of MIMO Systems Using Neuro-Fuzzy Models with a Shuffled Frog Leaping Algorithm
In this paper, a TSK-type Neuro-fuzzy Inference
System that combines the features of fuzzy sets and neural networks
has been applied for the identification of MIMO systems. The procedure of adapting parameters in TSK model employs a Shuffled
Frog Leaping Algorithm (SFLA) which is inspired from the memetic evolution of a group of frogs when seeking for food. To demonstrate
the accuracy and effectiveness of the proposed controller, two nonlinear systems have been considered as the MIMO plant, and results have been compared with other learning methods based on
Particle Swarm Optimization algorithm (PSO) and Genetic
Robust Adaptive Observer Design for Lipschitz Class of Nonlinear Systems
This paper addresses parameter and state estimation problem in the presence of the perturbation of observer gain bounded input disturbances for the Lipschitz systems that are linear in unknown parameters and nonlinear in states. A new nonlinear adaptive resilient observer is designed, and its stability conditions based on Lyapunov technique are derived. The gain for this observer is derived systematically using linear matrix inequality approach. A numerical example is provided in which the nonlinear terms depend on unmeasured states. The simulation results are presented to show the effectiveness of the proposed method.
Observer Based Control of a Class of Nonlinear Fractional Order Systems using LMI
Design of an observer based controller for a class of
fractional order systems has been done. Fractional order mathematics
is used to express the system and the proposed observer. Fractional
order Lyapunov theorem is used to derive the closed-loop asymptotic
stability. The gains of the observer and observer based controller are
derived systematically using the linear matrix inequality approach.
Finally, the simulation results demonstrate validity and effectiveness
of the proposed observer based controller.
Short Time Identification of Feed Drive Systems using Nonlinear Least Squares Method
Design and modeling of nonlinear systems require the
knowledge of all inside acting parameters and effects. An empirical
alternative is to identify the system-s transfer function from input and
output data as a black box model. This paper presents a procedure
using least squares algorithm for the identification of a feed drive
system coefficients in time domain using a reduced model based on
windowed input and output data. The command and response of the
axis are first measured in the first 4 ms, and then least squares are
applied to predict the transfer function coefficients for this
displacement segment. From the identified coefficients, the next
command response segments are estimated. The obtained results
reveal a considerable potential of least squares method to identify the
system-s time-based coefficients and predict accurately the command
response as compared to measurements.
Fault Detection via Stability Analysis for the Hybrid Control Unit of HEVs
Fault detection determines faultexistence and detecting
time. This paper discusses two layered fault detection methods to
enhance the reliability and safety. Two layered fault detection methods
consist of fault detection methods of component level controllers and
system level controllers. Component level controllers detect faults by
using limit checking, model-based detection, and data-driven
detection and system level controllers execute detection by stability
analysis which can detect unknown changes. System level controllers
compare detection results via stability with fault signals from lower
level controllers. This paper addresses fault detection methods via
stability and suggests fault detection criteria in nonlinear systems. The
fault detection method applies tothe hybrid control unit of a military
hybrid electric vehicleso that the hybrid control unit can detect faults
of the traction motor.
Nonlinear Optimal Line-Of-Sight Stabilization with Fuzzy Gain-Scheduling
A nonlinear optimal controller with a fuzzy gain
scheduler has been designed and applied to a Line-Of-Sight (LOS)
stabilization system. Use of Linear Quadratic Regulator (LQR)
theory is an optimal and simple manner of solving many control
engineering problems. However, this method cannot be utilized
directly for multigimbal LOS systems since they are nonlinear in
nature. To adapt LQ controllers to nonlinear systems at least a
linearization of the model plant is required. When the linearized
model is only valid within the vicinity of an operating point a gain
scheduler is required. Therefore, a Takagi-Sugeno Fuzzy Inference
System gain scheduler has been implemented, which keeps the
asymptotic stability performance provided by the optimal feedback
gain approach. The simulation results illustrate that the proposed
controller is capable of overcoming disturbances and maintaining a
satisfactory tracking performance.
Identification of a PWA Model of a Batch Reactor for Model Predictive Control
The complex hybrid and nonlinear nature of many processes that are met in practice causes problems with both structure modelling and parameter identification; therefore, obtaining a model that is suitable for MPC is often a difficult task. The basic idea of this paper is to present an identification method for a piecewise affine (PWA) model based on a fuzzy clustering algorithm. First we introduce the PWA model. Next, we tackle the identification method. We treat the fuzzy clustering algorithm, deal with the projections of the fuzzy clusters into the input space of the PWA model and explain the estimation of the parameters of the PWA model by means of a modified least-squares method. Furthermore, we verify the usability of the proposed identification approach on a hybrid nonlinear batch reactor example. The result suggest that the batch reactor can be efficiently identified and thus formulated as a PWA model, which can eventually be used for model predictive control purposes.
Robust Fuzzy Observer Design for Nonlinear Systems
This paper shows a new method for design of fuzzy observers for Takagi-Sugeno systems. The method is based on Linear matrix inequalities (LMIs) and it allows to insert H constraint into the design procedure. The speed of estimation can tuned be specification of a decay rate of the observer closed loop system. We discuss here also the influence of parametric uncertainties at the output control system stability.
Partial Stabilization of a Class of Nonlinear Systems Via Center Manifold Theory
This paper addresses the problem of the partial state
feedback stabilization of a class of nonlinear systems. In order to
stabilization this class systems, the especial place of this paper is
to reverse designing the state feedback control law from the method
of judging system stability with the center manifold theory. First of
all, the center manifold theory is applied to discuss the stabilization
sufficient condition and design the stabilizing state control laws for a
class of nonlinear. Secondly, the problem of partial stabilization for a
class of plane nonlinear system is discuss using the lyapunov second
method and the center manifold theory. Thirdly, we investigate specially
the problem of the stabilization for a class of homogenous plane
nonlinear systems, a class of nonlinear with dual-zero eigenvalues and
a class of nonlinear with zero-center using the method of lyapunov
function with homogenous derivative, specifically. At the end of this
paper, some examples and simulation results are given show that the
approach of this paper to this class of nonlinear system is effective
Modeling and Identification of Hammerstein System by using Triangular Basis Functions
This paper deals with modeling and parameter
identification of nonlinear systems described by Hammerstein model
having Piecewise nonlinear characteristics such as Dead-zone
nonlinearity characteristic. The simultaneous use of both an easy
decomposition technique and the triangular basis functions leads to a
particular form of Hammerstein model. The approximation by using
Triangular basis functions for the description of the static nonlinear
block conducts to a linear regressor model, so that least squares
techniques can be used for the parameter estimation. Singular Values
Decomposition (SVD) technique has been applied to separate the
coupled parameters. The proposed approach has been efficiently
tested on academic examples of simulation.
Controlled Synchronization of an Array of Nonlinear System with Time Delays
In this paper, we propose synchronization of an array of nonlinear systems with time delays. The array of systems is decomposed into isolated systems to establish appropriate Lyapunov¬Krasovskii functional. Using the Lyapunov-Krasovskii functional, a sufficient condition for the synchronization is derived in terms of LMIs(Linear Matrix Inequalities). Delayed feedback control gains are obtained by solving the sufficient condition. Numerical examples are given to show the validity the proposed method.
Computer Simulations of an Augmented Automatic Choosing Control Using Automatic Choosing Functions of Gradient Optimization Type
In this paper we consider a nonlinear feedback
control called augmented automatic choosing control (AACC)
using the automatic choosing functions of gradient optimization
type 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 minimizing the Hamiltonian
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.
Design of Nonlinear Observer by Using Chebyshev Interpolation based on Formal Linearization
This paper discusses a design of nonlinear observer by
a formal linearization method using an application of Chebyshev Interpolation
in order to facilitate processes for synthesizing a nonlinear
observer and to improve the precision of linearization.
A dynamic nonlinear system is linearized with respect to a linearization
function, and a measurement equation is transformed into
an augmented linear one by the formal linearization method which is
based on Chebyshev interpolation. To the linearized system, a linear
estimation theory is applied and a nonlinear observer is derived. To
show effectiveness of the observer design, numerical experiments
are illustrated and they indicate that the design shows remarkable
performances for nonlinear systems.
Simulation of the Performance of Novel Nonlinear Optimal Control Technique on Two Cart-inverted Pendulum System
The two cart inverted pendulum system is a good
bench mark for testing the performance of system dynamics and
control engineering principles. Devasia introduced this system to
study the asymptotic tracking problem for nonlinear systems. In this
paper the problem of asymptotic tracking of the two-cart with an
inverted-pendulum system to a sinusoidal reference inputs via
introducing a novel method for solving finite-horizon nonlinear
optimal control problems is presented. In this method, an iterative
method applied to state dependent Riccati equation (SDRE) to obtain
a reliable algorithm. The superiority of this technique has been shown
by simulation and comparison with the nonlinear approach.
Fuzzy Rules Emulated Network Adaptive Controller with Unfixed Learning Rate for a Class of Unknown Discrete-time Nonlinear Systems
A direct adaptive controller for a class of unknown nonlinear discrete-time systems is presented in this article. The proposed controller is constructed by fuzzy rules emulated network (FREN). With its simple structure, the human knowledge about the plant is transferred to be if-then rules for setting the network. These adjustable parameters inside FREN are tuned by the learning mechanism with time varying step size or learning rate. The variation of learning rate is introduced by main theorem to improve the system performance and stabilization. Furthermore, the boundary of adjustable parameters is guaranteed through the on-line learning and membership functions properties. The validation of the theoretical findings is represented by some illustrated examples.