Abstract: Nonlinearity is the inherent characteristics of all the industrial processes. The Classical control approach used for a generation often fails to show better results particularly for non-linear systems and in the systems, whose parameters changes over a period of time for a variety of reasons. Alternatively, adaptive control strategies provide very good performance. The Model Reference Adaptive Control based on Lyapunov stability analysis and classical PI control strategies are designed and evaluated for Continuous Stirred Tank Reactor, which shows appreciable dynamic nonlinear characteristics.
Abstract: In this paper, a new method for solution of second order linear Fredholm integral equation in power series form was studied. The result is obtained by using Banach fixed point theorem.
Abstract: In this work, the main problem considered is the
detection and the isolation of the actuator fault. A new formulation of
the linear system is generated to obtain the conditions of the actuator
fault diagnosis. The proposed method is based on the representation
of the actuator as a subsystem connected with the process system in
cascade manner. The designed formulation is generated to obtain the
conditions of the actuator fault detection and isolation. Detectability
conditions are expressed in terms of the invertibility notions. An
example and a comparative analysis with the classic formulation
illustrate the performances of such approach for simple actuator fault
diagnosis by using the linear model of nuclear reactor.
Abstract: In this paper, the modified Gauss-Seidel method with the new preconditioner for solving the linear system Ax = b, where A is a nonsingular M-matrix with unit diagonal, is considered. The convergence property and the comparison theorems of the proposed method are established. Two examples are given to show the efficiency and effectiveness of the modified Gauss-Seidel method
with the presented new preconditioner.
Abstract: In the following article we begin from a multi-parameter unstable nonlinear model of a Quadrotor. We design a control to stabilize and assure the attitude of the device, starting off a linearized system at the equilibrium point of the null angles of Euler (hover),
which provides us a control with limited capacities at small angles of rotation of the vehicle in three dimensions. In order to clear this obstacle, we propose the identification of models in different angles by means of simulations and the design of a controller specifically implemented for the identification task, that in future works will allow the development of controllers according to fast and agile angles of Euler for Quadrotor.
Abstract: In this paper, we present a new kind of the bilinear systems in the form of state space model. The evolution of this system depends on the product of state vector by its self. The well known Lotak Volterra and Lorenz models are special cases of this new model. We also present here a generalization of Kalman filter which is suitable to work with the new bilinear model. An application to real measurements is introduced to illustrate the efficiency of the proposed algorithm.
Abstract: 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.
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: To solve saddle point systems efficiently, several preconditioners have been published. There are many methods for constructing preconditioners for linear systems from saddle point problems, for instance, the relaxed dimensional factorization (RDF) preconditioner and the augmented Lagrangian (AL) preconditioner are used for both steady and unsteady Navier-Stokes equations. In this paper we compare the RDF preconditioner with the modified AL (MAL) preconditioner to show which is more effective to solve Navier-Stokes equations. Numerical experiments indicate that the MAL preconditioner is more efficient and robust, especially, for moderate viscosities and stretched grids in steady problems. For unsteady cases, the convergence rate of the RDF preconditioner is slightly faster than the MAL perconditioner in some circumstances, but the parameter of the RDF preconditioner is more sensitive than the MAL preconditioner. Moreover the convergence rate of the MAL preconditioner is still quite acceptable. Therefore we conclude that the MAL preconditioner is more competitive than the RDF preconditioner. These experiments are implemented with IFISS package.
Abstract: 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.
Abstract: In this paper, getting an high-efficiency parallel algorithm to solve sparse block pentadiagonal linear systems suitable for vectors and parallel processors, stair matrices are used to construct some parallel polynomial approximate inverse preconditioners. These preconditioners are appropriate when the desired target is to maximize parallelism. Moreover, some theoretical results about these preconditioners are presented and how to construct preconditioners effectively for any nonsingular block pentadiagonal H-matrices is also described. In addition, the availability of these preconditioners is illustrated with some numerical experiments arising from two dimensional biharmonic equation.
Abstract: Linear systems are widely used in many fields of science and engineering. In many applications, at least some of the parameters of the system are represented by fuzzy rather than crisp numbers. Therefore it is important to perform numerical algorithms or procedures that would treat general fuzzy linear systems and solve them using iterative methods. This paper aims are to solve fuzzy linear systems using four types of Jacobi based iterative methods. Four iterative methods based on Jacobi are used for solving a general n × n fuzzy system of linear equations of the form Ax = b , where A is a crisp matrix and b an arbitrary fuzzy vector. The Jacobi, Jacobi Over-Relaxation, Refinement of Jacobi and Refinement of Jacobi Over-Relaxation methods was tested to a five by five fuzzy linear system. It is found that all the tested methods were iterated differently. Due to the effect of extrapolation parameters and the refinement, the Refinement of Jacobi Over-Relaxation method was outperformed the other three methods.
Abstract: In this paper, we discuss semiconvergence of the alternating iterative methods for solving singular systems. The semiconvergence theories for the alternating methods are established when the coefficient matrix is a singular matrix. Furthermore, the corresponding comparison theorems are obtained.
Abstract: 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.
Abstract: In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) for nonlinear systems with constrained input. Constant terms which arise from section wise linearization of a given nonlinear system are treated as coefficients of a stable zero dynamics.Parameters included in the control are suboptimally selectedby extremizing a combination of Hamiltonian and Lyapunov functions 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, an magnetorheological (MR) mount with
fuzzy sliding mode controller (FSMC) is studied for vibration
suppression when the system is subject to base excitations. In recent
years, magnetorheological fluids are becoming a popular material in
the field of the semi-active control. However, the dynamic equation of
an MR mount is highly nonlinear and it is difficult to identify. FSMC
provides a simple method to achieve vibration attenuation of the
nonlinear system with uncertain disturbances. This method is capable
of handling the chattering problem of sliding mode control effectively
and the fuzzy control rules are obtained by using the Lyapunov
stability theory. The numerical simulations using one-dimension and
two-dimension FSMC show effectiveness of the proposed controller
for vibration suppression. Further, the well-known skyhook control
scheme and an adaptive sliding mode controller are also included in
the simulation for comparison with the proposed FSMC.
Abstract: In this paper the Huang-s method for solving a m×n fuzzy linear system when, m≤ n, is considered. The method in detail is discussed and illustrated by solving some numerical examples.
Abstract: 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.
Abstract: 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.
Abstract: Three novel and significant contributions are made in
this paper Firstly, non-recursive formulation of Haar connection
coefficients, pioneered by the present authors is presented, which
can be computed very efficiently and avoid stack and memory
overflows. Secondly, the generalized approach for state analysis of
singular bilinear time-invariant (TI) and time-varying (TV) systems
is presented; vis-˜a-vis diversified and complex works reported by
different authors. Thirdly, a generalized approach for parameter
estimation of bilinear TI and TV systems is also proposed. The unified
framework of the proposed method is very significant in that the
digital hardware once-designed can be used to perform the complex
tasks of state analysis and parameter estimation of different types
of bilinear systems single-handedly. The simplicity, effectiveness and
generalized nature of the proposed method is established by applying
it to different types of bilinear systems for the two tasks.