Abstract: The problem of nonlinear oscillations of a two-layer liquid completely filling a limited volume is considered. Using two basic asymmetric harmonics excited in two mutually perpendicular planes, ordinary differential equations of nonlinear oscillations of the interface of a two-layer liquid are investigated. In this paper, hydrodynamic coefficients of linear and nonlinear problems in integral relations were determined. As a result, the instability regions of forced oscillations of a two-layered liquid in a cylindrical tank occurring in the plane of action of the disturbing force are constructed, as well as the dynamic instability regions of the parametric resonance for different ratios of densities of the upper and lower liquids depending on the amplitudes of liquids from the excitations frequencies. Steady-state regimes of fluid motion were found in the regions of dynamic instability of the initial oscillation form. The Bubnov-Galerkin method is used to construct instability regions for approximate solution of nonlinear differential equations.
Abstract: Conditions corresponding to the unconditional stability
of convection in a mechanically anisotropic fluid saturated porous
medium of infinite horizontal extent are determined. The medium
is heated from below and its bounding surfaces are subjected to
temperature modulation which consists of a steady part and a
time periodic oscillating part. The Brinkman model is employed
in the momentum equation with the Bousinessq approximation.
The stability region is found for arbitrary values of modulational
frequency and amplitude using the energy method. Higher order
numerical computations are carried out to find critical boundaries
and subcritical instability regions more accurately.
Abstract: In this paper, we consider the control of time delay system
by Proportional-Integral (PI) controller. By Using the Hermite-
Biehler theorem, which is applicable to quasi-polynomials, we seek
a stability region of the controller for first order delay systems. The
essence of this work resides in the extension of this approach to
second order delay system, in the determination of its stability region
and the computation of the PI optimum parameters. We have used
the genetic algorithms to lead the complexity of the optimization
problem.
Abstract: Adaptive observers used in sensorless control of induction motors suffer from instability especally in regenerating mode. In this paper, an optimal feed back gain design is proposed, it can reduce the instability region in the torque speed plane .
Abstract: This paper considers the development of a two-point
predictor-corrector block method for solving delay differential
equations. The formulae are represented in divided difference form
and the algorithm is implemented in variable stepsize variable order
technique. The block method produces two new values at a single
integration step. Numerical results are compared with existing
methods and it is evident that the block method performs very well.
Stability regions of the block method are also investigated.
Abstract: In a wind power generator using doubly fed induction
generator (DFIG), the three-phase pulse width modulation (PWM)
voltage source converter (VSC) is used as grid side converter (GSC)
and rotor side converter (RSC). The standard linear control laws
proposed for GSC provides not only instablity against comparatively
large-signal disturbances, but also the problem of stability due to
uncertainty of load and variations in parameters. In this paper, a
nonlinear controller is designed for grid side converter (GSC) of a
DFIG for wind power application. The nonlinear controller is
designed based on the input-output feedback linearization control
method. The resulting closed-loop system ensures a sufficient
stability region, make robust to variations in circuit parameters and
also exhibits good transient response. Computer simulations and
experimental results are presented to confirm the effectiveness of the
proposed control strategy.
Abstract: In this paper, based on linear matrix inequality (LMI), by using Lyapunov functional theory, the exponential stability criterion is obtained for a class of uncertain Takagi-Sugeno fuzzy Hopfield neural networks (TSFHNNs) with time delays. Here we choose a generalized Lyapunov functional and introduce a parameterized model transformation with free weighting matrices to it, these techniques lead to generalized and less conservative stability condition that guarantee the wide stability region. Finally, an example is given to illustrate our results by using MATLAB LMI toolbox.