Comparison of methods of nonlinear control systems design

The issue of designing nonlinear control systems is a complex problem. A lot of methods are known that allow us to find a suitable control for a given nonlinear object that provides asymptotic stability of the nonlinear system equilibrium and an acceptable quality of the transient process. Many of these methods are difficult to apply in practice. Thus, comparing some of the methods in terms of simplicity of use is of great interest. Two analytical methods for the synthesis of nonlinear control systems are considered. They are the algebraic polynomial-matrix method that uses a quasilinear model, and the feedback linearization method that uses the Brunovsky model in combination with special feedbacks. A comparative analysis of the algebraic polynomial-matrix method and the feedback linearization method is carried out. It is found out that the algebraic polynomial-matrix method (APM) is much simpler than the feedback linearization method (FLM). A numerical example of designing a system that is synthesized by these methods is considered. It is found out that the system synthesized by the APM method has a region of attraction of the equilibrium position twice as large as the region of attraction of the system synthesized by the FLM method. It is reasonable to use the algebraic polynomial-matrix method with the quasilinear models in case of synthesis of control systems of objects with differentiable nonlinearities.

Optimization design for multiple dynamic vibration absorbers on damped structures using equivalent linearization method

The dynamic vibration absorber and tuned mass damper are widely used to suppress harmful vibration of the damped structures under external excitation. The multiple dynamic vibration absorbers have more benefit than the single dynamic vibration absorber. The multiple dynamic vibration absorbers are portability and easy to install because its size is significantly reduced compared to an individual damper. This paper proposes a design method to obtain optimal parameters of multiple dynamic vibration absorbers attached on damped primary structures by using the least squares estimation of equivalent linearization method. An explicit expression of damping ratio and tuning parameters of multiple dynamic vibration absorbers are determined for minimizing the maximum displacement of the primary structures based on the fixed-point theory. The new contribution is provided a reliable theoretical basis for optimizing parameters of the multiple dynamic vibration absorbers that are attached on the damped primary structures. The numerical results reveal the effectiveness of the proposed optimal parameters of multiple dynamic vibration absorbers in reduce vibration of damped primary structures. In the practical applications, this research results allow to divide a large dynamic vibration absorber into many equivalent small dynamic vibration absorbers, which are convenient for manufacturing and installing on the damped primary structures such as high buildings and cable-stayed bridges.

Dynamic Systems Enhanced by Electronic Circuits on 7D

Hybrid synchronization is one of the most significant aspects of a dynamic system. We achieve nonlinear control unit results to synchronize two comparable 7D structures in this study. Many dynamic systems are directly connected to health care and directly enhance health. We employed linearization and Lyapunov as analytical methods, and since the linearization method does not need updating the Lyapunov function, it is more successful in achieving synchronization phenomena with better outcomes than the Lyapunov method. The two methods were combined, and the result was a striking resemblance to the dynamic system’s mistake. The mathematical system with control and error of the dynamic system was subjected to digital emulation. The digital good outcomes were comparable to the two methods previously stated. We compared the outcomes of three hybrid synchronizations based on Lyapunov and linearization methods. Finally, we used the existing system, presenting it in a new attractor and comparing the findings to those of other similar systems.

Treatments of Thermal Neutron Scattering Data and Their Effect on Neutronics Calculations

In the conventional method to generate thermal scattering cross section of moderator materials, only one of the coherent elastic scattering and incoherent elastic scattering is considered in neutronics calculations. For the inelastic scattering, fixed incident energy grid is used in the nuclear data processing codes. The multipoint linearization method is used to refine the incident energy grid for inelastic scattering. We select ZrHx (zirconium hydride) as an example to analyze the effects of the above described treatments on the reactivity of several critical benchmarks. The numerical results show that the incident energy grid has an obvious effect on the effective multiplication factor (keff) of the analyzed reactors; simultaneously considering the coherent and incoherent elastic scattering also affects keff by tens of pcm.

Effects of Ion-Slip and Hall Currents on Magnetohydrodynamic Nanofluid Flow with Thermal Diffusion Using Spectral Quasi-Linearization Method

We scrutinize and numerically investigate the behavior of magnetic nanofluid flow in stagnation region in the presence of ion-slip and Hall currents. Employing similarity technique, the governing equations modeling the boundary layer flow are switched into highly nonlinear ODEs. The resultant equations are then solved numerically by the method of spectral quasi-linearization. The effect of varying various pertinent parameters within the fluid flow are taken into account and the results are analyzed graphically. It may be noted that the velocity increases in the x- as well as z-directions with an increment in the Hall parameter. The concentration indicates a decreasing trend with increasing values of the Eckert number. The computed results also show that the volume fraction effects diminishes as the Schmidt number increases.

Another class of nonterminating $_{3}F_{2}$-series with a free argument

By means of the linearization method, we evaluate another class of nonterminating $_{3}F_{2}$ F 2 3 -series with a free argument x and two perturbing integer parameters m and n.