In this paper, chaotic dynamic and nonlinear control in a glucose-insulin system in types I diabetic patients and a healthy person have been investigated. Chaotic analysis methods of the blood glucose system include Lyapunov exponent and power spectral density based on the time series derived from the clinical data. Wolf's algorithm is used to calculate the Lyapunov exponent, which positive values of the Lyapunov exponent mean the dynamical system is chaotic. Also, a wide range in frequency spectrum based on the power spectral density is also used to confirm the chaotic behavior. In order to control the chaotic system and reach the desired level of a healthy person's glucose, a novel fuzzy high-order sliding mode control method has been proposed. Thus, in the control algorithm of the high-order sliding mode controller, all of the control gains computed by the fuzzy inference system accurately. Then the novel control algorithm is applied to the Bergman's mathematical model that is verified using the clinical data set. In this system, the control input is the amount of insulin injected into the body and the control output is the amount of blood glucose level at any moment. The simulation results of the closed-loop system in various conditions, along with the performance of the control system in disturbance presence, indicate the proper functioning of this controller at the settling time, overshoot and the control inputs. Manuscript profile

This paper presents a control system for elimination of chaotic behaviors in spur gear system. To this end, at first different aspects of chaos are investigated by means of numerical tools including time series response, phase plane trajectories, bifurcation diagram, Poincare’ section, Lyapunov exponent and power spectrum density. The nonlinear dynamic model encompasses constant mesh stiffness and damping along the line of action, static transmission error and backlash. In order to suppress the chaotic oscillations, a novel controller on the basis of the Predictive Sliding Mode Control (PSMC) is proposed in which the sliding surface is predicted by the use of model predictive control theory and the control input is obtained. Consequently, the control system takes advantage of the both approaches in developing a robust controller. The simulation results of the feedback system depict the effectiveness of the controller in elimination of the chaotic vibrations along with reduction of settling time, overshoots, and energy consumption. Furthermore, stability and robustness of the system are guaranteed. Manuscript profile

The chaotic dynamics of Roto-Translatory motion for a triaxial Gyrostat satellite is considered in this study based on the Hamiltonian approach. Higher complexity in the coupled spin-orbit equations motivates the reduction of the Hamiltonian in the study of this nonlinear system. This reduction is done by the use of the Deprit canonical transformation developed here by the new Serret-Andoyer variables used as rotational and translational variables. The results obtained from the Hamiltonian reduction can be written as a perturbed equation near Integrable-Hamiltonian form, where the perturbed part of the equations consists the orbital and gravity gradient effects. Increasing the perturbation parameter causes the trajectories of the system to pass throughout heteroclinic bifurcation zone introducing chaos in the system. Also heteroclinic bifurcation and transversally stable and unstable manifolds are mathematically proven using Melnikov method. Through the Melnikov integral, the bounded variations in the design parameters are determined so as to prevent the system from a chaotic behavior. The simulation results based on the numerical methods such as the time series responses, trajectories of phase portrait, Poincare section, and Lyapunov exponent criterion quantitatively verify chaos in the system in the presence of perturbation influences.. Manuscript profile

In this paper, the nonlinear buckling behavior of two types of functionally graded sandwich beams was studied using a high-order sandwich beam theory. Type I consists of functionally graded layers coating a homogeneous core, while type II features an FG core covered by homogeneous face sheets. All materials are considered temperature dependent, with FGM properties modified through even and uneven porosity distributions modeled by a power law rule. The sandwich beam theory was adjusted to account for nonlinear Lagrange strains, thermal stresses of the face sheets, in-plane strain, and the transverse flexibility of the core. The governing equations were derived from the minimum potential energy principle, and a Galerkin method was employed to solve them for simply supported and clamped boundary conditions. Comparisons with existing literature demonstrate good agreement. The resultes showed that critical load parameter decreases with increasing temperature, power law index, length-to-thickness ratio, thickness, and porosity volume fraction in both distributions, but increases with the wave number. Additionally, the stability of type II sandwich beams surpasses that of type I in high-temperature conditions. Manuscript profile