Different controllers for suppressing oscillations of a hybrid oscillator via non-perturbative analysis.

To arrive at an equivalent linear differential equation, the non-perturbative approach (NPA) is established. The corresponding linear equation is employed for performing the structural analysis. A numerical computation demonstrates a high consistency with the precise frequency. The correlation with the numerical solution explains the reasonableness of the obtained solutions. For additional nonlinear kinds of oscillation, the methodology gives an exact simulation. The stable construction of the prototype is shown in a series of diagrams. Positive position feedback (PPF), integral resonant control (IRC), nonlinear integral positive position feedback (NIPPF), and negative derivative feedback (NDF) are proposed to get rid of the damaging vibration in the system. It is found that the NDF control is more efficient than other controllers for vibration suppression. The theoretical methodology is applied by using the averaging method for getting a perturbed solution. The stability and influence of various parameters of the structure are established at main and 1:1 internal resonance, which is presented as one of the worst resonance cases. Association concerning mathematical solution and computational simulation is achieved.

Dynamical analysis of an inverted pendulum with positive position feedback controller approximate uniform solution.

The inverted pendulum is controlled in this article by using the nonlinear control theory. From classical analytical mechanics, its substructure equation of motion is derived. Because of the inclusion of the restoring forces, the Taylor expansion is employed to facilitate the analysis. An estimated satisfactory periodic solution is obtained with the aid of the modified Homotopy perturbation method. A numerical technique based on the fourth-order Runge-Kutta method is employed to justify the previous solution. On the other hand, a positive position feedback control is developed to dampen the vibrations of an IP system subjected to multi-excitation forces. The multiple time scale perturbation technique of the second order is introduced as a mathematical method to solve a two-degree-of-freedom system that simulates the IP with the PPF at primary and 1:1 internal resonance. The stability of these solutions is checked with the aid of the Routh-Hurwitz criterion. A set of graphs, based on the frequency response equations resulting from the MSPT method, is incorporated. Additionally, a numerical simulation is set up with RK-4 to confirm the overall controlled performance of the studied model. The quality of the solution is confirmed by the match between the approximate solution and the numerical simulation. Numerous other nonlinear systems can be controlled using the provided control method. Illustrations are offered that pertain to implications in design and pedagogy. The linearized stability of IP near the fixed points as well as the phase portraits is depicted for the autonomous and non-autonomous cases. Because of the static stability of the IP, it is found that its instability can be suppressed by the increase of both the generalized force as well as the torsional constant stiffness of the spring. Additionally, the presence of the magnetic field enhances the stability of IP.

Avoiding over diagnosis of shoulder dystocia.

In this study, we aimed to distinguish true shoulder dystocia from mere difficulty with delivery of the shoulder, by investigating the risk factors that lead to shoulder dystocia. Shoulder dystocia is a bony problem which occurs when either the anterior or, less commonly, the posterior fetal shoulder impacts on the maternal symphysis pubis or sacral promontory. Failure to apply the Royal College of Obstetricians and Gynaecologists (RCOG) clinical diagnostic criteria for shoulder dystocia has made it susceptible to over-diagnosis due to inclusion of all difficult shoulder deliveries, including those related to an inappropriate maternal position. This was a retrospective analysis of risk factors associated with 56 cases of shoulder dystocia which occurred in West Middlesex University Hospital between 2003 and 2004. The cases were analysed in two categories, good outcome and poor outcome, and compared with each other. The poor outcome had represented true shoulder dystocia. The incidence of shoulder dystocia increased from 0.94% in 2003 to 1.37% in 2004. However, the incidence of those with a poor outcome decreased from 45.4% of the whole shoulder dystocia group in 2003, to 17.6% in 2004 (p = 0.03). There were no clear diagnostic criteria documented in the notes for the condition other than the birth attendants' opinion and the turtle sign. This may either reflect over-diagnosis from increased awareness or possibly improvement in the outcome due to training and education. Interestingly, at least four risk factors were identified in each of the cases with poor outcome. A registrar conducting the delivery, forceps delivery for delayed second stage and the turtle sign were significantly common findings among the true shoulder dystocia group. Multiple risk factors can be a good predictor for the occurrence of shoulder dystocia. Applying the RCOG diagnostic criteria for shoulder dystocia may lead to improvement in diagnosis and therefore a better understanding of the risk factors and future management of shoulder dystocia.