Recently the investigation of periodic motion of the delayed functional differential equations (DDEs) and the associated variation systems become the focus of many studies. One of the most important motivations is the milling process analysis. Different techniques are used to obtain approximate solutions for the delayed functional differential equations (DDE). All these models used the stability lobe diagrams in order to choose the maximum axial depth of cut, for a given spindle speed associated with the chatter free machining. In this work, a semi discretization method is briefly explained and has been applied for 1-DOF (degree of freedom) and 2-DOF milling system in order to build the stability lobe diagrams.

Bilayer of nickel and nickel oxide were deposited on glass substrates using RF magnetron sputtering technique. The magnetic properties of the prepared thin films were carried out at room temperature in both parallel and perpendicular magnetic field to the sample. The Preisach model was applied to provide a mathematical model of the magnetic hysteresis loop in the case of parallel geometry, along the easy axis of the bi-layer NiO / Ni. Good agreement was obtained between the theoretical and experimental results.

In this paper, an adaptive tracking controller for a piezo-actuated stage is designed considering the LUGRE model. The adaptation algorithm of the parameterized hysteretic function is used to achieve a displacement-tracking objective under the mechanical parameters uncertainties. The Lyapunov theory is used to derive an adaptive law for the system stability. The effectiveness of the proposed controller is validated considering real-time simulation. The validation results of the proposed controller presents good performances and robustness under an external load-disturbance and parameter uncertainties.