In this paper, we present the vector control of a permanent magnet synchronous machine (PMSM) by a PI regulator whose tracking performance; speed, stability, and precision are satisfactory. However, we can see the influence of the variation in the resistance and load torque on the behavior of the controlled system. we analyze the simulation results found and then we make an inventory of PI disadvantages. This work is modified with a novelty by introducing a new control law namely sliding mode and backstepping control law. Then we analyze the results found making a comparison to those of the PI regulator.

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This paper presents a nonlinear control of (PMSM) using backstepping. We will study the different performances and robustness of each type of control, by introducing a new Lyapunov function candidate with a large possibility of parameter choice. Simulation results clearly show that the speed and current tracking errors asymptotically converge to zeros. Compared with neural networks control schemes, we do not require the unknown parameters to be linear parametrizable. No regression matrices are needed, so no preliminary dynamical analysis is needed.

Based on our previous works concerning pseudo differential operators and their supersymmetric versions, we investigate to present an approach to interpret some results concerning the mapping between two superconformal field theories. As a direct result, we have reduced the number of super fields which parametrizes [Formula: see text] super W3-algebra theory. Such a decomposition can be interpreted physically as the interaction between a fermionic particle of conformal spin [Formula: see text] and a bosonic particle of spin [Formula: see text] ([Formula: see text], [Formula: see text] or [Formula: see text] for example) given rise to supersymmetric particles of total conformal spin [Formula: see text].

In this work, we explore the Schwarzschild geometry in a spherically symmetric gravitational field. We build the non-commutative equations of motion with the aid of the Hamiltonian function and modified algebra. We then study the implications of the non-commutative geometry on the trajectory of a light ray, traveling in null and particles geodesics. Also, we interpret the effect of non-commutativity in both the bending of light and the perihelion advance of Mercury. Therefore, introducing a non-commutative parameter provides a slight correction to the results of general relativity.