Theory Of Differential Calculus Research Articles

Linearized Fraction Order Control and Stability Analyses for Switched Reluctance Motor Drives

The nonlinearity and double salient pole of the switched reluctance motor make the control difficult and the torque fluctuation is large. To achieve good control performance, this study introduces a novel linearized fractional-order controller with the disturbance observer to regulate the speed and torque of a switched reluctance motor. Based on fractional differential calculus theory, the fractional-order proportional integral controller is designed. The disturbance observer is introduced to overcome the influence of nonlinearity on the switched reluctance motor and reduce the torque fluctuation. By using the extended state in the disturbance observer, the disturbances are estimated and compensated to achieve linearization and determinism. The parameter values of the proposed controller are obtained by employing the trial-and-error method. The frequency-domain analysis of the proposed controller shows that it has a good suppression performance for medium- and high-frequency disturbances. Through simulation, the performance of the system is analyzed. The results show good performance of the controller in speed change, current, and torque fluctuation reduction.

Algebraic and Geometric Theory of the Topological Ring of Colombeau Generalized Functions

AbstractWe continue the investigation of the algebraic and topological structure of the algebra of Colombeau generalized functions with the aim of building up the algebraic basis for the theory of these functions. This was started in a previous work of Aragona and Juriaans, where the algebraic and topological structure of the Colombeau generalized numbers were studied. Here, among other important things, we determine completely the minimal primes of and introduce several invariants of the ideals of (Ω). The main tools we use are the algebraic results obtained by Aragona and Juriaans and the theory of differential calculus on generalized manifolds developed by Aragona and co-workers. The main achievement of the differential calculus is that all classical objects, such as distributions, become C∞-functions. Our purpose is to build an independent and intrinsic theory for Colombeau generalized functions and place them in a wider context.