Hybrid Energy Storage System (HESS) has been implemented for better energy efficiency to Hybrid/Electric Vehicles (HEV/EV), in that the main source is Battery and Ultra Capacitor (UC) is the auxiliary source. The battery is connected to DC Bus through Boost Converter and Ultra Capacitor has been connected through Buck-Boost Converter. Battery and Ultra Capacitor voltages levels are maintained less than the DC bus voltage. The main aim of this paper is to design an intelligent controller for a smooth transition between the sources in the Hybrid Energy Storage System. Math function Based (MFB) Controller has been modelled and implemented to an electric motor for Electric/Hybrid Electric Vehicle Application. The MFB controller has to work based on the Speed of the motor and this controller makes the closed loop operation of the overall system with smooth operation between the energy sources. Proportional Integral (PI) controller was used here to maintain the constant voltage profile for various loads at the terminals of the electric motor. Combination of PI and MFB controllers has given closed loop operation of the entire model with smooth Switching between the sources. The total circuit has been simulated in MATLAB/Simulink and obtained the satisfactory results, which are discussed in the results section.

This paper introduces a novel concept of Boolean function{based hypergraph with respect to any given T. B. T(total binary truth table). This study de, nes a notation of kernel set on Switching functions and proves that every T. B. T corresponds to a Minimum Boolean expression via kernel set and presents some conditions on T. B. T to obtain a Minimum irreducible Boolean expression from Switching functions. Finally, we present an algorithm and so Python programming(with complete and original codes) such that for any given T. B. T, introduces a Minimum irreducible Switching expression.