Abdulkadir Iyyaka Audu - Computer Engineering Department, Faculty of Engineering, University of Maiduguri Maiduguri, Nigeria
Jibril Danladi Jiya - Mechatronics Engineering Department, Faculty of Engineering, Abubakar Tafawa Balewa University Bauchi, Nigeria

Hamilton-Jacobi Representations of Trapezoidal Uninterruptible Power Supply System is proposed. Fairly recently, Hybid-Fiber/Coax networks which allow for effective segmentation of services in telecommunication industries have been powered using trapezoidal-shaped ac. voltage waveform. The control strategy of Trapezoidal Uninterruptible Power Supply (TUPS) demands the system dynamics be understood. The development of frequency spectrum and subsequent analysis of state variable representation of TUPS using Hamilton-Jacobi approach yields a closed-loop solution in the form of an optimal-control law. This work considers Hamilton-Jacobi approach as an option to seek the solution for a whole family of initial conditions by state feedback instead of only one specific set of initial conditions. A linear quadratic regulator which could provide an optimal control law for the TUPS with a quadratic performance index is considered. The application of Hamilton-Jacobi approach to the control dynamics of TUPS will result in a matrix form of solution in the time domain known as the matrix Ricatti equations. These equations if solved would lead to a control law that is a function of the state variables, indicating that it yields closed-loop control system.

Trapezoidal waveform, optimal control, linear quadratic regulator, matrix Ricatti equations, performance index, frequency spectrum.