Design of Optimal Controllers using Block Pulse Function

Abstract

Orthogonal functions have been in existence for quite a long time but couldn’t gain much importance due to the difficulty in obtaining analytical solutions with desirable accuracy. Significant advancement was seen during the advent of digital era of computation when piecewise constant orthogonal functions were found to be compatible for digital computation. Block pulse functions belonging to this class of orthogonal functions was found to be the best fit for digital computation. Block pulse functions discretise continuous time functions into piecewise constant coefficients with every coefficient representing least square approximation in the interval. Disjointness property unique to block pulse functions reduces complex matrix differential and integral equations into simple matrix algebraic equations. Since block pulse functions provide approximate solutions, an error always exists but this error is tuneable using m (number of block pulses).Optimal control of multivariable continuous time systems using block pulse functions is depicted in this thesis. Algorithms developed in this work for system analysis, state estimation, linear quadratic regulator, linear quadratic tracking, linear quadratic Gaussian, and continuous time model predictive control were demonstrated on quadruple tank process and HDA process. Block pulse function solutions are compared with that of analytical solutions. Block pulse functions take less computational time compared to analytical solution with minimal error. Newer algorithms have been developed for linear quadratic tracking, linear quadratic Gaussian and continuous-time model predictive control.