Multirate Ripple-Free Deadbeat Control

Abstract

The design of multirate ripple-free deadbeat controllers is a complex and difficult task. The ripple-free deadbeat control problem can be solved using two approaches, the time domain approach and the polynomial approach. The time domain approach depends on a minimum energy solution and solves the problem in a state space setting. The polynomial approach depends on the solution of the Diophantine equation and solves the problem in a transfer function setting. One approach which has shown promise for solving multirate ripple-free deadbeat control (MRFDC) problems is the use of Diophantine equation parameters. This thesis proposes a hybrid two degree of freedom controller for the fixed-order constrained optimization problem addressing performance and robustness specifications utilizing the parameters of Diophantine equation to build a multirate ripple-free deadbeat control (MRFDC). The salient feature of the proposed approach is that it combines the concept of multirate input which was demonstrated by Salgado and Oyarzun and use this concept in the single rate which was demonstrated by Paz. This research discusses the single rate input, then it proposes the multirate input using the parameterization of the Diophantine equations. Simulation results show that the output signal tracks the input sinusoidal signal in short settling time either in single rate or multirate ripple – free deadbeat control. The time domain specification for the output signal, control signal, error signal and the output of the filter signal are computed and satisfied that it was guaranteed the requirement and constraint.