Problems in constructing a discrete-time controller using frequency response plots in w-plane

Abstract

Designing a discrete-time controller in w-plane offers an advantage that the well-developed and well-recognized frequency response plots (for example, Bode plot) can be employed to design a discrete-time controller. The frequency response plots cannot be used directly in z-plane to construct a controller. However, this paper describes the difficulties and issues in constructing a discrete-time controller through a w- plane by the use of Bode diagrams/frequency response plots. For this purpose, one of the extensively used switching converters, i.e., a DC-DC buck converter operating at a switching frequency of 1000 kHz is considered as a plant. The problem arises due to the introduction of a right-half-plane zero (RHPZ) when one intends to transform a plant in s-plane to z-plane and then from z-plane to w-plane for the sake of designing a discrete-time controller in w-plane. RHPZ behaves as a pole and additionally lags the phase, thus making the plant nonminimum phase characteristically. RHPZ limits the system bandwidth and causes sluggish response. The control of plants containing RHPZ becomes complicated. MATLAB/Simulink based simulation results are presented to highlight the issues associated with construction of the digital controller in w-plane.