Improvement in Gain Margin for a Dual-Rate System

Abstract

This paper proposes a new method for designing a digital control system, in which a plant in continuous time is controlled by updating a control input in discrete time. The controlled system is a dual-rate system in which the sampling period is restricted to be double the control period. Hence, a fast-rate control system cannot be obtained, and to obtain a single-rate control system, a designed system is a slow-rate control system, where the control input is updated at slow-rate (2T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ) and the plant output is sampled at slow-rate (2T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ). In this paper, the slow-rate single-rate system is a dual-rate system, where the control input is updated at fast-rate (T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ) and the plant output is sampled at slow-rate (2T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ). Further, the dual-rate system is redesigned for improving stability margin independent of the output response of the pre-designed slow-rate single-rate system. Numerical examples demonstrate the effectiveness of the proposed method.