Sampled-data fuzzy-model-based control systems: stability analysis with consideration of analogue-to-digital converter and digital-to-analogue converter

Abstract

This study investigates the system stability of sampled-data fuzzy-model-based control systems. To conduct the stability analysis, Takagi-Sugeno (T-S) fuzzy model is employed to represent the continuous-time non-linear plant. Based on the fuzzy model, a sampled-data fuzzy controller is proposed to perform the control task. By using a digital computer or microcomputer, the sampled-data fuzzy controller can be realised at low implementation cost. However, the following difficulties are needed to be addressed to put the sampled-data fuzzy controller into practice. First, as the zero-order-hold unit keeps the system states and control signal constant during the sampling period, the immediate system states cannot be accessed to compute the required control signal as what the continuous-time fuzzy control does. Second, the analogue-to-digital and digital-to-analogue converters introduce quantisation error to the control process, which is a source of instability. Third, the sampling activity introduces discontinuity to complicate the system dynamics, which makes the stability analysis difficult. Furthermore, it is due to the sampling activity and zero-order-hold unit, the nice property of continuous-time fuzzy-model-based control system for stability analysis vanishes which leads to conservative stability analysis results. In this study, these difficulties are addressed and the system stability is investigated based on the Lyapunov stability theorem. Membership function conditions are developed to facilitate the stability analysis. An application example is presented to illustrate the effectiveness of the proposed approach.