Approximate Time Rough Control: Concepts and Application to Satellite Attitude Control

Abstract

This paper presents an approach to the design of approximate time rough controllers. In this paper, the clocks used to measure durations required to achieve controller objectives are modeled as approximate time windows. An approximate time window (atw) partitions time relative to granules (clumps of similar timing measurements) such as early, ontime, late. An atw determines the degree of membership of each observed duration in each of its temporal partitions. Based on observations of the degree of overshoot, rise time, and settling time during the operation of a control system, the architecture of an approximate time rough control system is established. The rough controller is guided by rules derived from a real-time decision-making system. Rough sets theory is used to derive controller rules. Fuzzy sets theory is used to model decision system sensors as fuzzy implications. A roughly fuzzy Petri net model of an approximate controller is given. The approach taken in approximate time rough control is illustrated relative to controlling the pitch angle in an attitude control system for a small satellite.

Research supported by NSERC Industrial-Research Partnership Grant, Bristol Aerospace Ltd. Grant and Canadian Space Agency Grant