Generating rules in selecting controller gains: a combined rough sets/fuzzy sets approach

The combined application of approximate time windows (ATW) and rough sets in deriving rules for tuning controllers is discussed. The approach is to build an approximate reasoning system based approximate measures of controller performance, namely, overshoot, rise time, and settling time. Overshoot is the biggest deviation of step response from a particular steady state after the step response has reached a tolerance band for the first time. Rise time r_t is the time when a step response reaches 90% of its steady-state value for the first time, and settling time s_t is measured relative to rise time (i.e. the clock for s_t is reset at t=r_t). In this paper, the clocks used to measure durations required to achieve controller objectives are modeled as ATWs. An 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. The focus of this paper is a description of how rough control rules derived from a real-time decision system table have been used in fine-pointing for attitude control of a small satellite. The contribution of this paper is the application of rough sets, fuzzy sets and approximate time windows in the design of approximate time rough control systems