Qualitative control with quantitative models

This contribution addresses the issue of qualitative control based on quantitative models: A continuous plant is controlled via symbolic, or quantized, measurement and control signals. Quantization levels may be arbitrarily coarse (e.g. “temperature is too high“, “ok” or “too low”, “valve is open” or “closed”). Sensor quantization is assumed to partition the plant output space into rectilinear boxes, where each box is associated with a unique measurement symbol. Measurement symbols are processed by a control algorithm to give a sequence of control symbols. This sequence is then mapped back into the space of real-valued input signals and fed into the plant. The usual way to deal with such a situation is to determine a qualitative (discrete event) plant model, e.g. by “abstracting up” the original quantitative plant description, and then to use this qualitative model for controller design purposes. In contrast to this approach, it is argued here that, in many cases it might be more appropriate to design the symbol-manipulating controller directly on the basis of a quantitative, or numerical, model