Overview

The synthesis of a control law passes through the utilization of patterns which are nothing other than an imperfect representation of reality: besides the fact that the laws of physics provide only a global representation of phenomena, valid only in a certain range, there are always the uncertainties of pattern establishment because the behavior of the physical process cannot be exactly described using a mathematical pattern.

Even if we work with patterns whose validity is limited, we have to take into account the robustness of the control law, i.e. we have to be able to guarantee not only the stability but also certain performances related to incertitude patterns. This last issue requires completing the pattern establishment work with a precise description of pattern uncertainties, to include them in a general formalism enabling us to take them into account and to reach certain conclusions.

The synthesis of a control law is hence articulated around two stages which are being alternatively repeated until the designer reaches satisfactory results:

• controller calculation: during this stage only certain performance objectives and certain robustness objectives can be taken into account;

• analysis of the controlled system properties, from the perspective of its performances as well as their robustness.

The approaches presented in this chapter are articulated around these two concepts.

15.1. The H _? Approach

The preoccupation for robustness, which is inherent among the methods used by traditional automatic control engineering, reappears around the end of the...