Multi‐input/single‐output computer‐aided control design using the quantitative feedback theory

The quantitative feedback theory is an engineering design technique of uncertain feedback systems having robust stability and robust performance specifications. The crux of the quantitative feedback theory is a transformation of robust stability and robust performance specifications into domains in the complex plane, referred to as bounds, where a nominal loop transmission should lie within. To date, a quantitative feedback theory design is being carried out using manual (i.e. graphical) procedures or search algorithms. This paper shows that there exists a formal map from the uncertain plant and each closed‐loop specification to these bounds. In particular, it is shown that each map has a closed form consisting of a quadratic inequality. These maps greatly simplify the computational aspects of the quantitative feedback theory in design of single‐loop feedback systems. Based on this new development, a simple‐to‐implement, efficient computer algorithm is outlined.