Frequency Domain Design of a Series Structure of Robust Controllers for Multi-Input Single-Output Systems

The regulation of a disturbed output can be improved when several manipulated inputs are available. A popular choice in these cases is the series control scheme, characterized by a sequential intervention of loops and faster loops being reset by slower loops, to keep their control action around convenient values. This paper tackles the problem from the frequency-domain perspective. First, the working frequencies for each loop are determined and closed-loop specifications are defined. Then, Quantitative Feedback Theory (QFT) bounds are computed for each loop, and a sequential loop-shaping of controllers takes place. The obtained controllers are placed in a new series architecture, which unlike the classical series architecture only requires one controller with integral action. The benefits of the method are greater as the number of control inputs grow. A continuous stirred tank reactor (CSTR) is presented as an application example.