Controller Design for Two-Input Single-Output Systems Exploiting Plant/Controller Alignment

Due to the unique structure of TISO feedback systems, several closed loop properties can be characterized using the concepts of plant and controller “directions” and “alignment”. Poor plant/controller alignment indicates significant limitations in terms of closed loop performance. In general, it is desirable to design a controller that is well aligned with the plant in order to minimize the size of the closed loop sensitivity functions and closed loop interactions. Although the concept of alignment can be a useful analysis tool for a given plant/controller pair, it is not obvious how a controller should be designed to achieve good alignment. We present a new controller design approach, based on the well-known “PQ method”, which explicitly incorporates knowledge of alignment into the design process. This is accomplished by providing graphical information about the alignment angle on the Bode plot of the PQ frequency response. We show the utility of this approach through a design example.