Improved multivariable quantitative feedback design for tracking error specifications

An improved design procedure for multi-input/multi-output (MIMO) quantitative feedback theory (QFT) problems involving tracking error specifications (TESs) has been presented. Appropriate transformation of the MIMO system to a series of equivalent single-input/single-output (SISO) problems is presented that motivates an improved synthesis procedure using feedback compensator and pre-filter transfer function matrices (TFMs). The key features of the procedure are that, for each equivalent SISO problem, (i) interactions and the effects of uncertainty are treated as an output disturbance, and (ii) sufficient conditions can be determined that assure desired levels of robust performance within the bandwidth region at a transformation cost that can be computed a priori. This paper also considers how the individual elements of the pre-filter TFM can be designed for MIMO QFT problems with a reduced level of conservatism and over-design using existing SISO methods. A benchmark quadruple-tank process is considered to illustrate the benefits of the new design paradigm.