Design of quantitative feedback theory non-diagonal controllers for use in uncertain multiple-input multiple-output systems

A fully populated matrix controller allows a designer considerably more design flexibility to govern multiple-input multiple-output (MIMO) processes than the classic diagonal controller structure. A methodology is presented to extend the classic diagonal quantitative feedback theory (QFT) controller design for MIMO plants with model uncertainty to a fully populated matrix controller design. Three cases are considered: (i) reference tracking; (ii) external disturbance rejection at the plant input; and (iii) external disturbance rejection at the plant output. The role played by the non-diagonal controller elements is analysed in order to state a fully populated matrix controller design methodology for QFT. Three coupling matrices and a quality function of the non-diagonal elements are defined and then used to quantify the amount of loop interaction and to design the non-diagonal controllers respectively. This yields a criterion that allows the proposal of a sequential design methodology for the fully populated matrix controller, in the QFT robust control frame. As a consequence the diagonal elements of the proposed non-diagonal method need less bandwidth than the diagonal elements of currently existing diagonal methods. The technique is verified by using the designed controller to control a SCARA robot manipulator.