Multiloop controller design for multivariable plants

The extension of the SISO (single-input single-output) relay tuning method to a class of multivariable plans is demonstrated. These are diagonally dominant n-by-n plants which are gain stabilizable and with all elements having low-pass characteristics. Gain stabilizability is required in order to lend any purpose to the procedure while the others ensure some accuracy to the information obtained. The requirement of diagonal dominance is made clear. The extension of the theory of describing functions to MIMO (multiple-input multiple-output) systems is given. An example is used to illustrate the analysis. This is followed by preliminary results on controller design which show that Ziegler-Nichols rules can still be used to design multiloop PI (proportional plus integral) controllers for multivariable systems