First and second-order-like structures in linear multivariable-control-systems design

With the philosophy that many physical multivariable systems can, for the purposes of control-systems design, be approximately represented by much simpler forms, and that the analysis of such models can provide valuable insight into the time and frequency-domain characteristics of the system, the paper provides an analysis of two types of multivariable structure and derives closed-form solutions for proportional and proportional plus integral feedback controllers. The structures considered are shown to be direct multivariable generalisations of the classical 1st-order lag and the classical unity rank, minimum phase, overdamped 2nd-order system.