Fundamental Analysis of the Perturbation Rejection Characteristics of Single-Input-Multiple-Output Systems Subject to Multiple Perturbations

Single-Input-Multiple-Output (SIMO) systems are found in several applications. Some of the main concerns are (1) the possibility of stabilizing all the outputs and (2) the possibility of attaining independent tracking control of all the outputs. Whereas the first issue can be easily be elucidated, the second has proven to be impossible in all but a few systems. In many cases one practical option is to use the input to drive a main output, taking care that the behavior of the remaining secondary outputs is acceptable. In this configuration, in addition to the features of the main control loop, the perturbation rejection properties of the secondary outputs become important. This article analyzes the structural properties, stability, and perturbation rejection characteristics of SIMO systems. The article presents fundamental conclusions regarding the relationship of the main control loop and the perturbation rejection characteristics of the secondary outputs. A simple and intuitive example is used to show how the theoretical findings can be used to improve the design of the main control loop through its frequency domain characteristics. The results are developed using simple frequency domain theoretical elements, making the findings relevant for both engineering applications and deriving further theoretical developments.