Research Article Fundamental Analysis of the Perturbation Rejection Characteristics of Single-Input-Multiple-Output Systems Subject to Multiple Perturbations Luis Amezquita-Brooks, 1 Jesús Ulises Liceaga-Castro, 2 Eduardo Liceaga-Castro, 1 Daniel Martinez-Vazquez, 1 and Octavio Garcia-Salazar 1 1 Centro de Investigaci´ on e Innovaci´ on en Ingenier´ ıa Aeron´ autica, Facultad de Ingenier´ ıa Mec´ anica y El´ ectrica, Universidad Aut´ onoma de Nuevo Le´ on, San Nicolas de los Garza, NL, Mexico 2 Departamento de Electr´ onica, Universidad Aut´ onoma Metropolitana Unidad Azcapotzalco, Mexico City, Mexico Correspondence should be addressed to Luis Amezquita-Brooks; luis.amezquitabrk@uanl.edu.mx Received 9 October 2016; Revised 30 March 2017; Accepted 11 April 2017; Published 19 June 2017 Academic Editor: Francisco Gordillo Copyright © 2017 Luis Amezquita-Brooks et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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 frst 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 confguration, in addition to the features of the main control loop, the perturbation rejection properties of the secondary outputs become important. Tis article analyzes the structural properties, stability, and perturbation rejection characteristics of SIMO systems. Te 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 fndings can be used to improve the design of the main control loop through its frequency domain characteristics. Te results are developed using simple frequency domain theoretical elements, making the fndings relevant for both engineering applications and deriving further theoretical developments. 1. Introduction Single-Input-Multiple-Output (SIMO) systems appear on many industrial and technological applications where there is the need for closed-loop control, for instance, in electric machine control [1, 2], airplane control [3–5], and automotive active suspension control [6]. Te difculty of such systems is that in most cases it is not possible to attaint total control of all outputs using a single input. In particular, fully independent reference tracking control may be impossible [7]. In some cases a bandwidth separation and nested closed-loop control allow a degree of control over several output variables. Tis strategy has been historically used with success in aeronautical applications and other electromechanical systems [8–10]. Te stability of SIMO control systems is an issue of ongoing interest. For instance, in [11, 12] the stability of state feedback SIMO systems are studied from a theoretical point of view. While the stability of any control system is of prime importance, it is well-known that for actual practical applications the stability is only a starting requirement. Other more common strategy which uses modern control tools is the use of optimal controllers in which all the outputs are considered on the cost function [7, 13]. While these control approaches may yield good results, the design pro- cedure for such controllers still requires the calibration of the Hindawi Mathematical Problems in Engineering Volume 2017, Article ID 1905704, 17 pages https://doi.org/10.1155/2017/1905704