Linear Algebra Based Controller - Design and Applications

SCAGLIA, GUSTAVO; SERRANO, EMANUEL; ALBERTOS PEDRO

Springer International Publishing

Año: 2020 p. 147

978-3-030-42817-4

The trajectory tracking problem is a very important one in control theory. The main goal is that the systemvariables follow a given evolution in the predefined time. These reference signals are often obtained by meansof some optimization procedure (for example, determining the feed profile of a reactor to maximize production)or they can be generated online through the references that human operators give to robots in rescue operations,recognition or vigilance. Also, robots that transport loads between production lines and warehouses and morerecently the case of vehicles moving without human intervention through the cities fall into this category.This book presents a new methodology for the design of controllers for trajectory tracking, where the controllerdesign problem is linked to that of solving a system of linear equations. In this way it is possible to deal with acomplex problem from a simpler point of view. Moreover, in general when a problem can be presented from asimpler point of view, it is easier to obtain conclusions about the behavior of the system under study, and thusknow what modifications to make to improve its performance. An important step in the design procedure is toanalyze under which conditions the system of equations has an exact solution. This allows to determine thedesired value of some of the state variables whose reference is not given and may momentarily take values notwell a priori defined. For that reason, we have called them as sacrificed variables. The greatest contribution ofthis book is to outline a procedure to follow to design the controller that ensures that the system follows thereference signals. The system can be linear, nonlinear, monovariable or multivariable, the only condition is thatit should be minimum phase and the model should be affine in the control.This book is based on the research we have carried out since 2005, when the methodology based on linearalgebra was applied for the first time design the control of a mobile robot based on its cinematic model. Thenthe technique was applied to more complex systems such as ships, airplanes, quad rotor, chemical processes,etc., as shown in the publications listed as references. Other than the basic procedure, the modifications of theoriginal algorithm to take into account the perturbations and the uncertainty in the model are also described.This final structure of the book is based on the work we have done in our research group as well as on thecourses and seminars taught in different universities. The book can be used to introduce control of trajectorytracking as part of an advanced control course for undergraduates. On the whole, it can be used for apostgraduate course on control of trajectory tracking. The book has a practical orientation and is also suitablefor process engineers.