Vectorization Blocks for Simulink

The paper presents two blocks that extend Simulink range of applicability to varying matrices, allowing the user to build (without writing a single line of code) dynamical systems that can be both complex and suitable for real time simulations. First of all, the three common techniques to build dynamical system with Simulink will be presented, showing the advantages and disadvantages of each of them. Then we will explain why (when dealing with complex multivariable systems) neither of the three can be at the same time easy to use and suitable for real time simulations. Two Simulink blocks will then be proposed that solve this problem by allowing varying matrices to be handled directly in the Simulink environment. The aspect, the user interface, and the most important part of the code of these blocks will be discussed, and their use will finally be explained by means of some examples. In particular, we will present an example on how to implement a complex multilayer adaptive neural network using these two blocks. Introduction: S-functions S-functions are the way in which a dynamical system is represented inside Simulink environment. Every Simulink object (block, composition of blocks, schemes) is a dynamical system; hence, every object (included the entire simulation scheme) is represented by an S-function. Typically, the built in Simulink blocks are associated with precompiled S-functions, while user added Sfunctions are obtained joining blocks or directly written in a language such as Matlab, C, C++, Fortran. ______________________________ †Professor, Associate Fellow AIAA ‡Research Assistant Professor, currently with Department of Mechanical and Aerospace Engineering, West Virginia University, Morgantown, WV, USA Copyright © 2000 by Mario Innocenti and Giampiero Campa, Published by the American Institute of Aeronautics and Astronautics, Inc., with permission Matlab and Simulink are trademarks of The Mathworks Inc. Whatever the language in which the S-function is written in, it must interact with Simulink in the same way, that is, it must have the structure shown in [1]. Different ways to build S-functions Joining together Simulink blocks Perhaps the most common way to build dynamical systems (hence S-functions) in Simulink, is just to join together Simulink blocks. For example, if we have two blocks that represent two systems and we would like to have the system consisting of the series of the two, the easiest way to obtain the series system is just drawing a wire that connects the output of the first system to the input of the second one. We can then group the two systems together using the Simulink “Group” function in order to obtain a block that appears as any Simulink block and represents our “new” dynamical system. The ease of operations like the one depicted above has been maybe the principal cause of Simulink success as an interface to deal with dynamical systems, indeed in this way we can build a dynamical system straightforwardly without the need to write a single line of code. In some cases however assembling subsystems may not be the best choice, this is true especially if we already have the input-state-output equations of the system that we are going to build, and especially for nonlinear multivariable systems. Let’s consider for example a system in which the output depends from the state vector in this way: