Description

 SATAW-Tool (SATuration AWare Tool) is intended to gather multiple theoretical results regarding the presence of saturation elements in the control loop. At this date, simple functions for manipulating saturation elements in the control loop are provided. They allow performing analysis and control design operations for linear systems interconnected with saturation elements. LMI based functionalities are provided.
For the saturation modeling, sector conditions are used. In this representation, the saturation term is replaced by a dead-zone nonlinearity. Hence, sector conditions, locally or globally valid, can be used to relax stability and stabilization conditions.
The package is yet in development and will be updated at odd times. It is intended to include several functions for:
    * state-feedback or output feedback analysis, in presence of position saturation and/or rate saturation;
    * state-feedback design, in presence of position saturation (done) and/or rate saturation (to be provided before summer 20113);
    * static and dynamic anti-windup analysis, in presence of various saturated-based nonlinear elements (done currently only for position saturation elements);
    * static and full anti-windup design, in presence of various saturated-based nonlinear elements (to be provided before summer 20113).

The theoretical results and the formalisms used in SATAW-Tool have been fully described in our recently published book. Please refer to it when you use this toolbox:

@book{TGGQ/2011,
    Address = {London (UK)},
    Author = {S. Tarbouriech and G. Garcia and J.M. {Gomes da Silva Jr.} and I. Queinnec},
    Publisher = {Springer},
    Title = {Stability and Stabilization of Linear Systems with Saturating Actuators},
    Year = {2011}}

License agreement

SATAW-Tool is entirely written in Matlab and uses YALMIP for parsing LMIs. SATAW-Tool is free of charge and openly distributed, in the hope that the will be useful, but without any warranty. You are free to use any of the files of the following toolbox for personal or academic use. It may not be re-distributed as a part of a commercial product.  Neither the authors nor CNRS accept any responsibility or liability with regard to this software that is licensed on an "as is" basis. 

Download

SATAW-Tool - V0 (25 March 2013) can be downloaded as a zip archive, including this documentation. It is supported for Matlab 7.2 and higher. Remember that it most certainly contains bugs. 

To install, delete any old SATAW directory, unzip the downloaded file, and update your path:
>> addpath whereIputTHEdirectory/SATAW

Note that the functions are provided using YALMIP. You can then use any SDP solvers among those listed here.

Note also that it makes use (as an option) of Matlab objects ssmodels initially defined for RoMulOC. It is recommended to install RoMulOC, which is entirely based on m-code and you just need to unzip romuloc.zip and to add the required path.

SATAW-Tool strongly benefits from our cooperation with João-Manoel Gomes da Silva Jr. Many thanks to him!