DSMC-a symbolic toolbox for robust nonlinear dynamic sliding mode control design

Sliding mode control has long been recognised as providing an appropriate solution to the robust control problem. Up to this point the majority of design methodologies have been based around linear uncertain systems or specific types of nonlinear systems. The latter may involve particular application areas, such as robotics, or require that relatively stringent conditions are met by members of the system class, for example the system class may be required to be feedback linearisable. It is obviously desirable to have a sliding mode control methodology which will be applicable to a fairly broad class of nonlinear system representations, exhibit robustness while yielding appropriate performance and lend itself to the development of appropriate toolboxes for controller design. This paper will suggest that dynamic sliding mode control policies based around differential input-output system representations are sufficiently general to meet this remit. It will also describe the progress made to date in the development of DSMC, a symbolic package which is being developed in Mathematica, to implement the design method. A design strategy using the DSMC will consider the development of a robust controller for a planar vertical take-off and landing aircraft.