Control design on the basis of approximate nonlinear models: the inverted pendulum example

The main interest of linear models is the wide panel of control structures that are available. This also motivated a large amount of work to extend these structures to nonlinear plants, either by local or exact linearization, or by introducing robustness properties. At the same time other works dealt with control of some classes of nonlinear systems. One of these families concerns flat systems for which it is possible to design reference trajectories that are admissible both for state variables and control input. However nonlinear plants may not exhibit such flatness properties since analysis is
done in the whole state space. Since in many situations the process evolution is confined in a reduced domain, one solution consists in building an equivalent nonlinear model which exhibits flatness properties in order to use related control design tools. The inverted pendulum system is used to illustrate the procedure.