A sliding mode control approach to the benchmark problem for nonlinear control design

The nonlinear benchmark problem involves the design of a controller for the nonlinear rotation/translational actuator system. Partial feedback linearization of the system dynamics results in a structure that is particularly suitable far the sliding mode control approach. In this paper, a bounded discontinuous sliding mode control law is presented that results in excellent response to a class of initial conditions and rejection of a class of disturbances. However, since this control law may not be practical because of the nondiminishing effort required, a continuous approximation of the discontinuous control is proposed which avoids its drawbacks while resulting in only a slight performance degradation