Circumventing the relative degree condition in sliding mode design

Classical sliding mode design approaches assume the transfer function matrix between the driving signal and the measured output of interest must be minimum phase and relative degree one. For the control case, the driving signal will be the control input and for the observer problem the driving signal is likely to be an unknown input which the observer seeks to reconstruct. This chapter demonstrates that the relative degree condition can be weakened if the nominal linear system used for the controller or observer design is combined with sliding mode exact differentiators to essentially generate additional independent output signals from the available measurements. It is shown that the transmission zeros of the original plant appear directly in the reduced order sliding mode dynamics relating to the augmented system in both cases. In the case of output feedback sliding mode control design for MIMO systems of any relative degree, a super twisting control algorithm is shown to provide robust control performance. Nonlinear simulation results for a ninth order nonlinear description of a web transport system, which does not satisfy the usual relative degree one condition, are used to demonstrate both the control design approach and the design of an unknown input observer.