Automatic identification of the relative degree of nonlinear systems: Application to sliding mode control design and experimental assessment

This paper deals with the design and the experimental-based assessment of a scheme to identify the relative degree of a system in order to correctly design the controller. The system is assumed to have an unknown dynamics, and the output is measured in a discrete-time fashion. Provided that a prescribed input signal is applied, it is proven that a set of inequalities holds only for the
th time derivative of the output, where
is the relative degree. A practical algorithm for the relative degree identification is also formulated, which is written in a pseudo-code notation. In the paper, a special reference is made to the design of sliding mode controllers. Specifically, a self-configuring sliding mode control strategy is presented, which automatically selects the controller in case of changes to the relative degree. The scheme is implemented in a practical set-up composed of a lab-scale overhead crane mechanically coupled with a 12 Volts DC motor. The aim is to identify the relative degree of the position of the crane (the output), with respect to the DC motor armature voltage (the control input). The experimental results reveal the high accuracy of the proposed strategy for the identification of the relative degree.