Generalized Relative Degree Approach to Sliding Mode Control Design for Nonminimum Phase Systems

The relative degree (RD) approach is a powerful tool for obtaining system's input-output dynamics used for output tracking controller designs of minimum phase systems. Designs based on the RD approach alone may fail due to instability of internal dynamics attributed to nonminimum phase systems. The use of generalized relative degree allows for the elimination of internal dynamics via replacing it by the unstable dynamic extension. An algorithm for generating a bounded solution of this unstable dynamic extension is proposed, allowing for a sliding mode controller (SMC) design for nonminimum phase systems. The efficacy of the proposed approach is demonstrated on a nonminimum phase rocket attitude control problem analytically and via simulations.