Higher/Second Order Sliding Mode Control in Nonminimum Phase Systems Using Generalized Relative Degree: Aerospace Application

Output tracking control design in nonminimum phase systems (NMP) using a relative degree (RD) approach can fail due to the instability of zero dynamics attributed to NMP systems. The use of Generalized Relative Degree (GRD) in NMP systems allows eliminating internal dynamics while yielding control dynamic extension that exhibits the instability. A proposed methodology of using GRD for designing continuous Higher/Second Order Sliding Mode Control (HOSMC/2-SMC) in perturbed NMP systems is presented. An algorithm for generating a bounded solution of the unstable dynamic extension is used in concert with HOSMC/2-SMC, allowing a robust control design for NMP systems. The efficacy of the proposed design is demonstrated on an NMP rocket attitude control problem solution.