Adaptive Super-Twisting Control of Nonminimum Phase Systems Using Generalized Relative Degree Approach

The output tracking control design in perturbed minimum phase systems using the relative degree (RD) approach is a very effective control paradigm. The RD-based control approach in nonminimum phase (NMP) perturbed systems is challenged by an instability of internal/zero dynamics, attributed to the NMP phenomenon and by the external sufficiently smooth bounded perturbation with unknown bounds. For the first time, the challenge is addressed in this work via employing the generalized relative degree (GRD) approach in concert with adaptive continuous second-order (super-twisting) sliding mode control. The unstable internal/zero dynamics are eliminated, while the unstable dynamically extended control (DEC) emerges once the GRD technique is applied to the perturbed NMP system. The algorithm for generating a bounded solution of the unstable DEC equation is employed. This algorithm is integrated with adaptive super-twisting (ASTW) control for the first time, allowing a robust continuous control design for perturbed NMP systems with not-overestimated control gains. The efficacy of the proposed GRD-based ASTW control design algorithm is demonstrated in controlling a perturbed canard-controlled (NMP) rocket attitude both analytically and via simulation.