U-model-based double sliding mode control (UDSM-control) of nonlinear dynamic systems

This study proposes a double sliding mode control-augmented U-control ( $ {\textrm{U}_{\textrm{DSM}}} $ UDSM-control) method for a class of single-input single-output nonlinear systems with internal uncertain parameters, model mismatching and external system noise/disturbance to improve robustness in nonlinear dynamic inversion in the U-control system design. For the configuration, the $ {\textrm{U}_{\textrm{DSM}}} $ UDSM-control system takes up (1) a double sliding mode dynamic inverter to cancel nonlinearities and dynamics of the plant, (2) a linear invariant controller, the other dynamic inverter of the specified whole desired system performance, so that the whole system dynamic inversion is split into two designs in double feedback loops. For using the framework, this study analyses the associated properties on (1) global stability, (2) double sliding from a switching control driving the states to a sliding band and an equivalent control driving the states to a sliding line and (3) robustness against uncertainties/disturbances and a potential data-driven prototype. To validate the developed control system, it selects bench test examples for simulation studies using Matlab/Simulink, which demonstrates the $ {\textrm{U}_{\textrm{DSM}}} $ UDSM-control in terms of accuracy, tracking, and robustness. The tests also present a step-by-step design procedure for potential applications.