Dynamic sliding manifold-based control in systems with unmodeled cascade dynamics

Unmodeled cascade dynamics in sliding mode control systems present a significant issue, known as chattering, to be resolved. This dissertation solves the chattering problem caused by unmodeled cascade dynamics using the concept of the dynamic sliding manifold. The dynamic sliding manifold is defined as a realizable dynamic operator acting on the original sliding variable. Following the standard sliding mode control design algorithm, the control function is designed to provide finite time convergence of the state trajectory to the dynamic sliding manifold. Once the state trajectory reaches the dynamic sliding surface, it is maintained on the dynamic sliding surface for all subsequent time. The original sliding variable, designed to provide the desired closed loop system performance, also converges to zero in a controlled manner.; Both linear and nonlinear dynamic sliding manifolds have been developed in this dissertation to accommodate first and second order cascade unmodeled dynamics. Linear dynamic sliding manifolds provide for finite time convergence to the dynamic sliding manifold and asymptotic convergence of the original sliding variable to zero. Nonlinear dynamic sliding manifolds provide for finite time convergence of both the dynamic sliding variable and the original sliding variable to zero.; The developments of this dissertation are a major improvement from a practical implementation perspective over existing higher order sliding mode techniques which require multiple differentiations of the sliding variable. The nonlinear dynamic sliding manifold-based sliding mode differentiator developed in this dissertation is robust to noise effects. The application of the dynamic sliding manifold-based control to a case study that considers a two-link, planar robot manipulator verifies the performance and efficiency of the developed design methodology.