Variable structure regulation of a flexible arm with a translational base

Presents an exponentially stable variable structure controller (VSC) for a distributed-parameter system: a flexible arm with a translational base. Such a system can be found in many industrial applications, e.g., the SCARA/Cartesian robots which are widely used in automatic manufacturing assembly. Exponential stability is achieved through explicitly solving the corresponding boundary value problem of the partial differential equations (PDEs) of the system. As a result, some disadvantages associated with the traditional truncated-model-base controller design approaches are essentially avoided. Numerical simulations are provided to verify the effectiveness of the presented method