On variable structure robotic control with integral sliding surfaces

Dynamic behavior of a system in the sliding mode is entirely defined by the sliding surface. Customarily, the surface is selected as a hyperplane in the system state-space resulting in a PD type sliding surface. This is not the only possible structure, and other designs with more complex or time-varying surfaces may provide definite advantages. Slotine and Spong (1985) included an integral term in the sliding surface expression that resulted in a type of PID sliding surface. In this paper we present a new design procedure and stability analysis for robotic variable structure controllers with PID like sliding surface. Two versions of the controllers are presented: regular and adaptive. The former is very simple and can operate with an unknown robot dynamic model; the only information required is a bound on one parameter. The latter provides an online estimation for this bound. Both controllers are robust with respect to bounded external disturbances and some unmodeled dynamic effects. The simulation results have demonstrated stable, with minimum chattering transient responses that may be significantly faster than responses of traditional PD-manifold controllers under the same conditions