Variable structure control of robotic manipulator with PID sliding surfaces

Dynamic behaviour of a system in sliding mode is entirely defined by the sliding surface. Customarily, the surface is selected as a hyperplane in the system's 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 included an integral term in the sliding surface expression that resulted in a type of PID sliding surface. However, the advantages of such a design were not elaborated in following publications of these or other researchers. In this paper we present a new design procedure and stability analysis for robotic variable structure controllers with PID-like sliding surfaces. Two versions of the controller are presented: regular and adaptive. The former is very simple and can operate with an unknown dynamic model; the only information required is a bound on one parameter. The latter provides an on-line estimation for this bound. Both controllers are robust with respect to bounded external disturbances and some unmodelled dynamic effects. The simulation results have demonstrated stability, with minimum transient responses that may be significantly faster than responses of traditional PD-manifold controllers under the same conditions.