Tracking control of non-linear systems using sliding surfaces, with application to robot manipulators†

We develop a methodology of feedback control to achieve accurate tracking in a class of non-linear, time-varying systems in the presence of disturbances and parameter variations. The methodology uses in its idealized form piecewise continuous feedback control, resulting in the state trajectory sliding along a time-varying sliding surface in the state space. This idealized control law achieves perfect tracking; however, non-idealities in its implementation result in the generation of an undesirable high frequency component in the state trajectory. To rectify this, we show how continuous control laws may be used to approximate the discontinuous control law to obtain robust tracking to within a prescribed accuracy and decrease the extent of high frequency signal. The method is applied to the control of a two-link manipulator handling variable loads in a flexible manufacturing system environment.