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

A methodology is presented of feedback control to achieve accurate tracking for a class of nonlinear time-varying systems in the presence of disturbances and parameter variations. The methodology uses in its idealized form piecewise continuous feedback control laws, resulting in the state trajectory `sliding´ along a discontinuity surface in the state space. The idealized form of the methodology results in perfect tracking of the required signals; however certain non-idealities associated with its implementation cause the trajectory to ´chatter´ along the sliding surface resulting in the generation of an undesirable high-frequency component which may excite high-frequency unmodelled dynamics of the control systems. To rectify this situation, it is shown how continuous control laws which approximate the discontinuous control law may be used to obtain disturbance and parameter variation insensitive tracking. At the same time, the continuous control laws decrease the extent of unwanted high-frequency signals.