Novel sliding mode observers for a class of uncertain systems

Sliding mode observers designed for systems with matched uncertainty require an upper bound to be known exactly. To remove this requirement, two novel sliding mode observers are proposed by modifying Walcott-Zak observer and Edwards-Spurgeon observer. Their novelty lies in the mechanism introduced to update the sliding mode observer gain for counteracting uncertainty. Due to this, the knowledge of its upper bound is not needed. It is proved that the two observers can guarantee the state estimation error goes to zero globally and asymptotically. To address the chattering problem, we modify the discontinuous components in the observers and the update law of the sliding mode observer gain accordingly. The way to modify the discontinuous components in the observers is not new, the novelty in the modified observer lies in the observer gain update law for counteracting uncertainty, where a design term is intentionally introduced to make the uncertainty estimation to track the uncertainty faster and more accurately. The sliding mode observer gain for counteracting uncertainty is only updated when the output estimation error is outside the desired region. The modified observers can guarantee the state estimation error is bounded and can be driven to an arbitrarily small neighborhood of the origin. Inspired by the idea to estimate the faults using SMO in the paper by Edwards et al. (2000), a method of estimating the uncertainty is also derived when the modified sliding mode observers are applied, and can be used in applications such as in fault diagnosis. To compare our novel SMO based on Edwards-Spurgeon observer with the sliding mode observer of Edwards et al. (2000), the inverted pendulum example studied is used and simulation results are given.