Unmatched uncertainties compensation based on high‐order sliding mode observation

Abstract

SUMMARY The problem of compensation of the effects of unmatched uncertainties ∕ perturbations is considered. High‐order sliding mode observers are employed for exact state and uncertainties ∕ perturbations reconstruction. A sliding mode control design is proposed ensuring theoretically exact compensation of the uncertainties ∕ perturbations for the corresponding unmatched states based on the identified perturbation values. An inverted pendulum simulation example is considered illustrating the feasibility of the proposed approach.Copyright © 2012 John Wiley & Sons, Ltd.

High-Order Mismatched Disturbance Compensation for Motion Control Systems Via a Continuous Dynamic Sliding-Mode Approach

“…Another alternative approach to attenuate mismatched uncertainties is proposed in [26], [27], which is called enhanced SMC (ESMC) via a disturbance observer. The sliding surface in [26], [27] for system (1) is defined as…”

“…Due to the importance of compensating mismatched disturbances in both theory and engineering applications, several researchers have engaged in solving such a problem via DOBC, for example see [20]- [27]. In [24], the offset caused by mismatched disturbance is removed in the context of model predictive control by correcting the prediction error via a disturbance observer.…”

“…By designing a specific disturbance compensation gain, a new DOBC framework was proposed to compensate mismatched disturbances for linear systems in [23] and also nonlinear systems in [20]. In [26] and [27], a new DOBC method was proposed to counteract the mismatched uncertainties in the system via designing a dynamic sliding surface incorporating the information of mismatched disturbances. When the sliding motion is realized, the prescribed specification including robust stability and disturbance attenuation can be achieved.…”

“…When the sliding motion is realized, the prescribed specification including robust stability and disturbance attenuation can be achieved. However, it is noticed that, the mismatched disturbances in [20]- [27] are required to be a constant, which is not reasonably satisfied for many practical engineering issues [5], [28]. Taking the MAGLEV suspension vehicle as an example, the track input disturbance would not be a constant but fluctuates continuously with a high-order timevarying feature [5].…”

“…Taking the MAGLEV suspension vehicle as an example, the track input disturbance would not be a constant but fluctuates continuously with a high-order timevarying feature [5]. The presence of high-order mismatched disturbances will result in undesirable static and dynamic performance for methods in [20]- [27], which may constrain their applications in practical systems.…”