Globally stable output-feedback sliding mode control with asymptotic exact tracking
Proceedings of the 2004 American Control Conference
An output-feedback sliding mode controller is proposed for uncertain plants with relative degree higher than one in order to achieve asymptotic exact tracking of a reference model. To compensate the relative degree, a lead filter scheme is proposed such that global stability and asymptotic exact tracking are obtained. The scheme is based on a convex combination of a linear lead filter with a robust exact differentiator, based on second order sliding modes. keywords: Sliding Mode Control,
... in Systems, Tracking Control, Model Reference, Exact Differentiator. I. INTRODUCTION Robustness and adaptation are the main trends to cope with systems with poor modeling or large uncertainties, including parameter variations, unmodeled dynamics and external disturbances. An important technique to control systems under large uncertainties, effective in several practical applications in engineering, is variable structure control based on sliding modes, or, for short, sliding mode control (SMC). Recently, a growing number of research papers about the subject, both on theoretical and application grounds can be observed. The power of the SMC to deal with nonlinear plants together with newly introduced concepts like terminal sliding mode control , higher order sliding modes ,  and also the progress in output feedback SMC , , , , have significantly widened the range of applicability of SMC. In the recent papers ,  , interesting output feedback SMCs based on higher order sliding were proposed for plants of arbitrary relative degree. The main idea that allowed the completion of the feedback control scheme was the so called robust exact differentiator introduced in . The class of controllers, based on exact differentiators, may lead to exact output tracking but, so far, stability or convergence has been proved only locally  . On the other hand, an earlier output feedback SMC scheme, named, VS-MRAC (Variable structure Model Reference Adaptive Control), introduced in ,  has the capability of guaranteeing global exponential stability. However, for plants of relative degree higher than one, the tracking error becomes arbitrary small but not necessarily zero. This paper represents a preliminary attempt to achieve global stability and asymptotic exact tracking controllers using exact differentiators. To this end, we have restricted the detailed theoretical development to SISO (single-input/single-output) uncertain linear plants of relative degree two. Extension to higher relative degree seems quite immediate using the differentiators introduced in ,  , while extension to nonlinear plants could be done using the recent extensions of the VS-MRAC to MIMO (multi-input/multioutput) and nonlinear plants , . This work was supported in part by FAPERJ, CNPq and CAPES.