Abstract
This paper is concerned with model-based robust observer designs for state observation and its application for unknown input reconstruction. Firstly, a sliding mode observer (SMO), which provides exponential convergence of estimation error, is designed for a class of multivariable perturbed systems. Observer gain matrices subject to specific structures are going to be imposed such that the unknown perturbation will not affect estimate precision during the sliding modes; Secondly, to improve discontinuous control induced in the SMO as well as pursue asymptotic estimate precision, a proportional-integral type observer (PIO) is further developed. Both the design procedures of the SMO and PIO algorithms are characterized as feasibility issues of linear matrix inequality (LMI) and thus the computations of the control parameters can be efficiently solved. Compared with the SMO, it will be demonstrated that the PIO is capable of achieving better estimation precision as long as the unknown inputs are continuous. Finally, a servo-drive flexible robot arm is selected as an example to demonstrate the applications of the robust observer designs.
Highlights
Sliding Mode Control (SMC) is a well-known control theory owing to its outstanding robustness properties against to parametric uncertainties and external disturbances [1]
Sliding mode observer (SMO) is a high performance state estimator well suited for nonlinear uncertain systems [2,3] with only output information available
In [4], SMOs are designed for flux estimation of induction motors
Summary
Sliding Mode Control (SMC) is a well-known control theory owing to its outstanding robustness properties against to parametric uncertainties and external disturbances [1]. Sliding mode observer (SMO) is a high performance state estimator well suited for nonlinear uncertain systems [2,3] with only output information available. A better way is to replace these equations by inequalities and the design problem can be effectively solved by using linear matrix inequalities (LMIs) [11,12]. In this decade, multi-object LMI techniques have been widely applied for the existence problem of robust continuous/discrete time observer designs [13,14]. The fault reconstruction ideas [20] to develop a SMO design for achieving state estimation as well as unknown input recovery. Comparison studies are carried out and the estimation properties of the SMO and the PIO are discussed
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