Improved high gain observer design for a class of disturbed nonlinear systems

Abstract

This paper provides a redesigned version of the Standard High Gain Observer (SHGO) to cope with the peaking phenomenon occurring during the transient periods as well as the sensitivity to high frequency measurement noise. The observer design is performed for a class of uniformly observable systems with noise free as well as noisy output measurements and the resulting observer is referred to as Non Peaking Filtered High Gain Observer (NPFHGO). The NPFHGO shares the same structure as its underlying SHGO and differs only by its corrective term which is still parameterized by a unique positive scalar up to an appropriate expression involving nested saturations. Of a fundamental interest, the power of the scalar parameter does not exceed one unlike in the case of the SHGO where this power grows from 1 to the system dimension. Moreover, it is shown that the equations of the NPFHGO become identical to those of the SHGO after a transient time horizon that can made arbitrarily small for sufficiently high values of the design parameter. A particular emphasis is put on the case of systems with noisy output measurements. It is shown how a multiple integrator of the corrupted outputs can be cascaded with the original system leading to an augmented system included in the class of systems for which the NPFHGO has been designed. The performance and main properties of the NPFHGO are highlighted and compared to those of its underlying SHGO through simulation results involving a single link robot arm system.

Towards improving the estimation performance of a given nonlinear observer: a multi-observer approach

“…, η N `1u and Πpηq " argmin kPt1,...,N `1uztσu η k , for all η P R N `1 ě0 . We also argue that, implementing (12) online, which requires the knowledge of the derivative of the monitoring variables, is not an issue. Remark 4.…”

“…In this context, an alternative consists in aiming at improving the estimation performance of a given observer. To the best of the authors' knowledge, existing works in this direction either concentrate on specific classes of systems (see e.g., [4]- [6] for linear systems or e.g., [7]- [12] in the context of high-gain observers) or on specific properties like robustness to measurement noise (see, e.g., [13], [14]) or the reduction of the undesired effect of the peaking phenomenon (see e.g., [15] for a general approach and [8], [10], [12] for specific solutions in the context of high-gain observer). An exception is [16], where two observers designed for a general nonlinear system are "united" to exploit the good properties of each.…”

Canceling output disturbances in observer design through internal model filters

“…and design an observer for the resulting system (9). Although this is a perfectly valid approach for linear systems, it cannot be easily extended to the nonlinear case.…”

“…Alternatively, one can couple the observer with a system that filters-out some spectral components of the output error signal. An example of this methodology is the Proportional-Integral observer [5][6][7], which combines the output-estimation error with its integral, see also the extensions [8,9] to more general low-pass filters. Recently, [10] proposed the use of nonlinear dynamic dead-zones or dynamic saturations.…”

Filtered High Gain Observer for an Electric Vehicle's Electro-hydraulic Brake: Design and Optimization Using Multivariable Newton-Based Extremum Seeking

“…Another drawback of using a large gain value is peaking phenomenon [9] . Therefore, research on the design of filtered high-gain observers has been a long-standing issue [10][11][12][13] . Therefore, this study proposes a filtered high-gain observer (FHGO) for EHB systems.…”