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.
Highlights
An intensive research activity has been devoted to the observer design for uniformly observable systems over the last four decades
The structure of a Standard High Gain Observer (SHGO) is very simple since it consists in a copy of the system dynamics up to a corrective term given by the product of the observer gain by the output observation error
Design is to cope with the peaking phenomenon occurring during the transient periods and to improve the sensitivity of the observer with respect to output measurements noise
Summary
An intensive research activity has been devoted to the observer design for uniformly observable systems over the last four decades (see for instance [1,2,3,4,5,6,7,8,9,10] and references therein). Though the observer dimension is equal to 2(n − 1), the underlying observer gain is parameterized by a scalar design parameter the power of which is limited to 2 Such a design feature allows to enhance the observer performance with respect to the ubiquitous measurement noise. The unifying of both cases is made possible by considering a class of uniformly observable systems where the expression of the outputs only depends on the system state Such outputs may coincide with the system real outputs if the latter are assumed to be noise free. A Non Peaking High Gain Observer (NPHGO), the structure of which is very similar to that of its underlying SHGO, is designed for the above class system.
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