Design of a Saturated Filtered High Gain Observer for a Class of Disturbed Nonlinear Systems

ABSTRACT This paper provides a redesigned version of the Standard High Gain Observer (SHGO) allowing to significantly reduce its underlying peaking phenomenon while improving its sensitivity to noise measurements. The redesign of the SHGO is performed in two steps respectively leading to a Filtered High Gain Observer (FHGO) and a Saturated Filtered High Gain Observer (SATFHGO). The FHGO is obtained by incorporating a suitable filtering process into the SHGO design reducing thereby its sensitivity to noise measurements. This is simply achieved by adding to the SHGO a linear filter of an arbitrary order whose input is the SHGO output observation error which is substituted by the filter output in the SHGO equation. Of fundamental interest, a suitable analysis of the steady‐state response of the FHGO shows that it performs better in the presence of high‐frequency signal measurements. The SATFHGO is obtained by substituting the components of the correction term in the FHGO by appropriate nested saturation functions leading thereby to a free peaking observer. A systematic procedure is proposed to compute the gain of the SATFHGO. The effectiveness of the proposed SATFHGO is highlighted through probing simulation results involving a single link robot arm system.