《Adaptive Observers for Single Output Nonlinear Systems》.pdf

1054 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 35, NO. 9, SEPTEMBER 1990 fining the filter, the process of choosing the initial covariances is Adaptive Observers for Single Output Nonlinear Systems somewhat heuristic. In the absence of a standard for force sensor statis- tics, it was found that Ro = (10-s)Z4x4 and Qpo = (0.00s)19.9 gave RICCARDO MARINO good results, even when measurement noise of variance 4 = 0.1 was used. An Ro value too large causes slow estimate convergence because Absmct-An adaptive version of the nonlinear observer obtained in of the doubt it casts on measurement readings, and an too small re- 111is presented. As an intermediate step, necessary and sufficient condi- sults in invertibility problems in the measurement update equations. The tions are given for a nonlinear system to be transformed by state-space value Qpo is chosen small to avoid a poor transient response, but not so change of coordinates into the special adaptive observer form used in small that convergence is slow. It was found that values between 0.1 and [2] to design adaptive observers. O.ooO1 all provided similar transient characteristics. Because no physical force sensor is available for this study, it is desired that the tuned filter I. INTRODUCTION perform well subject to a ra