On the design of integral observers for unbiased output estimation in the presence of uncertainty

Abstract

Integral observers are useful tools for estimating the plant states in the presence of non-vanishing disturbances resulting from plant-model mismatch and exogenous disturbances. It is well known that these observers can eliminate bias in all states, given that as many independent measurements are available as there are independent sources of disturbance. In the most general case, the dimensionality of the disturbance vector affecting the plant states corresponds to the order of the system and thus all states need to be measured. This condition, which is termed integral observability in the literature, represents a fairly restrictive situation. This study focuses on the more realistic case, where only the output variables are measured. Accordingly, the objective reduces to the unbiased estimation of the output variables. It is shown that both stability and asymptotically unbiased output estimation can be achieved if the system is observable, regardless of the dimensionality of the disturbance vector. Furthermore, a condition is provided under which, using output measurements, the errors in all states can be pushed to zero. It is also proposed to use off-line output measurements to tune the observer using a calibration-like approach. Integral observers and integral Kalman filters are evaluated via the simulation of a fourth-order linear system perturbed by unknown non-vanishing disturbances.

State estimation for MISO non–linear systems in controller canonical form

“…Noise and uncertainty are not critical factors in such a context. This can be very different in the case of industrial processes, as shown in a recent study by Bodizs et al (2011), where the performances of observers using an ELO, EKF or integrated Kalman filters (IKFs) are compared. The influence of noise and uncertainty on these observer types was emphasized, with more reliable results produced by ELOs, which permit exact state reconstruction of highly perturbed systems.…”

State estimation for a class of nonlinear systems

“…Noise and uncertainty are not critical factors in such a context. This can be very different in the case of industrial processes, as shown in a recent study by Bodizs et al (2011), where the performances of observers using ELOs, EKFs or Integrated Kalman Filters (IKFs) are compared. The influence of noise and uncertainty on these observer types was emphasized, with more reliable results produced by ELOs, which permits the exact state reconstruction of highly perturbed systems.…”

Parameter selection of an adaptive PI state observer for an induction motor

“…It comes from the form of the characteristic polynomial (8), in which the angular speed ω occurs only in even powers in this case.…”

“…Another difficulty is the fact, that there exists a class of observed systems, for which the PI observer is always unstable, independently of its gains. The dependence of stability on the numbers of outputs and state variables is stated in [8]. The induction motor is the exemplary system that belongs to this class.…”