Adaptative high-gain extended Kalman filter and applications

tel-00559107, version 1 - 24 Jan 2011
%
$
#
"
#
m2 = 1.8
+(,-!,.(/ 0.1.)*2*1 3!4
4.3 real-time Implementation
!
!
%
"! #! $! %! &!!
'()*
5//67.2(6/
&"! &#! &$! &%! "!!
$
"
!
! "! #! $! %! &!!
'()*
&"! &#! &$! &%! "!!
Figure 4.20: Innovation for a low m2 parameter.
4.3 real-time Implementation
In order to investigate in depth the way the adaptive high-gain extended Kalman filter
works, we implemented the filter on a DC machine in our laboratory, at the University of
Luxemburg. The issues which concerned us when performing those experiments were:
− the study of the feasibility of a real time implementation, since:
1. a solution of the Riccati equation requires the integration of n(n+1)
2 differential
equations, where n denotes the dimension of the state space,
2. the computation of innovation appears to be time intensive 12 ,
− the study of the influence of unknown and non-estimated modeling errors on the adaptation
scheme and finding a way to handle them.
We considered the real-time part of this problem as being the major issue of this set of
experiments. Therefore we decided to use a hard real-time operating system.
4.3.1 Softwares
In computer science, real-time computing is the study of hardware and software systems
that are subject to operational deadlines from event to system response. The real-time
framework can be divided into two parts: soft and hard real-time. A requirement is considered
12 This question was also raised by M. Farza and G. Besançon at an early stage of this work, at the occasion
of the conference [25].
76