Sc. Patwardhan et Kp. Madhavan, IMPROVED TECHNIQUES FOR THE DEVELOPMENT OF QUADRATIC PERTURBATION MODELS, Industrial & engineering chemistry research, 35(11), 1996, pp. 4281-4290
In this paper, the quadratic model developed by Patwardhan and Madhava
n (1993) using the regular perturbation approach has been further refi
ned to produce a better estimate of second-order effects. As an altern
ate to the regular perturbation model, a structurally better form of t
he quadratic model has also been derived that does not require any of
the simplifying assumptions that were used in our previous work (Patwa
rdhan and Madhavan, 1993). The coefficients of this model are computed
using the solutions of the first- and second-order sensitivity equati
ons. A recursive form of quadratic perturbation models is also develop
ed for the systems with a nonlinear output map. The computational adva
ntages of the proposed quadratic models have been presented. The impro
ved prediction capabilities of the quadratic models obtained using the
proposed modifications have been demonstrated using a simulation exam
ple. The analysis of the model structure and the simulation results in
dicate that the quadratic model developed using the sensitivity equati
on approach is a better choice for approximating the local behavior of
a highly nonlinear system and, consequently, for the development of a
n nonlinear model predictive control scheme.