IMPROVED TECHNIQUES FOR THE DEVELOPMENT OF QUADRATIC PERTURBATION MODELS

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.