Improved Techniques for the Development of Quadratic Perturbation Models

Abstract

In this paper, the quadratic model developed by Patwardhan and Madhavan (1993) using the regular perturbation approach has been further refined to produce a better estimate of second-order effects. As an alternate to the regular perturbation model, a structurally better form of the quadratic model has also been derived that does not require any of the simplifying assumptions that were used in our previous work (Patwardhan and Madhavan, 1993). The coefficients of this model are computed using the solutions of the first- and second-order sensitivity equations. A recursive form of quadratic perturbation models is also developed for the systems with a nonlinear output map. The computational advantages of the proposed quadratic models have been presented. The improved prediction capabilities of the quadratic models obtained using the proposed modifications have been demonstrated using a simulation example. The analysis of the model structure and the simulation results indicate that the quadratic model developed using the sensitivity equation approach is a better choice for approximating the local behavior of a highly nonlinear system and, consequently, for the development of an nonlinear model predictive control scheme.