Application of Homotopy Analysis Method in Model Based Controls

Homotopy Analysis Method (HAM) is a semi-analytical technique that has been successfully applied to solve several forms of nonlinear, ordinary as well as partial differential equations. HAM yields a family of solutions at any given order of approximation with selection of appropriate value of an auxiliary linear operator / convergence control parameter, typically denoted as h. In this paper, application of HAM has been specifically proposed for solving nonlinear dynamical systems that are in the input affine form which are quite prevalent in nonlinear controls theory. Dynamic Matrix Control (DMC) is a very popular and proven linear control technique that has been successfully deployed in several process plants. Simplicity in deployment and operation makes DMC a more popular choice than several nonlinear controls techniques. DMC uses the step-response models of a given system to achieve desired control action. The model assumes that the nonlinear plant behaviour can be reasonably approximated with a linear model around a specific region of operation. However, the continuous time varying nature of the plant and changes in the set-point far away from the original operating point pose major challenges for the DMC implementation. This is primarily due to the inadequacy of the original linear step-response model to capture the change in dynamics of a nonlinear plant, because of which the control performance is compromised. The work presented here shows application of the HAM to accomplish both objectives easily so that a better control action is achieved for a given class of non-linear system.