The Use of Approximate Models and Exact Linearization for Control of Nonlinear Processes

Nonlinear control techniques such as global linearization can be advantageous, especially when process characteristics vary with the operating point. Differential geometric control techniques exactly linearize nonlinear systems so that linear feedback control can be applied. However, this requires that a nonlinear model of the process be available. This paper focuses on developing an empirical input-linear model for nonlinear processes by approximating transformations. As a simplification, we assume that process nonlinearities are essentially imbedded in the steady state relationships and steady-state input-output gains can be fitted by algebraic equations. This type of model can be linearized exactly using input-output transformations, leading to a simple control law based on linear system theory. Three linearization methods are proposed in this paper and compared to the previously developed Hammerstein and Wiener series compensation techniques, using a simulation model of a heat exchanger.