Nonlinear Optimal Control by Use of Extra Linear States to Represent Nonlinearities

Abstract

This paper describes a technique which extends the application of the Kalman linear state variable feedback controller to practical nonlinear systems. This technique involves the linearization of the system model with residual nonlinearities retained. Extra linear states are then used to represent the residual nonlinearities in formulating the optimal controller. The use of the technique is illustrated by generating a controller for a simplified model of a hydroelectric plant. The advantages are shown by a comparison between the response of the nonlinear system with a controller generated using all of the nonlinearities as extra states and one using only one of the nonlinearities as an extra state. This technique could be used to design a nonlinear analog controller with fixed coefficients or an extremely simple control routine for an online digital computer.