The effect of process nonlinearity on linear controller performance in discrete-time systems

The general approach to the design of control systems consists in the development of linear models of the process and the design of a suitable linear controller to regulate its local behavior. Although this strategy can yield acceptable control system performance in most cases, the nonlinearity of the underlying process can greatly affect the resulting design. The question of interest for many control engineers is: “When can a nonlinear process be controlled by a linear controller with the intended controller performance?” This question, which has received a great deal of interest over the last 10 years, remains open. In this paper, a local measure of nonlinearity is introduced for linear controllers operating on a nonlinear plant described by a discrete-time nonlinear control system model. The measure, called the performance sensitivity measure (PSM), quantifies the departures from optimality of locally linear quadratic regulators. The measure applies to discrete-time nonlinear systems that admit a controllable and observable linearization.