This grant provides funding for the development of theory and techniques for design of controllers in feedback systems with linear plants and nonlinear sensors and actuators. This type of systems, referred to as linear plant, nonlinear instrumentation (LPNI) systems, often appear in aerospace, automotive and other applications, where plants can be linearized but the instrumentation is fundamentally nonlinear due to cost, power, weight and other physical constraints. Within this project, all main problems of control, i.e., disturbance rejection, reference tacking, conservation laws, etc., will be addressed. The approach is based on the method of stochastic linearization, whereby the nonlinearities of the instrumentation are replaced by static gains, calculated as functions of the variance of the signals at their inputs. Unlike local (i.e., Jacobian) linearization, this method is semi-global in the sense that it approximates the original system in arbitrarily large domains, defined by the signals at the inputs of the nonlinearities. The set of techniques, to be derived using this approach, is envisioned as extensions of corresponding linear control tools, augmented by nonlinear relationships that account for instrumentation nonlinearities. This set of tools is referred to as quasi-linear control theory (QLCT). If successful, the results of this work will lead to improvements in design of controllers for a wide range of practical LPNI. Today, such controllers are often designed using linear theory and then time-consuming and expensive validations and incremental improvements, based on simulations, are carried out. QLCT will, to a large extent, eliminate the necessity of extensive simulations, since the optimal controllers will be designed directly taking into account instrumentation nonlinearities. Initial application of these techniques for design of air-to-fuel ratio controllers at Ford Motor Co. is planned.
