Control Methods for Systems with Nonlinear Instrumentation: Root Locus, Performance Recovery, and Instrumented LQG.

Abstract

A well-designed control system intends to keep the plant in the vicinity of some operating point. To accomplish this may require measurement of small signals within the deadzone of a sensor or large actuation efforts that may be subject to saturation. Thus, the so-called Linear Plant/Nonlinear Instrumentation (LPNI) control system is of particular interest. Controller design methods for such systems are sparse due to analytical difficulties resulting from the nonlinearities. However, when the exogenous inputs are random, the method of stochastic linearization provides a sufficiently accurate approximation, and thus, yields an analytically tractable formulation. Random excitations are important in control theory, traditionally in disturbance rejection, but also in tracking. Accordingly, this research uses stochastic linearization to develop three controller design methodologies for LPNI systems: (1) The S-Root Locus, for tracking random references; (2) Boosting, for recovering linear performance; and (3) ILQR/ILQG, for simultaneously designing disturbance rejecting controllers and the instrumentation. These methods take the form of standard linear control theory, but augmented with additional equations to account for the nonlinearities. It is asserted that the results fill a substantial gap in the area of control analysis and design.