An Investigation of State Feedback Gain Sensitivity Calculations

Abstract

*† ‡ § A nonlinear feedback control strategy is presented where the feedback control is augmented with feedback gain sensitivity partial derivatives for handling model uncertainties. Applications to optimal feedback and robust control theories are presented. The OCEA (Object Oriented Coordinate Embedding) computational differentiation method is used for generating the partial derivatives. An array.of.arrays data structure is introduced for (1) tracking the derivative terms arising during a derivation of the tensor necessary conditions, and (2) assembling a generalized state space model for integrating the state and tensor differential equation models. Both scalar and vector applications are presented. Sensitivity calculations are developed for open.loop and feedback solutions for optimal control and robust control problem formulations. The pre. calculation of the sensitivity gains significantly reduces the computational effort required for implementing the handling of real.time plant parameter variations and equation of motion nonlinearities. The methodology is demonstrated on a general tracking problem which uses Taylor expansions of the gain calculations for handling nonlinear parameter and model errors. Several examples are presented that demonstrate the impact of nonlinear response behaviors, as well as the effectiveness of the generalized sensitivity enhanced feedback control strategy. A nonlinear spacecraft attitude tracking problem is presented for demonstrating the effectiveness of the proposed approach. The methodology of this paper is expected to be broadly useful for applications in science and engineering.