Adaptive Feedback Linearization for Tracking Control of Nonlinear Systems Exhibiting Mode-Locking

In this paper we demonstrate the importance of weak nonlinear coupling effects in closed loop tracking performance of servomechanisms using a simple benchmark problem. The objective is to demonstrate that performance degradation can be readily observed in steady state, periodic responses of tracking control loops with small amplitude motions, and that tracking performance can be significantly improved through the use of dynamic inversion of known nonlinearities via feedback linearization. Robustness of feedback linearizing control to parametric model uncertainty can be extended by modified Model Reference Adaptive Control methods. This paper focuses attention on testing and validation of feedback linearizing control laws for multiloop tracking systems with nonlinear plants by observing the qualitative change in harmonic response of tracking loops with variation in the amplitude and frequency of periodic command signals. That qualitative changes will occur generically in harmonic response of tracking loops is predicted by the theory of mode-locking. Simulation results are given for two examples including a rigid body spacecraft attitude control problem.