Improved Simple Noise Filtering for Fixed Point Iteration-based Adaptive Controllers

For controlling dynamical systems certain controllers directly observe the physical response of the controlled systems and feed back the observed response for stabilization purposes. For instance, in robotics, where the rules of Classical Mechanics govern the behavior of the controlled system, this is the acceleration that is measured and fed back by the Acceleration Feedback Controllers. In quite different manner, the Fixed Point Iteration (FPI)-based adaptive controllers also feed back such observed information. If the driving forces act on a robot link through some deformable, elastic component, the relative order of the control task can be higher than two, and the system's response can be a higher order time-derivative of the observable coordinate. In this case the numerical derivatives of the noise-burdened measurement signals suffer from huge fluctuations due to which the need for the application of noise filtering techniques arises. Generally, any noise filtering corresponds to some “averaging” of the fresh, recent dynamic information with older, more or less “obsolete” one so it may corrupt the operation of the FPI-based control. The extent of this degradation depends on the “dynamics” of the nominal trajectory to be tracked, the nonlinearities in the dynamic model of the controlled system and cannot be tackled at high level generality. In the present paper a new, simple noise filtering technique is recommended for use in the FPI-based adaptive controller. Its corruption effect is investigated for a chirp signal independently of any dynamic control issue, then its application in the FPI-based adaptive control of a popular, nonlinear benchmarking system, the Duffing oscillator is studied via numerical simulations.