Frequency-Dependent Feedback in Fixed Point Iteration-Based Adaptive Control

The Fixed Point Iteration-based Adaptive Controller was invented to substitute the Lyapunov function-based design in order to guarantee prescribed decrease of the absolute value of certain individual tracking error components instead of making some quadratic norm of the tracking components monotonically decrease, because in this latter case no monotonic behavior of the individual components can be assured. Instead of refining some initial analytical model this adaptive method feeds back the controlled system’s observed dynamic response that in the case of mechanical systems normally is the second time-derivative of the generalized coordinates. For this reason it is expected to be efficient in the highly dynamical regime of the controlled motion, while in the “static” regime it feeds back rather unnecessary sensor noise that far exceeds the essential dynamic content of the observed signal. Since the mechanical systems normally are strongly nonlinear ones it cannot be expected that frequency domain-based considerations are appropriate to their dynamic control. However, in this paper it is shown that within the mathematical framework of the Fixed Point Iteration-based approach these simple considerations can refine the operation of this adaptive controller. Simulation investigations are presented for the adaptive dynamic control of 3 Degree of Freedom rotary robot arm.