Efficient and Simple Noise Filtering for Stabilization Tuning of a Novel Version of Model Reference Adaptive Controller

In order to avoid the mathematical difficulties related to the application of Lyapunov's "Direct Method" in the adaptive control of imprecisely and partially modeled nonlinear systems a novel class of "Model Reference
Adaptive Controllers (MRAC)" was recently proposed. This MRAC scheme applies "Robust Fixed Point Transformations (RFPT)" that result in a convergent iterative \learning sequence" of a local and normally bounded region of convergence. In order to make this method competitive with the results of Lyapunov functions based techniques normally guaranteeing global stability this new approach was completed with a tuning rule modifying only one adaptive parameter in order to keep the iterative sequence in the vicinity of the xed point that is the solution of the control task. In the case of an "nth order system" normally a PID-like direct feedback containing only the observation of the (n - 1)th time{derivative of the motion is needed for the novel controller that also observes the nth time{derivative of the coordinates but utilizes them in a relatively robust, insensitive way when no parameter tuning is applied. However, the application of adaptive tuning increases this sensitivity for the reduction of which a simple noise ltering method is recommended. In the paper extended simulation results are presented for the adaptive control of a pendulum of indenite mass center point caused by the presence of dynamic coupling with an internal degree of freedom imprecisely modeled by the controller. It was found that the simple ltering recommended considerably reduced the sensitivity of the novel method proposed.