The paper proposes a model based adaptive control algorithm to control the ball and beam system with unknown parameters. The algorithm is based on an error metric which combines the trajectory tracking of the ball and the stabilization of the beam. The proposed adaptive control algorithm is improved in such a way to avoid the singularity problem which can arise in nonlinear adaptive control systems. Using the Barbalat lemma, it can be shown that the tracking error of the ball motion on the beam converges to a small residual set even in the presence of parameter uncertainty. Experimental results are provided to show the performances of the proposed control scheme

A linear autonomous differential equation with small delay is considered in this paper. It is shown that under a smallness condition the delay differential equation is asymptotically equivalent to a linear ordinary differential equation with constant coefficients. The coefficient matrix of the ordinary differential equation is a solution of an associated matrix equation and it can be written as a limit of a sequence of matrices obtained by successive approximations. The eigenvalues of the approximating matrices converge exponentially to the dominant characteristic roots of the delay differential equation and an explicit estimate for the approximation error is given.

This paper focuses on the hardware development of an indoor ultrasound based robot localization system. The problems related to the ultrasound based distance measurements are presented and solutions are proposed related to Time of Flight measurements and measurement synchronization. An optimization based compensation method is introduced to attenuate the effect of the ambient temperature on the distance measurement precision. Experimental measurements were performed to analyze the applicability of the developed system and measurement methods.