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

The paper deals with the stability properties of discrete time linear model predictive control systems. The closed loop systems are optimized using different performance criterions in a receding horizon fashion, and then the eigenvalue properties of the closed loop systems are investigated for the different conditions. Performance criterions may be combinations of terms belonging to state, control and state error at the horizon end. Eigenvalue properties of each class of cost functions depending on the horizon length are elaborated based on some new control theoretical results. Behaviors of receding horizon control algorithms are presented on a classical control problem, the stabilization of the inverted pendulum around the upper unstable equilibrium

In this paper, a friction model is proposed which can easily be introduced in adaptive control algorithms. Based on the model, a robust adaptive friction compensation algorithm is developed for high precision positioning systems. It is shown that the proposed compensation scheme guarantees a prescribed accuracy for trajectory tracking. The paper also presents experimental results to demonstrate the applicability of the proposed control algorithm.