Adaptive X-tracking for linear systems with higher relative degree — The continuous adaptation case

This paper presents a simple adaptive controller which universally achieves so-called X-tracking for linear systems where only little structural information about the system to be controlled is needed. The paper extends previous results to the case of systems with higher relative degree. Stability and convergence of the adaptation is proven for tracking arbitrary but sufficiently smooth reference trajectories. The design of the controller is very simple and intuitive and only few parameters have to be tuned. The robustness is increased by the introduction of a dead-zone in the adaptation, whose width λ can be chosen by the user. In this paper a continuous adaptation law is used as opposed to the discrete law suggested in earlier papers. There are several advantages in using a continuous adaptation: Besides displaying a simpler structure the necessary gain to achieve the control goal will also be significantly lower in general. To demonstrate the performance the controller is applied to the model of a ball and plate experiment.