Adaptive $\lambda$-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 X 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. The’re
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.