Speaker
Description
For the design of reference tracking controllers for nonlinear systems linearising controllers are often applied. Especially input-output linearisation is a widely used approach. However, this is only applicable for a specific system class. In particular, a system output with well defined relative degree must exist, and there are several systems that do not fulfill this requirement.
One well-known example of such a system is a rolling ball on a beam, which can be tilted by a control input. The linearization of this system in any equilibrium is controllable, and we find that a linear combination of the ball position and the beam tilt is a flat output. Thus, a feedforward control can be directly computed and any stable error dynamics may be prescribed. However, for the nonlinear system the relative degree of this flat output is not everywhere well defined: While the relative degree is one less than the state dimension for most states, it increases especially at those instants where the beam is at rest. Thus, one cannot construct a controller based on input-output linearization.
Several authors have studied this particular system and gave different approaches for approximate or even exact tracking controllers. In this contribution we construct a sequence of tracking controllers that approximate a prescribed error dynamics with different accuracy, starting with a linear controller for the linearised system. These controllers impose higher demands on the differentiability of the reference trajectory. However, the tracking error can be reduced in the vicinity of an equilibrium. This method is applicable also for other systems, whose linearization is controllable.
