Controller Design Based on the Cascaded Structure

Abstract

In the previous chapter a quite general approach to the control of flexible joint robots was treated, which was not at all restricted to the special problem of Cartesian impedance control. The main disadvantage of the singular perturbation approach is that only very weak stability statements can be made. The reason for this is that in the singular perturbation analysis some coupling terms between the slow and the fast dynamics are neglected. In this chapter it will be investigated, in which way the controller must be modified in order to allow stronger stability statements.

Two different approaches will be analyzed. The first one, which is discussed in Section 6.1, is based on the control theory for cascaded systems. While the flexible joint robot model from Section 2.2.3 is not in cascaded form, it can be brought into this form by an inner feedback loop. The second method is based on the backstepping approach and will be discussed in Section 6.2.