ABSTRACT
As a closed-loop shaping method, the KYP Lemma-based approach allows designers to impose performance requirements over selected finite frequency ranges so as to have the desired sensitivity function that is able to reject the disturbances in these specific frequency ranges. Subsequently, the positioning accuracy can be improved to some extent. However, the KYP Lemma-based loop shaping method does not count for overall positioning error minimization which can be translated into the H 2 optimal control problem by taking into consideration the disturbance and noise models. On the other hand, the H 2 control design which incorporates all disturbance and noise models can result in an average performance across the entire frequency range and a high order controller. Thus it usually does not have the flexibility to specifically reject disturbances at certain frequency ranges, which however may be dominant factors that influence the overall performance. Therefore there is a need to suppress disturbances of specific frequencies when minimizing the positioning error. This motivates us to incorporate the KYP Lemma-based method with the H 2 control method in this chapter. With the selected specific disturbances handled by the KYP Lemma-based design, the H 2 control is formulated with a lower order disturbance model, excluding the disturbances covered in the above design. This will not only release the computation burden in the H 2 control design but also result in a lower order controller.
