Youla–Kučera Parametrization with no Coprime Factorization—Single-Input Single-Output Case

We present a generalization of the Youla—Kučera parametrization to obtain all stabilizing controllers for single-input and single-output plants. This uses three parameters and can be applied to plants that may not admit coprime factorizations. In this generalization, at most two rational expressions of plants are required, while the Youla–Kučera parametrization requires precisely one rational expression.

Online Identification of System Uncertainties Using Coprime Factorizations With Application to Hard Disk Drives

In hard disk drive (HDD) magnetic recording bit patterned media (BPM), data are written in predetermined paths. The deviation of these paths from the perfect circle is categorized as repeatable run-out (RRO) which needs to be tracked. An adaptive RRO following algorithm was developed in [1,2] in order to track the RRO. This algorithm uses models of the closed-loop sensitivity transfer functions, from the feedforward injection points to position error signal (PES), to estimate the feedforward control actions that are needed to track the RRO. The phase difference between these models and the actual transfer functions must be less than 90 degrees, in order to guarantee the convergence of the adaptive RRO following algorithm. The dual-stage actuators’ gains and resonance modes are affected by temperature variations, which in turn affect all closed loop sensitivity transfer functions. As a consequence, the 90-degree criteria may be violated unless these transfer functions are periodically updated. In this paper, the coprime factorizations method has been used to factorize and identify the uncertain part of the model instead of identifying the entire transfer function of the model. Experimental results conducted on a hard disk drive equipped with dual-stage actuation, confirm the effectiveness of the proposed estimation algorithm.