2.1 Introduction

The purpose of this chapter is to revisit some basic theories and solutions of system identification, which are to be used later in the coming chapters to model various HDD systems. In general, the goal of system identification is to determine a mathematical model for a system or a process. Mathematical models may be developed either by use of "laws of nature", commonly known as modeling or based on experimentation, which is known as system identification [57]. In order to achieve a certain desirable performance for a given plant, it is necessary to derive a model for the plant that is adequate for controller design. The conventional design techniques in linear control systems require either parametric or nonparametric models. For example, design methods via root locus or robust control technique require a transfer function or a state-space description of the plant to be controlled. The plant model is either described by the coefficients of certain polynomials or by the elements of state-space matrices. In either case, we call these polynomial coefficients or matrix elements the parameters of the model. The category of such models is a parametric description of the plant model. On the other hand, design based on Nyquist, Bode and Nichols methods requires curves of amplitude and phase of transfer function from input to the output as functions of real frequency ?. If we have experimental data from a typical frequency response test, then we will be able to obtain certain...