Venkatakrishnan Venkataramanan

Discrete-time composite nonlinear feedback control with an application in design of a hard disk drive servo system

In a typical disk drive servo system, two or more types of controllers are used for track seeking, track following, and track settling modes. This leads to the problem of mode switching among these controllers. We present in this paper a unified control scheme, the discrete-time composite nonlinear feedback control, which can perform all the above functions in hard disk drive (HDD) servo systems with actuator saturation. The proposed scheme is composed by combining a linear feedback law and a nonlinear feedback law. The linear feedback law is designed to yield a fast response, while the nonlinear feedback law is used to increase the damping ratio of the closed-loop system as the system output approaches the command input. In the face of actuator saturation, this control law not only increases the speed of closed-loop response, but also improves the settling performance. Implementation results show that the proposed method outperforms the conventional proximate time-optimal servomechanism by about 30% in settling time.

A new approach to the design of mode switching control in hard disk drive servo systems

In a modern large-capacity magnetic hard disk drive (HDD), both fast track seeking and perfect positioning of the read/write head are required. Mode switching control (MSC) approaches are widely used to meet these requirements. This paper proposes a new approach in designing MSC with an application to HDD servo systems. The proposed scheme uses a proximate time-optimal servomechanism in the track seeking mode, and a robust perfect tracking (RPT) controller in the track following mode. Unlike the conventional MSC approaches, the new method does not require an initial value compensation during mode switching. This is because the RPT controller in the second stage is capable of rendering the Lp-norm ð1ppoNÞ of the resulting tracking error arbitrarily small in the presence of external disturbances and initial conditions. Simulation and experimental results show that the proposed method improves the seek and settling time by about 10% over the conventional approaches. r 2002 Elsevier Science Ltd. All rights reserved.

Composite nonlinear feedback control: Theory and an application

Abstract The composite nonlinear feedback control technique is developed for a class of linear systems with actuator saturation, which consists of a linear and a nonlinear feedback parts without any switching element. The linear part is to yield a quick response in face of the actuator limits for the desired input levels. The nonlinear part is to reduce the overshoot caused by the linear part as the system output approaches the target. It is shown that the technique is capable of beating the time-optimal control in asymptotic tracking situations and can be applied to design servo systems that deal with “point-and-shoot” fast targeting. Copyright ©2002 IFA C

Design and implementation of discrete-time composite nonlinear feedback law for a hard disk drive

A discrete-time composite nonlinear feedback control law is proposed in this paper for a hard disk drive (HDD) servo system. This control law is composed by combining a linear and nonlinear parts. The linear part is designed to yield a fast response, while the nonlinear part is to reduce overshoot of the closed-loop system as the system output approaches the step command input. This control law is more suitable for the track seeking mode of HDD servo though it call be used in the track following mode. In the face of actuator saturation, the designed control law improves the system specifications such as the rising time and the overshoot. Implementation results show that the proposed method out-performs the conventional proximate time-optimal servomechanism by 50% in seeking time.

Nonlinear Control Techniques

Every physical system in our real life has nonlinearities and very little can be done to overcome them. Many practical systems are sufficiently nonlinear so that important features of their performance may be completely overlooked if they are analysed and designed through linear techniques. In HDD servo systems, major nonlinearities are frictions, high-frequency mechanical resonances and actuator saturation nonlinearities. Among all these, the actuator saturation could be the most significant nonlinearity in designing an HDD servo system. When the actuator saturates, the performance of the control system designed will seriously deteriorate. Interested readers are referred to a recent monograph by Hu and Lin [97] for a fairly complete coverage of many newly developed results on control systems with actuator nonlinearities.

Design of a Piezoelectric Actuator System

We present in this chapter a case study on a piezoelectric bimorph actuator control system design using an H ∞ optimisation approach, which was originally reported by Chen et al.[20]. Piezoelectricity is a fundamental process in electromechanical energy conversion. It relates electric polarisation to mechanical stress/strain in piezoelectric materials. Under the direct piezoelectric effect, an electric charge can be observed when the materials are deformed. The converse, or the reciprocal piezoelectric effect, is when the application of an electric field can cause mechanical stress/strain in the piezo materials. There are numerous piezoelectric materials available today, including PZT (lead zirconate titanate), PLZT (lanthanum modified lead zirconate titanate), and PVDF (piezoelectric polymeric polyvinylidene fluoride) to name a few (see Low and Guo [111]).

Linear Control Techniques

We now present some common linear control system design techniques, such as the well-known PID control, H 2 and H ∞ optimal control, linear quadratic regulator (LQR) with loop transfer recovery design (LTR), together with some newly developed design techniques, such as the robust and perfect track ing (RPT) method. We will first introduce the precise problem definitions of these techniques and then provide detailed solutions explicitly constructed by closely examining the structural properties of the given systems. Most of these results will be intensively used later in the design of HDD servo systems, though some are presented here for the purpose of easy reference for general readers.

Introduction and Preview

The state space representation of linear systems is fundamental to the analysis and design of dynamical systems. Modern control theory relies heavily on the state space representation of dynamical systems, which facilitates characterization of the inherent properties of dynamical systems. Since the introduction of the concept of a state, the study of linear systems in the state space representation itself has emerged as an ever active research area, covering a wide range of topics from the basic notions of stability, controllability, observability, redundancy and minimality to more intricate properties of finite and infinite zero structures, invertibility, and geometric subspaces. A deeper understanding of linear systems facilitates the development of modern control theory. The demanding expectations from modern control theory impose an ever increasing demand for the understanding and utilization of subtler properties of linear systems.

System Identification Techniques

The purpose of this chapter is to revisit some basic theories and solutions of system identification, which will 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 modelling or based on experimentation, which is known as system identification [35]. 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 ω. If we have experimental data from a typical frequency response test, then we will be able to obtain certain functional curves for the plant.

Resonance and Disturbance Rejection

The prevalent trend in hard disk design is towards smaller hard disks with increasingly larger capacities. This implies that the track width has to be smaller, leading to lower error tolerance in the positioning of the head. The controller for track following has to achieve tighter regulation in the control of the servomechanism. To read (or write) the data reliably from (or to) the disk, the absolute track following error with respect to the target track centre, which is commonly called track mis-registration (TMR), must be less than 10% of the track pitch. For example, for a 3.5″ HDD with 25 kTPI, the track pitch is about 1 μm and its TMR must be less than 0.1 μm. Thus, for 70 kTPI, TMR must be less than 0.036 μm. This requires rigorous analysis of the sources of TMR and development of advanced techniques to overcome or eliminate these sources to meet the increasing demand for higher TPI. Figure 10.1 shows a typical disk drive servo channel indicating the various sources of disturbances and errors.