Vibration suppression beyond Nyquist frequency in hard disk drives

Basing on lifting technology, this paper researches a design method for multirate sampled-data control system in the background of flight control system design, which consummates the theory of multirate sampled-date control system design for further steps, and provides a method to design multirate sampled-data controller. As the reason of uncertainty in the aircraft model and the need of different sampling frequencies in different control loops, H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> -optimal multirate sampled-data control is considered. First, multirate sampled-data control system is outlined, and then the signal description are presented. Because of multirate sampled-data system is time-variant, the direct digital controller design becomes difficult. The equivalent discrete time-invariant systems can be converted from the linear time-variant systems through lifting technology. Then the H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> discretization of multirate sampled-data systems is researched. After the sampled-data control system was lifted, the equivalent L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> [0, h) -induced norm is proven. Base on the above, the method of H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> -optimal multirate sampled-data control is summarized. A height control is simulated using a simplified aircraft model to illustrate the design. The simulation shows that the multirate Sampled-data control system can achieve the satisfactory objective accurately and optimally.

So far, Two-Degree-of-Freedom control system has been used to realize desirable transient response in the tracking system of a Hard Disk Drive (HDD). It is easy to realize a high speed seek, if the actuator of the HDD has a resonance mode at a much higher frequency domain than the desired control domain. However, it is generally difficult to design an actuator that has a resonance mode in a high frequency domain. So, in order to realize a high speed seek, it is important to design a digital control system in consideration of the resonance mode of the actuator. In this case, if the Nyquist frequency of the control system is higher than the resonance mode of the actuator, the control system can be designed by using a method such as a H∞ control theory in consideration of the resonance mode. However, if the Nyquist frequency isn't higher than the resonance mode of the actuator, it is very difficult to realize a high speed seek without mechanical vibration using a conventional method. Then, in this paper the method of applying the N-Delay control theory to the design of the feedforward controller in a Two-Degree-of-Freedom system, and searching for the optimum time allocation of the N-Delay controller based on an evaluation function are proposed. Using these methods, the frequency component of the feedforward control signal can be diminished at the desired frequency point higher than the Nyquist frequency. The validity of the proposed method is confirmed by the numerical and experimental results with a miniature 2.5-inch hard disk drive.

Many of nonlinear control systems are sampled-data system, i.e. the continuous-time nonlinear plants are controlled by digital controllers. So it is important to investigate that if the solution of the discrete-time output regulation problem is effective to sampled-data nonlinear control systems. Recently a feedforward neural network based approach to solving the discrete regulator equations has been presented. This approach leads to an effective way to practically solve the discrete nonlinear output regulation problem. In this paper the approach is used to sampled-data nonlinear control system. The simulation of the sampled-data system shows that the control law designed by the proposed approach performs much better than the linear control law does.

This paper studies the problem of signal tracking and disturbance rejection for sampled-data control systems, where the pertinent signals can reside beyond the so-called Nyquist frequency. In light of the sampling theorem, it is generally understood that manipulating signals beyond the Nyquist frequency is either impossible or at least very difficult. On the other hand, such control objectives often arise in practice, and control of such signals is much desired. This paper examines the basic underlying assumptions in the sampling theorem and pertinent sampled-data control schemes, and shows that the limitation above can be removed by assuming a suitable analog signal generator model. Detailed analysis of multirate closed-loop systems, zeros and poles are given, which gives rise to tracking or rejection conditions. Robustness of the new scheme is fully characterized; it is shown that there is a close relationship between tracking/rejection frequencies and the delay length introduced for allowing better performance. Examples are discussed to illustrate the effectiveness of the proposed method here.

In sampled-data positioning control systems, the vibrations caused by the mechanical resonances around a sampling frequency are not only the difficult to observe but readily excited by the control input in transient-state characteristics. To address this problem, we developed a control method that can suppress the zero-order-hold induced residual vibration in the sampled-data positioning control system. The study is on a shock response spectrum (SRS) analysis that handles the transient-state characteristics of mechanical resonances. The control method uses multi-rate notch filters that modify the acceleration input signals beyond the Nyquist frequency. We designed the notch filter based on the SRS analysis because the frequency response on the Bode diagram was not suitable for analyzing transient characteristics. The results of SRS analyses showed that the multi-rate notch filter was able to decrease the amplitude of residual vibrations caused by the mechanical resonances around the sampling frequency. To demonstrate the validity of the proposed method, simulations were conducted on a sampled-data positioning control system.

In a hard disk drive, residual vibrations induced by a zero-order-hold may lead to destruction of user data. Therefore, we developed a control method that can reduce such residual vibrations in the head-positioning control system of a hard disk drive. This study is based on a shock response spectrum (SRS) analysis that handles the transient-state characteristics of mechanical resonances. The control method uses multirate notch filters that modify the acceleration input signals beyond the Nyquist frequency. The results of the SRS analyses showed that the multirate notch filter was able to decrease the amplitude of residual vibrations caused by the mechanical resonances around the sampling frequency. Simulation and experimental results for a track-seeking control in a hard disk drive demonstrated the validity of the proposed method.

This paper is concerned with the digital implementation of the linear quadratic controller in the case of the sampled-data system. By applying the bilinear transformation, a way of computing a stabilizing suboptimal digital controller which does not require the resolution of the discrete Riccati equation is proposed. Corresponding values of the optimal and suboptimal discrete-time cost functions are estimated with respect to the sampling period and the degradation is evaluated. A simple numerical example is given to support the theoretical results.

Multirate, sampled-data control systems are analyzed in the frequency domain, taking the inter-sample behavior into account. The focus of the analysis is both on the rejection of disturbances within a certain frequency region, and on the robust stability properties. Due to the periodic behavior of such systems, a distinction is made between the performance frequency response (PFR) and the robust frequency response (RFR). The RFR is related to current frequency response approaches for sampled-data systems.

&lt;div class="htmlview paragraph"&gt;In this work we study the stability of digital controls of flexible/Vibratory aerospace/automobile systems by the graph norm technique, occurring in sampled-data control systems due to sampling period variations. To do so, this work tries to establish regions (graphs) of stability and instability in a Banach Space, the distances (norms) between them and a given design to detect analytically and/or numerically its margins of stability or conditions of instability. Based on that, we sketch the first steps for a design methodology of stable digital controllers of flexible/vibratory systems embedded in a sampled-data system with adjustable sampling periods of A/D and D/A converters. A short tutorial about the graph norm technique is also given and some theoretical results as well numerical results are shown. This work was done in two folds to unmask the stability secrets hidden in a general sampled-data control system, until today not revelated. The first part we have used the graph norm and at the second part we made use of the Liapunov stability theory.&lt;/div&gt;

Analysis of performance criteria in sampled-data fault detection

This paper presents a general framework based on lifting technique for sampled-data systems with input time delays. By analyzing the properties of operator-valued matrices of lifted systems with input time delays, an extended lifting technique is obtained. It is then shown that, with the proposed lifting technique, the complex behavior of the system can be illustrated by two simple lifted systems, which construct the extended lifted system. The extended lifted system has the same induced norm as that of the original system with an input time delay, since the proposed lifting technique is an isometric isomorphism. Through applying the proposed lifting technique to sampled-data systems with input time delays, the time-invariant discrete-time system with infinite-dimensional input and output spaces is obtained. The equivalent discrete-time system, which is derived from the extended lifted system, can satisfy the problem of H2 sampled-data control systems with input time delays. Simulation results are given to show that the proposed method can guarantee a more stable system response than the conventional H2 sampled-data controller for the sampled-data systems with the various input time delays.

In this work we are interested in the stability and ℒ2-gain of hybrid systems with linear flow dynamics, periodic time-triggered jumps and nonlinear possibly set-valued jump maps. This class of hybrid systems includes various interesting applications such as periodic event-triggered control. In this paper we also show that sampled-data systems with arbitrarily switching controllers can be captured in this framework by requiring the jump map to be set-valued. We provide novel conditions for the internal stability and ℒ2-gain analysis of these systems adopting a lifting-based approach. In particular, we establish that the internal stability and contractivity in terms of an ℒ2-gain smaller than 1 are equivalent to the internal stability and contractivity of a particular discrete-time set-valued nonlinear system. Despite earlier works in this direction, these novel characterisations are the first necessary and sufficient conditions for the stability and the contractivity of this class of hybrid systems. The results are illustrated through multiple new examples.

THE purpose of this paper is to extend the utility of certain synthesis techniques, which have proved useful in the design of continuous feedback systems, to the study of sampled-data systems. In recent publications,1,3,6 the z-transformation has been utilized to advantage in simplifying the analysis of sampled-data systems. However, several useful techniques applicable to the design of continuous-data systems have not been made available for the design of sampled-data systems. In this paper, by means of an extension of the concepts embodied in the z-transformation, the application to sampled-data systems of root-locus plots, asymptotic frequency plots, and Routh's criterion is shown to be feasible. Through the use of these techniques, a digital program giving the desired system compensation is readily synthesized.

The robust stability criterion for sampled-data control systems with a sector nonlinearity was presented in our previous papers (1996, 1998). Although it is applicable only to the sampled-data control system of a certain class, a usual discrete-time control system belongs to this type of class. The criterion contains the robust stability condition in regard to the nonlinear allowable band (sector) for continuous-time systems and the linear allowable gain band (interval set) for discrete-time systems. The paper focuses primarily on the concept of robust stability in order to analyze a nonlinear element by the linear gain band, in other words, the validity of Aizerman's conjecture extended into discrete-time systems.

The paper proposes a method for optimizing sampled-data systems over a set of reduced order controllers. The method is based on the concept of parametric transfer function and finding a subset of solutions for polynomial Diophantine equation with the order not exceeding the preset number. The method is applied to optimization of H2-norm of sampled-data submarine motion control system.