TRACK-FOLLOWING CONTROLLER FOR HARD DISK DRIVE ACTUATOR USING QUANTITATIVE FEEDBACK THEORY

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1 Proceedings of the IASTED International Conference Modelling, Identification and Control (AsiaMIC 2013) April 10-12, 2013 Phuket, Thailand TRACK-FOLLOWING CONTROLLER FOR HARD DISK DRIVE ACTUATOR USING QUANTITATIVE FEEDBACK THEORY Takat Benjalersyarnon 1, Withit Chatlatanagulchai 2 Control of Robot and Vibration Laboratory, Faculty of Engineering, Kasetsart University 50 Paholyothin Rd., Chatuchak, Bangkok, Thailand 1 g @ku.ac.th, 2 fengwtc@ku.ac.th ABSTRACT Hard disk drives have been highly improved in capacity due to advance in technology. Thus the position control system must be well designed in order to control their read/write heads more precisely within ±10% of the track width. Many control approaches are proposed to solve the track-following problem in a hard disk drive under a disturbance. However most approaches increase an order of the system, resulting in higher computational resource while the conventional controller cannot overcome the disturbances and the uncertainty of parameters. In this paper, we present a track-following controller that is designed for a hard disk drive using Quantitative Feedback Theory (QFT) which is a robust controller design method based on a frequency domain. The result shows that the proposed controller can attenuate plant uncertainty and plant output disturbance. The time response can meet specifications with 0.4ms 5% settling time. Comparing with PID controller, the advantage of the proposed controller is consideration of plant uncertainty and disturbance sources in design process. KEY WORDS Hard Disk Drive, Track-Following Control, Quantitative Feedback, Robust Control. NRRO which may cause the position error, external force, etc. Many control approaches have been proposed to solve the problems as mentioned earlier, from classical to advanced control approach. The technique which is well known in robust control approach is H optimal loop shaping control. However, the controller s order is usually high and is difficult to implement in the real product [1-2]. In this paper, a QFT controller design is proposed for the track-following problem in the hard disk drive. In Section 2, we introduce a hard disk drive servo system and modelling. Section 3 presents the controller design steps using QFT. Section 4 shows the result by QFT controller. The conclusion is in Section 5. In this work, the controller design and the simulation are based on Matlab and QFT Toolbox [3]. 2. HDD Servo System and Modelling The hard disk drive servo system consists of magnetic actuator called voice coil motor (VCM), read/write heads, arm, and media platters coated by the recording medium for both data storage and position signal feedback. Figure 1 shows some major components of the commercial hard disk drive. 1. Introduction Nowadays, the hard disk drive is the main storage device in the computer system. Many portable devices such as laptops, tablets, and music players prefer the data storage with higher capacity while its size needs to be smaller. These lead the requirement of tighter data density. To cope with the continuous increasing in capacity, higher track density is required that means the track width is narrower. Recently, data density reaches one terabit per square inch that requires head position error less than 10 nm. There are two main controllers in HDD servo control, track seeking and track following. Track seeking performance can improve access time or "speed" and track following performance can improve track misregistration or "capacity" To design an effective controller, an accurate model is desired for design of the actuator controller to meet the purpose and attenuate the disturbance such as RRO, Figure 1. Hard disk drive components. The control problem called track-following is the process to control the read/write head position at the center of the track. The error between the read/write head DOI: /P

2 and the center of the track must be minimized, which can be measured by position error signal (PES). The read/write head is actuated by the voice coil motor (VCM) which rotates around the pivot bearing. In the track-following case, the output can be assumed to move in a straight line when the current input u is provided. In general, there are two methods to obtain the mathematical model of the hard disk drive servo system; analytical method and system identification method. The analytical method determines the physical of plant and physical laws while the system identification method bases on experiment in the range of attended frequency. In this work, we use HDD Benchmark Problem from [4]. The plant model was proposed by the Institute of Electrical Engineers of Japan (IEEJ), and the author claimed that the benchmark problem uses a precise model, reflecting all physical properties of an actual HDD. Table 1 Parameters of VCM Parameter Description Value Unit Input delay s Force constant N/A Equivalent mass kg Track pitch m Table 2 Parameters of i (Hz) Figure 2. Block diagram of the HDD servo control system. Various disturbance sources are found in HDD servo control. In this work, only plant output disturbance is considered. The plant output disturbance is defined as a white Gaussian noise with standard deviation of A and a square wave with period of 5ms. Figure 3 shows the disturbance in this work. The block diagram of the HDD servo control is shown in Figure 2. is defined as the transfer function of HDD servo control or "plant". The head position is the output with unit "track" (1 track = µm) and the current is the input to the VCM in Ampere (A). The exponential term refers to time delay of system. The time delay block is replaced by the transfer function The second square box in Figure 2 is a combination of constant coefficients and the third box is model of resonant modes where which represents in the -type or parallel connecting. The parameters of VCM and are shown in Table 1 and Table 2. (1) Figure 3. Disturbance signals. A control system is designed to move the read/write head from track 0 to track 1 under three conditions; an over shoot is less than 5% of the track width, 5% of settling time of step response is short as possible, and the steady state error under disturbances is less than ±5 % of the track width. 3. QFT Controller Design Quantitative Feedback Theory (QFT) was proposed by Horowitz in 1959 [5] and then was continuously developed [6]. Currently, the QFT method is widely used for practical design of the feedback system. The QFT has two main advantages. 1. The design is based on intuitive graphical methods (Nichols plot and Bode plot). 182

3 2. The design results in lower-order controllers compared to other robust control approaches. 3.1 QFT Design Procedure and dotted line refers to the true model. From (1), with n=1, the simplified model is (2) The block diagram of the QFT controller design is shown in Figure 4. denotes a system that we want to control. are output, control signal, feedback error and reference signal, respectively. H is sensor model. G is a designed controller and F is designed pre-filter. and are noise, plant input disturbances and plant output disturbance, respectively. The basic steps for QFT controller design are described as follows. For high frequency flexible mode, we have (3) r n d I d o F e G u P y H The in (2) and (3) is a part of time delay and constant as shown in Figure (2) Overall plant transfer function P f is combined from (2) and (3). (4) Figure 4. Two degree of freedom feedback control structure Step 1. Specify the plant models from data. The plant model with plant parameter uncertainty is defined on Nichols chart, called plant template. Plant templates describe gain-phase variations due to process parametric and non-parametric uncertainty. The nominal plant is selected for later design step. Step 2. All specifications of the system such as tracking, disturbance rejection, control effort, etc. are converted into frequency domain form. Each specification on each frequency is shown in a boundary on Nichols chart. Step 3. Use plant templates to develop stability contours on Nichols chart. Step 4. On Nichols chart with stability contours and specification boundaries, the designer can synthesize the loop transmission function as desired aided by CAD package. This step is called loop shaping. Step 5. Synthesize pre-filter by pre-filter shaping for the desired tracking transfer function. Step 6. Simulation and analysis for the system time response on each of uncertain plants to verify the controller. For more details, see [7-9]. P s(s) P f(s) Figure 5. Bode plots of the true plant (solid) and the simplified plant (dash) 3.2 Plant Models and Plant Templates To design the controller using QFT based on Nichols chart, we simplify the HDD plant model by reducing its order for less complexity in loop shaping step. The simplified model is obtained by truncating the high-order resonant mode, given in Table 2. Frequency responses of the true model and the simplify model are shown in Figure 5, where solid line refers to the simplified model 183

4 W/O notch filters With notch filters Figure 6. Bode plots of plant without notch filters (solid) and with notch filters (dash). The notch filters are used to handle some resonant modes. Four notch filters are perceptible through the frequency response of the system, which are given by The frequency responses of plant with and without notch filters are shown in Figure 6. The characteristic of the plant with notch filters in Figure 6 is similar to that of the simplified plant in Figure 5. Then the QFT is used to synthesize a controller for, according to (2). Some parameter uncertainties Δ = ±10% to is added in order to test the robustness of the control system. We have The plant templates of simplified plant uncertainty is shown in Figure 7. with Figure 7. Plant Templates of. 3.3 Plant Output Disturbance Rejection The frequency-domain specification of the plant output disturbance rejection is given as (5) Equation (5) is the bound of the transfer function from to. So, the desired value of should be near zero to reject the disturbance. We define. 3.4 Tracking In tracking case, two bounds are defined (upper bound and lower bound) by transfer functions. The tracking specification is (6) (7) where and in (7)-(8) are two transfer functions, defined to meet the objectives in Section Controller Design ( Loop Shaping) (8) The loop shaping method adjusts the loop transfer function to meet all specifications (5) and (6). The quality of loop-shaping design depends on experience of the designer. Some information about loop shaping technique is presented in [1], [5-7]. The controller consists of two-poles, one real zero, one complex zero, one integrator, and one real pole. We have 184

5 The loop transfer function is shown in Figure 8 (before shaping) and Figure 9 (after shaping as (9)). (9) α β 4. Results Figure 10. Pre-filter shaping of. Figure 8. Loop transfer function, Fig. 3 Loop shaping Figure 9. Loop transfer function, 3.6 Pre-Filter Design (before shaping). (after shaping). The pre-filter F is designed by adjusting the gains to be within tracking bounds (Figure 10). We have The simulation in Figure 11 shows that the proposed controller meets the robust stability specification (4dB) at all frequencies. The proposed controller and the pre-filter also satisfy the tracking specification in Figure 12. The overshoot of the step response is less than 5% of the track width and 0.4 ms of 5% settling time is obtained as expected. The QFT controller is compared to PID controllers obtained from two tuning methods under the same reference signal. The first PID controller is tuned by the well-known PID tuning method, Ziegler-Nichols. From Figure 13 (dash-dotted line), the closed loop system is stable but it does not meet the specifications as needed in Section 2. The second PID controller is tuned by trial and error method. The step response can meet the specifications as shown in Figure 13 (solid line). However, this cannot guarantee the stability of uncertain plant because the design process does not consider the uncertainty of the plant. Figure 14 shows the time responses of uncertain plant. Some of the uncertain plant with PID controller is outside of bounds while the uncertain plant with QFT controller is inside. Finally, the plant output disturbance is fed as Gaussian white noise signal (Figure 15a) and square wave signal (Figure 15b) in order to test the robustness of the plant. The plant output can be stabilized around reference signal (zero). (10) 185

6 QFT PID Figure 11. Closed-loop stability margins. Figure 14. Comparision between QFT and PID. Upper bound Output, y Lower bound (a) Disturbance, d o Figure 12. Step response of the system (QFT controller with nominal plant). Output, y (b) Figure 15. Plant output disturbance rejection (a) Gaussian white noise (b) square wave. Trial and error Ziegler-Nichols 5. Conclusion This paper proposes the hard disk drive head positioning control using QFT under parameter uncertainty and disturbance. The proposed controller can handle both parameter uncertainty and disturbance and meet the desired specifications. The advantages of this method compared to conventional method are the consideration of the plant uncertainty and external disturbance during the controller design. The controller is well practical with the desired performances obtained. Figure 13. Step response of the system (PID controller with nominal plant). Acknowledgement This work was funded by DSTAR, KMITL and NECTEC, NSTDA (HDD D). We would like to thank Craig Borghesani and Terasoft for their evaluation copy of the QFT Matlab toolbox. 186

7 References [1] A.A. Mamun, G. Guo and C. Bi, Hard disk drive mechatronics and control (Boca Raton, FL: CRC Press, 2007). [2] B.M. Chen, T.H. Lee, K. Peng & V. Venkataramanan, Hard Disk Drive Servo System, 2nd ed. (London: Springer-Verlag, 2006). [3] C. Borghesani, Y. Chait & O. Yaniv, The QFT frequency domain control design toolbox user's guide (Terasoft, 2003). [4] T. Yamaguchi, M. Hirata & C. K. Pang, High-speed precision motion control (Boca Raton, FL: CRC Press, 2012). [5] I. Horowitz, Fundamental theory of automatic linear feedback control systems, IRE Transactions on Automatic Control, 4(3), 1959, [6] I. Horowitz, Survey of quantitative feedback theory, International Journal of Robust and Nonlinear Control, 11(10), 2001, [7] O. Yaniv, Quantitative feedback design of linear and nonlinear control systems (Kluwer, Massachusetts, 1999). [8] C.H. Houpis, S.J. Rasmussen & M. Garcia-Sanz, Quantitative feedback theory fundamental and applications (Boca Raton, FL: CRC Press, 2006). [9] W. Chatlatanagulchai, System modelling and control (Bangkok: Kasetsart University, 2011). 187